(selections from chs.1, 2, 7 of text.)

1

11.431/15.426JReal Estate Finance & Investments I:

Fundamentals & Micro-Level AnalysisFall 2006

Introductory Lecture SlidesIntroductory Lecture Slides

(Selections from Chs.1, 2, 7 of text.)

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Overview:

1. Magnitude of Real Estate Investment

2. Performance of R.E. Investment

3. The “Real Estate System” (role of capital mkts)

4. The space market

5. The asset market & investment industry

6. Example real world R.E. development investment



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Magnitude

Figure 1a:Net Asset Value of U.S. Structures ($ billions, 2003, source BEA)

Total = $ 23,747

Houses, $11,917

Commercial R.E., $6,079

Govt. R.E., $5,751



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Magnitude

Figure 1b:Net Asset Value of U.S. Commercial Real Estate Structures ($ billions,

2003, source BEA)Total = $ 6,079 Billion

Office, $1,131

Retail, $1,313

Industrial*, $958

Residential (apts), $1,168

Hotel & Recreational,

$554

Institutional, $955



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U.S. Commercial R.E. Physical Space (SF)

Apartment41%

Warehouse16%

Office18%

Retail25%

U.S.Commercial R.E. Capital Value ($)

Apartment25%

Warehouse9%

Office32%

Retail34%

U.S. Institutional Commercial Real Estate

Physical Stock: 44B SF Capital Value: $3.3 Trillion

Source: PPR, 2003

Magnitude



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Exhibit 1Exhibit 1--5: Major Types of Capital Asset 5: Major Types of Capital Asset Markets and Investment ProductsMarkets and Investment Products

Public Markets:

Private Markets:

Equity Assets:

StocksREITsMutual funds

Real PropertyPrivate firmsOil & Gas Partnerships

Debt Assets:

BondsMBSMoney

instruments

Bank loansWhole MortgagesVenture Debt

Asset Mkt



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1.2.4 The Magnitude of Real Estate in the 1.2.4 The Magnitude of Real Estate in the overall Capital Marketoverall Capital Market……

Exhibit 1Exhibit 1--7 US Capital Market Sectors, a $70 Trillion Pie7 US Capital Market Sectors, a $70 Trillion Pie……

* Corporate real estate owned by publicly-traded firms, plus REITs.Source: Authors’ estimates based on Miles & Tolleson (1997).

Magnitude

U.S. Capital Market Sectors, a $70 Trillion Pie

Public Debt (22% RE), 30%

Public Equity (17% RE*),

24%

Private Equity (78% RE), 30%

Private Debt (49% RE), 16%

*Corporate real estate owned by publicly traded firms, plus REITs.Source: Authors' estimates based on Miles & Tolleson (1997) updated with FRB statistics.



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Exhibit 1Exhibit 1--8: US 8: US InvestableInvestable Capital Market with Real Estate Capital Market with Real Estate Components Broken OutComponents Broken Out

Magnitude

U.S. Investable Capital Market with Real Estate Components Broken Out. (Source: Based on Miles & Tolleson 1997)

Stocks26%

REIT Equity0%

Agricultural/Timberlands2%

Commercial Real Estate Equity

7%House Equity17%

Private Residential Mortgages

6%

RMBS6%

CMBS1%

Private Commercial Mortgages

2%

Bonds24%

Private Debt9%



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Performance

Investment Total Return Performance (per annum avg) as of June 30, 2006

-5.00%

0.00%

5.00%

10.00%

15.00%

20.00%

Real Estate(NCREIF)

Stocks(SP500)

Bonds(Lehman G/C)

T-Bills CPI

1yr. 3yr. 5yr. 10yr.

Total Investment Return asReal EstateStocks (SP Bonds (Leh T-Bills CPI 1yr. 18.68% 8.63% -1.52% 3.95% 4.01% 3yr. 15.79% 11.21% 1.60% 2.31% 3.27% 5yr. 12.01% 2.50% 5.13% 2.16% 2.59% 10yr. 12.42% 8.35% 6.25% 3.68% 2.59% 20yr. 8.17% 11.02% 7.32% 4.68% 3.12%



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Exhibit 2Exhibit 2--2: The 2: The ““Real Estate SystemReal Estate System””: Interaction of the Space Market, Asset Market, & Development I: Interaction of the Space Market, Asset Market, & Development Industryndustry

SPACE MARKET

SUPPLY(Landlords)

DEMAND(Tenants)

RENTS&

OCCUPANCY

LOCAL&

NATIONALECONOMY

FORECASTFUTURE

ASSET MARKET

SUPPLY(Owners

Selling)

DEMAND(InvestorsBuying)

CASHFLOW

MKTREQ’D

CAPRATE

PROPERTYMARKETVALUE

DEVELOPMENTINDUSTRY

ISDEVELPT

PROFITABLE?

CONSTRCOSTINCLULAND

IFYES

ADDSNEW

CAPITAL MKTS

= Causal flows.

= Information gathering & use.



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1.1.1 The Space Market1.1.1 The Space Market……Supply:

Property Owners(Landlords)

Demand:

Property Users(Tenants)

MARKET

•Rents (e.g.$/SF)

•Occupancy



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Exhibit 1Exhibit 1--3: Change in Supply & Demand & 3: Change in Supply & Demand & Rent over TimeRent over Time

$5

$10

$15

$20

$25

QUANTITY OF SPACE (Mil

REAL RENT

3.5 4 4.5 5 5.5 6 6.5

D0

D1

D2

S1 S2

LRMC16

13

Space Mkt



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1.2 The Real Estate Asset Market (Property 1.2 The Real Estate Asset Market (Property Market)Market)……

Supply:

InvestorsWanting to Sell

Demand:

InvestorsWanting to Buy

MARKET

Property Prices:“Cap Rates”

1/($Asset/$Income)www.bsscommunitycollege.in www.bssnewgeneration.in www.bsslifeskillscollege.in


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WHY DO PEOPLE WHY DO PEOPLE INVEST?...INVEST?...

Individuals:– THE 25-YR-OLD "YUPPY" ? . . .– THE 25-YR-OLD "DINC" COUPLE ? . . .– THE 35-YR-OLD "YOUNG FAMILY" ? . . .– THE 45-YR-OLD "MID-LIFE CRISIS" ? . . .– THE 65-YR-OLD "RETIREE" ? . . .

DIFFERENT LIFE STYLES, LIFE CYCLES, PERSONAL GOALS, LEVELS OF WEALTH

Asset Mkt



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Institutions:– LIFE INSURANCE COMPANIES– PENSION FUNDS– MUTUAL FUNDS– BANKS– FOUNDATIONS

DIFFERENT CONSTITUENCIES, EXPERTISE, LIABILITIES, REGULATIONS, SIZES

Asset Mkt



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===> DIFFERENT TIME HORIZONS, RISK TOLERANCES, NEEDS FOR INCOME vsGROWTH

Therefore, . . . (opportunities for new product development in the investment industry)

Asset Mkt



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TWO MAJOR INVESTMENT TWO MAJOR INVESTMENT OBJECTIVESOBJECTIVES::

1) GROWTH (SAVINGS) -RELATIVELY LONG-TERM HORIZON (NO IMMEDIATE NEED);

2) INCOME (CURRENT CASH FLOW) --SHORT-TERM & ON-GOING NEED FOR CASH.

Asset Mkt



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MAJOR CONSTRAINTS & MAJOR CONSTRAINTS & CONCERNS:CONCERNS:

- RISK- LIQUIDITY- TIME HORIZON- MANAGEMENT BURDEN, EXPERTISE- AMOUNT OF FUNDS AVAILABLE FOR

INVESTMENT (SIZE)- CAPITAL CONSTRAINT

Therefore (again), . . . What?

Asset Mkt



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Montague Court Development Cost Budget:

Hard Costs Total Cost Cost/Sq.Ft.

1. Land $15,124,000 $ 66.33

2. Base Shell & Sitework 9,111,000 39.96

3. Tenant Improvements 7,399,000 32.45

Total Hard Costs: $ 31,634,000 $ 138.75

Soft Costs

4. Architect/Engineers $ 262,000 $ 1.15

5. Permits/Fees 768,000 3.37

6. Legal/Title/Taxes 171,000 0.75

7. Marketing 46,000 0.20

8. Leasing Commissions 1,790,000 7.85

9. Developer Fee 228,000 1.00

10. Contingency 556,000 2.00

11. Construction Interest 1,074,000 4.71

Total Soft Costs: $ 4,895,000 21.46

Total Project Cost: $ 36,529,000 $ 160.21

Example



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Montague Court Development Project Cash Flow Projection:Year 0 Year 1 Year 2 Year 3

For the Years Ending 2000 2001 2002POTENTIAL GROSS REVENUEBase Rental Revenue $222,735 $3,410,017 $4,349,783Absorption & Turnover Vacancy $0 $0 $0Schoduled Base Rental Revenue $222,735 $3,410,017 $4,349,763Expense Reimbursement RevenueOper. Expenses $36,196 $565,778 $725,706Total Reimbursement Revenue $36,196 $565,778 $725,706TOTAL POTENTIAL GROSS REVENUE $268,931 $3,975,795 $5,075,489General Vacancy -$10,357 -$159,032 -$203,020Collection Loss -$5,179 -$79,516 -$101,510EFFECTIVE GROSS REVENUE $243,395 $3,737,247 $4,770,959

OPERATING EXPENSESOper Expenses $243,395 $704,520 $725,656TOTAL OPERATING EXPENSES $243,395 $704,520 $725,656

NET OPERATING INCOME $0 $3,032,727 $4,045,303

LEASING & CAPITAL COSTSTenant Improvements $0 $0 $0Leasing Commissions $0 $0 $0Cap Reserves $0 $35,226 $36,283Construction Costs (Payoff constr loan) $0 $21,405,000 $0

TOTAL LEASING & CAPITAL COSTS $0 $0 $21,440,226 $36,283

LAND $15,124,000

CASH FLOW BEFORE DEBT SERVICE & INCOME TAX -$15,124,000 $0 -$18,407,499 $4,009,020www.bsscommunitycollege.in www.bssnewgeneration.in www.bsslifeskillscollege.in


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Evaluating the development project…

Cap rates forR&D/Office properties in Milpitas, CA.= 9.35%.

Stabilized NOI (Yr.3) = $4,045,303.

What is expected value of the finished project at end of development phase (end of Yr.2)?…

Example



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273,265,43$0935.0

303,045,4$===

CapRateNOIValue

Example



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$43,265,273

What is expected return (IRR) on the development project?…

Example



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Compute return as discount rate to equate future expected cash flows to present land cost (opportunity value)…

( ) ( )TT

IRRCF

IRRCF

IRRCF

CostLand+

+++

++

=111 2

21 K

In the present example…

( )

( )

( )

%2.28

1774,857,24$0000,124,15$

1273,265,43$499,407,18$

10000,124,15$

1)0935.0/303,045,4($499,407,18$

10000,124,15$

2

2

2

=⇒

++=

++−

++

=

++−

++

=

IRR

IRR

IRRIRR

IRRIRR



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( ) ( )TT

IRRCF

IRRCF

IRRCF

CostLand+

+++

++

=111 2

21 K


( )

( )

( )

%2.28

1774,857,24$0000,124,15$

1273,265,43$499,407,18$

10000,124,15$

1)0935.0/303,045,4($499,407,18$

10000,124,15$

2

2

2

=⇒

++=

++−

++

=

++−

++

=

IRR

IRR

IRRIRR

IRRIRR

Should we do the development?…



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( ) ( )TT

IRRCF

IRRCF

IRRCF

CostLand+

+++

++

=111 2

21 K


( )

( )

( )

%2.28

1774,857,24$0000,124,15$

1273,265,43$499,407,18$

10000,124,15$

1)0935.0/303,045,4($499,407,18$

10000,124,15$

2

2

2

=⇒

++=

++−

++

=

++−

++

=

IRR

IRR

IRRIRR

IRRIRR

Should we do the development?…

Is 28.2% a sufficient expected return, given the risk?…



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( )

( )

( )

%3.79

1358,599,48$0000,124,15$

1857,006,67$499,407,18$

10000,124,15$

1)14.0/960,380,9($499,407,18$

10000,124,15$

2

2

2

=⇒

++=

++−

++

=

++−

++

=

IRR

IRR

IRRIRR

IRRIRR

What actually happened with this investment . . .

Actual Ex Post Devlpt IRR: 79.3%!

Leased the entire project in late 2000, lease through 2010 to Cisco, at more than double the pro-forma rent!



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( )

( )

( )

%6.46

1448,307,4$0000,124,15$

1947,714,22$499,407,18$

10000,124,15$

1)095.0/920,157,2($499,407,18$

10000,124,15$

2

2

2

−=⇒

++=

++−

++

=

++−

++

=

IRR

IRR

IRRIRR

IRRIRR

What could very easily have happened with this 1999 investment . . .

Result would have been an Ex Post Devlpt IRR: -46.6%!

The tech bubble burst in 2001, driving market rents on new leases down to $0.90/SF by 2002 (vs $1.59 in pro-forma), and that’s if you could find a tenant at all!



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Chapter 10:Chapter 10:

BASIC MICRO-LEVEL VALUATION: "DCF" & “NPV”



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THE THE famousfamous DCF VALUATION DCF VALUATION PROCEDURE...PROCEDURE...

1. FORECAST THE EXPECTED FUTURE CASH FLOWS;

2. ASCERTAIN THE REQUIRED TOTAL RETURN;

3. DISCOUNT THE CASH FLOWS TO PRESENT VALUE AT THE REQUIRED RATE OF RETURN.

THE VALUE YOU GET TELLS YOU WHAT YOU MUST PAY SO THAT YOUR EXPECTED RETURN WILL EQUAL THE "REQUIRED RETURN" AT WHICH YOU DISCOUNTED THE EXPECTED CASH FLOWS.



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where:CFt = Net cash flow generated by the property in period “t”;

Vt = Property value at the end of period “t”;

E0[r] = Expected average multi-period return (per period) as of time “zero” (the present), also known as the “going-in IRR”;

T = The terminal period in the expected investment holding period, such that CFT would include the re-sale value of the property at that time (VT), in addition to normal operating cash flow.

( ) ( ) ( )TT

TT

rECFE

rECFE

rECFE

rECFEV

][1][

][1][

][1][

][1][

0

01

0

102

0

20

0

100 +

++

+++

++

= −−L



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Numerical example...Numerical example...

Lease:

Year: CF:

2001 $1,000,000

2002 $1,000,000

2003 $1,000,000

2004 $1,500,000

2005 $1,500,000

2006 $1,500,000

• Single-tenant office bldg• 6-year “net” lease with a “step-up”...• Expected sale price year 6 =

$15,000,000• Required rate of return (“going-in

IRR”) = 10%...• DCF valuation of property is

$15,098,000:

)(1.,000516+

)(1.,00051+

)(1.,00051+

)(1.0,0001+

)(1.0,0001+

)(1.0,0001 = 1 65432 08

00,08

00,08

00,08

00,08

00,08

00,000,098,5



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Why is the DCF procedure Why is the DCF procedure importantimportant??1.1. Recognizes asset valuation Recognizes asset valuation fundamentally dependsfundamentally depends upon upon

future net future net cash flowcash flow generation potentialgeneration potential of the asset.of the asset.

2.2. Takes Takes longlong--term term perspective appropriate for investment perspective appropriate for investment decisiondecision--making in illiquid markets (multimaking in illiquid markets (multi--period, typically period, typically 10 yrs in R.E. applications).10 yrs in R.E. applications).

3.3. Takes the Takes the total returntotal return perspective necessary for successful perspective necessary for successful investment.investment.

4.4. Due to the above, the Due to the above, the exerciseexercise of going through the DCF of going through the DCF procedure, procedure, if taken seriouslyif taken seriously, can help to protect the investor , can help to protect the investor from being swept up by an asset market from being swept up by an asset market ““bubblebubble”” (either a (either a positive or negative bubble positive or negative bubble –– when asset prices are not related to when asset prices are not related to cash flow generation potential)cash flow generation potential)..



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Remember:

Investment returns are inversely relatedinversely related to the price paid going in for the asset.e.g., in the previous example, if we could get the asset for $14,000,000 (instead of $15,098,000), then our going-in return would be 9.6% (instead of 8%):

)(,000516+

)(,00051+

)(,00051+

)(0,0001+

)(0,0001+

)(0,0001 = 65432 0962.1

00,0962.100,

0962.100,

0962.100,

0962.100,

0962.100,000,000,14

vs.

What is the fundamental economic reason for this inverse relationship? [Hint: What determines fut. CFs?]

)(1.,000516+

)(1.,00051+

)(1.,00051+

)(1.0,0001+

)(1.0,0001+

)(1.0,0001 = 1 65432 08

00,08

00,08

00,08

00,08

00,08

00,000,098,5



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Match the discount rate to the risk. . .Match the discount rate to the risk. . .

r = rf + RP

Disc.Rate = Riskfree Rate + Risk Premium

(Riskfree Rate = US T-Bill Yield.)



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Projected operating CFs will be contractual (covered by leases). 1st 6 yrs in current lease, remainder in a subsequent lease. Prior to signing, lease CFs are more risky (interlease disc rate), once signed, less risky (intralease disc rate). DCF Valuation:

Hypothetical office building net cash flows: Year 1 2 3 4 5 6 7 8 9 10 CFt $1 $1 $1 $1.5 $1.5 $1.5 $2 $2 $2 $22

Here we have estimated the discount rate at 7% for the relatively low-risk lease CFs (e.g., if T-Bond Yld = 5%, then RP=2%), and at 9% for the relatively high-risk later CFs ( 4% risk premium).

Implied property value = $18,325,000.

10.2.1 Match the Discount Rate to the Risk:10.2.1 Match the Discount Rate to the Risk:IntraleaseIntralease & & InterleaseInterlease Discount RatesDiscount Rates

( ) ( ) ( ) ( ) ( )10

4

1

6

46

3

1 09.120$

07.12$

09.11

07.15.1$

07.11$000,325,18$ +⎟⎟

⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛++= ∑∑∑

=== tt

tt

tt



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Current practice usually is not this sophisticated for typical properties. If the lease expiration pattern is typical, a single“blended” discount rate is typically used.

Thus, for this building, we would typically observe a “going-in IRR” of 8.57%, applied to all the expected future CFs…

( ) ( ) ( ) ( )10

10

7

6

4

3

1 0857.120$

0857.12$

0857.15.1$

0857.11$000,325,18$ ∑∑∑

===

+++=t

tt

tt

t

In principle, this can allow “arbitrage” opportunities if investors are not careful (especially as the ABS mkt develops…)

10.2.2 Blended IRR:10.2.2 Blended IRR:A single Discount RateA single Discount Rate



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Example:Suppose property with 7 yrs (instead of 6 yrs) remaining on vintage lease but same expected CFs as before.Purchase for $18,325,000, then sell lease for $7,083,000 and property residual for $11,319,000, for a profit of $77,000:

( ) ( ) ( )10

3

17 09.1

20$07.12$

09.11000,319,11$ +⎟⎟

⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛= ∑

=tt

Hypothetical office building net cash flows: Year 1 2 3 4 5 6 7 8 9 10 CFt $1 $1 $1 $1.5 $1.5 $1.5 $2 $2 $2 $22

1st 6 CFs in Lease $18.325M Value 1st 7 CFs in Lease $18.402M Value

( ) ( ) ( )7

6

4

3

1 07.12$

07.15.1$

07.11$000,083,7$ ∑∑

==

++=t

tt

t



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Valuation shortcuts: Valuation shortcuts: ““Ratio valuationRatio valuation””......

1) DIRECT CAPITALIZATION:1) DIRECT CAPITALIZATION:

A WIDELY-USED SHORTCUT VALUATION PROCEDURE:

· SKIP THE MULTI-YEAR CF FORECAST

· DIVIDE CURRENT (UPCOMING YEAR) NET OPERATING INCOME (NOI) BY CURRENT MARKET CAP RATE (YIELD, NOT THE TOTAL RETURN USED IN DCF)

10.3 Ratio Valuation Procedures10.3 Ratio Valuation Procedures



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The idea behind direct capitalization…

IF "CAP RATE" = NOI / V ,

THEN:

V = NOI / CAP RATE

(FORMALLY, NOT CAUSALLY)

MOST APPROPRIATE FOR BLDGS W SHORT-TERM LEASES IN LESS CYCLICAL MARKETS, LIKE APARTMENTS.



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EXAMPLE:250 UNIT APARTMENT COMPLEXAVG RENT = $15,000/unit/yr5% VACANCYANNUAL OPER. EXPENSES = $6000 / unit8.82% CAP RATE (KORPACZ SURVEY)

VALUATION BY DIRECT CAPITALIZATION:

POTENTIAL GROSS INCOME (PGI) = 250*15000 = $3,750,000- VACANCY ALLOWANCE (5%) = 0.5*3750000 = 187,500- OPERATING EXPENSES = 250*6000 = 1,500,000------------------------------------- -------------------NET OPER.INCOME (NOI) = $2,062,500

V = 2,062,500 / 0.0882 = $23,384,354, say approx. $23,400,000



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2) GROSS INCOME MULTIPLIER (GIM):2) GROSS INCOME MULTIPLIER (GIM):

GIM = V / GROSS REVENUE

COMMONLY USED FOR SMALL APARTMENTS. (OWNER'S MAY NOT RELIABLY REVEAL GOOD

EXPENSE RECORDS, SO YOU CAN'T COMPUTE NOI (= Rev - Expense), BUT RENTS CAN BE OBSERVED INDEPENDENTLY IN THE RENTAL MARKET.)

IN PREVIOUS APT EXAMPLE THE GIM IS:

23,400,000 / 3,750,000 = 6.2.



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Empirical cap rates and market values. . .Empirical cap rates and market values. . .

Cap rates are a way of quoting observed market prices for property assets (like bond “yields” are the way bond prices are reported).

E.g., Korpacz Survey M

alls

Strip

Ctrs

Indu

st.

Apt

s

CBD

Off

ice

Subu

rb.O

ff.

Hou.

Off

SF O

ff

0%

2%

4%

6%

8%

10%

12%

*Source: Korpacz Investor Survey, 1st quarter 1999

Exh.11-6b: Investor Cap Rate Expectations for Various Property Types*

Institutional 8.41% 9.76% 9.14% 8.83% 8.82% 9.17% 9.43% 8.42%

Non-institutional 9.88% 11.97% 10.21% 9.83% 10.56% 10.83% 10.75% 9.58%

Malls Strip Ctrs

Indust. Apts CBD Office

Suburb.Off.

Hou.Off SF Off



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DANGERS DANGERS IN MKTIN MKT--BASED RATIO VALUATION. . .BASED RATIO VALUATION. . .

1) 1) DIRECT CAPITALIZATION CAN BE MISLEADING FOR MARKET VALUE IF PROPERTY DOES NOT HAVE CASH FLOW GROWTH AND RISK PATTERN TYPICAL OF OTHER PROPERTIES FROM WHICH CAP RATE WAS OBTAINED. (WITH GIM IT’S EVEN MORE DANGEROUS: OPERATING EXPENSES MUST ALSO BE TYPICAL.)

2) 2) Market-based ratio valuation won’t protect you from “bubbles”!



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10.4 Typical mistakes in DCF application to 10.4 Typical mistakes in DCF application to commercial property...commercial property...

CAVEAT!BEWARE OF “G.I.G.O.”===> Forecasted Cash Flows:

Must Be REALISTIC Expectations(Neither Optimistic, Nor Pessimistic)

===> Discount Rate should be OCC:Based on Ex Ante Total Returns in Capital Market(Including REALISTIC Property Market Expectations)

· Read the “fine print”.· Look for “hidden assumptions”.· Check realism of assumptions.



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Three most common mistakes in R.E. DCF practice:

1. Rent & income growth assumption is too high—aka: “We all know rents grow with inflation, don’t we!”?... Remember: Properties tend to depreciate over time in real terms (net of

inflation). Usually, rents & income within a given building do not keep pace with inflation, long run.

2. Capital improvement expenditure projection, &/or terminal cap rate projection, are too low –Remember: Capital improvement expenditures typically average at least

10%-20% of the NOI (1%-2% of the property value) over the long run.Going-out cap rate is typically at least as high as the going-in cap rate

(older properties are more risky and have less growth potential).

3. Discount rate (expected return) is too high –This third mistake may offset the first two, resulting in a realistic estimate of

property current value, thereby hiding all three mistakes!



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Numerical example:Numerical example:Two cash flow streams . . .

First has 5%/yr growth,Second has 1%/yr growth.Both have same initial cash flow level ($1,000,000).Both have PV = $10,000,000: First discounted @ 15%, Second discounted @ 11%.

Year:

1 2 3 4 5 6 7 8 9 10

$1,000,000 $1,050,000 $1,102,500 $1,157,625 $1,215,506 $1,276,282 $1,340,096 $1,407,100 $1,477,455 $17,840,274

$1,000,000 $1,010,000 $1,020,100 $1,030,301 $1,040,604 $1,051,010 $1,061,520 $1,072,135 $1,082,857 $12,139,907

As both streams have same starting value & same PV, both may appear consistent with observable current information in the space and property markets. (e.g., rents are typically $1,000,000, and property values are typically $10,000,000 for properties like this.)

Suppose realistic growth rate is 1%, not 5%. Then the first CF projection gives investors an unrealistic return expectation of 15%.“Unfair” comparisons (e.g., bond returns cannot be “fudged” like this).Investor is “set up” to be disappointed in long run.



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Results of these types of mistakes:Results of these types of mistakes:

Unrealistic expectations

Long-run undermining credibility of the DCF valuation procedure

Wasted time (why spend time on the exercise if you’re not going to try to make it realistic?...)



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10.610.6DCF and Investment Decision Rules:DCF and Investment Decision Rules:

the the NPVNPV Rule...Rule...DCF Property value (“V”) . . .But how do we know whether an investment is a “good deal”

or not?...How should we decide whether or not to make a given

investment decision?NPV = PV(Benefit) – PV(Cost)i.e.: NPV = Value of what you get – Value of what you

give up to get it,All measured in equivalent “apples-to-apples” dollars,

because we have discounted all the values to present using discount rates reflecting risk.



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“THE NPV INVESTMENT DECISION RULE”:

1) MAXIMIZE THE NPV ACROSS ALL MUTUALLY-EXCLUSIVE ALTERNATIVES; AND

2) NEVER CHOOSE AN ALTERNATIVE THAT HAS: NPV < 0.



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The NPV Investment Decision RuleThe NPV Investment Decision Rule

IF BUYING: NPV = V – PIF SELLING: NPV = P – V

Where:V = Value of property at time-zero (e.g.,

based on DCF)P = Selling price of property (in time-zero

equivalent $)



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Example:Example:

DCF V = $13,000,000You can buy @ P = $10,000,000.NPV = V-P = $13M - $10M = +$3M.



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Note: NPV Rule is based Note: NPV Rule is based directlydirectly on on the the ““Wealth Maximization PrincipleWealth Maximization Principle””. . .. . .

WEALTH MAXIMIZATION ⇒ The NPV Rule

Maximize the current value of the investor’s net wealth. Otherwise, you’re “leaving

money on the table”.



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NPV Rule Corollary:NPV Rule Corollary:

"Zero NPV deals are OK!“

Why? . . .Why? . . .



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Zero NPV deals are not zero profit.(They only lack “super-normal” profit.)A zero NPV deal is only “bad” if it is prevents

the investor from undertaking a positive NPV deal.

In fact, on the basis of “market value” (MV)…



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Based on “market value” (MV),

NPV(Buyer) = V-P = MV-P

NPV(Seller) =P-V = P-MV = -NPV(Buyer)

Therefore, if both the buyer and seller apply the NPV Rule (NPV≥0), then:

(i) NPV(Buyer) ≥ 0 ⇒ -NPV(Seller) ≥ 0 ⇒ NPV(Seller) ≤ 0;

(ii) NPV(Seller) ≥ 0 ⇒ -NPV(Buyer) ≥ 0 ⇒ NPV(Buyer) ≤ 0;

(i)&(ii) together ⇒ NPV(Buyer) = NPV(Seller) = 0.

Thus, measured on the basis of MV, we actually expect that:

NPV = 0.



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Sources of Sources of ““illusionsillusions”” of big positive of big positive NPVsNPVs

1) OCC (discount rate) is not the cost of borrowed funds (e.g., mortgage interest rate).

2) Land value? (not just historical cost)

3) Search & Management Costs?

4) “Private Info”? (But MV is based on publicinfo.)



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However, in Real Estate it is possible to However, in Real Estate it is possible to occasionallyoccasionally find deals with substantially find deals with substantially positive, or negative, NPV, even based on MV.positive, or negative, NPV, even based on MV.

Real estate asset markets not informationallyefficient:- People make “pricing mistakes” (they can’t observe MV for sure for a given property)- Your own research may uncover “news”relevant to value (just before the market knows it)



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What about What about uniqueunique circumstances or abilities? . . .circumstances or abilities? . . .

Generally, real uniqueness does not affect MV.

Precisely because you are unique, you can’t expect someone else to be willing to pay what you could, or be willing to sell for what you would. (May affect “investment value” –IV, not MV.)



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10.6.2 Choosing Among Alternative Zero10.6.2 Choosing Among Alternative Zero--NPV InvestmentsNPV Investments

• Alternatives may have different NPVs based on “investment value”, even though they all have equal (zero) NPV based on “market value”. (See Sect. 12.1.)

• One alternative may be preferable for macro or strategic reasons (portfolio target, administrative efficiency, property size preference, etc.).

• Alternatives may present different expected return “attributes” (initial yield, cash flow change, yield change). (See Appendix 10B & Sect. 26.1.1.)



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10.6.3. Hurdle Rate Version of the Investment Rule: 10.6.3. Hurdle Rate Version of the Investment Rule: IRR vs. NPVIRR vs. NPV

SOMETIMES IT IS USEFUL (anyway, it is very common in the real world) TO "INVERT" THE DCF PROCEDURE...

INSTEAD OF CALCULATING THE VALUE ASSOCIATED WITH A GIVEN EXPECTED RETURN,CALCULATE THE EXPECTED RETURN (IRR) ASSOCIATED WITH A GIVEN PRICE FOR THE PROPERTY.

I.E., WHAT DISCOUNT RATE WILL CAUSE THE EXPECTED FUTURE CASH FLOWS TO BE WORTH THE GIVEN PRICE?...

THEN THE DECISION RULE IS:1) MAXIMIZE DIFFERENCE BETWEEN:

IRR AND REQUIRED RETURN (ACROSS MUT.EXCLU ALTS)

2) NEVER DO A DEAL WITH:IRR < REQ'D RETURN

REQ’D RETURN = “HURDLE RATE” = rf + RPwww.bsscommunitycollege.in www.bssnewgeneration.in www.bsslifeskillscollege.in


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When using the IRR (hurdle) version of the basic When using the IRR (hurdle) version of the basic investment decision rule:investment decision rule:

Watch out for Watch out for mutually exclusivemutually exclusive alternativesalternativesof of different scalesdifferent scales..

e.g., $15M project @ 15% is better than $5M project @20% if cost of capital (hurdle) in both is 10%.



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Appendix 10A: Appendix 10A: A Method to Estimate A Method to Estimate InterleaseInterlease Discount RatesDiscount Rates

Suppose in a certain property market the typical:• Lease term is 5 years;• Cap rate (cash yield) is 7%;• Long term property value & rental growth rate is 1%/yr (typically equals inflation minus real depreciation rate);• Leases provide rent step-ups of 1%/yr (per above);• Tenant borrowing rate (intralease disc rate) is 6%...

( )( ) 29.4$

11)06.1/1($

06.11$)01.1(

06.11)$01.1(

06.11$

06.101.1

506.101.1

5

4

2 =−

−=+++ L

Then (assuming pmts in arrears), PV of a lease, per dollar of initial net rent, is:



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L+⎟⎠⎞

⎜⎝⎛+

+⎟⎠⎞

⎜⎝⎛+

+= 29.4$1

01.129.4$1

01.129.4$105

rrS

A stylized space in this market has PV equal to S, as follows (ignoring vacancy between leases), assuming interlease discount rate is r:

( )5101.1129.4$

r

S+−

=

This is a constant-growth perpetuity, so (using geometric series formula from Chapter 8) we can shortcut this as:

From the market’s prevailing cap rate we also know that:

07.1$

=S



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Putting these two together, we have:

( )

( ) %48.81)29.4($07.101.1

129.4$

07.1$

5/1

51

01.1

=−−=

⇒

−=

+

r

r

The implied interlease discount rate is 8.48%.

This is almost 250 bps above the intralease rate of 6%.

But it is only about 50 bps above the blended going-in IRR of 8% (determined based on the same constant-growth perpetuity model, as the cash yield plus the growth rate: 7% + 1% = 8%).



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Appendix 10B (& Ch.26 Sect. 26.1.1)Appendix 10B (& Ch.26 Sect. 26.1.1)

PropertyProperty--LevelLevelInvestment Performance Investment Performance

AttributionAttribution



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Real Estate InvestmentReal Estate Investment““Performance AttributionPerformance Attribution””

DEFINITION: DEFINITION: The The decompositiondecomposition (or (or ““breaking downbreaking down””, or , or ““parsingparsing””) of ) of the total investment return of a subject property or the total investment return of a subject property or portfolio of properties (or an investment manager).portfolio of properties (or an investment manager).

PURPOSE:PURPOSE:To assist with the To assist with the diagnosisdiagnosis and understanding of what and understanding of what caused the given investment performance.caused the given investment performance.

USAGE:USAGE:By investment managers (agents) and their investor By investment managers (agents) and their investor clients (principals).clients (principals).



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Two levelsTwo levelsat which performance attribution is performed:at which performance attribution is performed:

•• Property levelProperty levelPertains to individual properties or static portfolios of Pertains to individual properties or static portfolios of multiple properties.multiple properties.

•• Portfolio levelPortfolio levelPertains to dynamic portfolios or investment manager Pertains to dynamic portfolios or investment manager (or fund) level.(or fund) level.



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Major Major attributesattributes (return components):(return components):

At the PROPERTY LEVEL:At the PROPERTY LEVEL:Initial Cash YieldInitial Cash Yield

Cash Flow ChangeCash Flow ChangeYield ChangeYield Change

At the PORTFOLIO LEVEL:At the PORTFOLIO LEVEL:AllocationAllocationSelectionSelection

InteractionInteraction



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42

““Performance AttributionPerformance Attribution””::

Portf Tot.Return – Bnchmk Tot.Return

Allocation Selection Interaction

Portfolio Level:Portfolio Level:

Prop.IRR – Bnchmk Cohort IRR

Init.Yield CF Growth Yield Chge

Property Level:Property Level:

•• Often useful for Often useful for diagnosticdiagnostic purposes to compare purposes to compare subjectsubject portfolio portfolio or mgr with an appropriateor mgr with an appropriate benchmarkbenchmark . . .. . .



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PropertyProperty--Level Performance Attribution Level Performance Attribution . . .. . .

Property level performance attribution focuses on Property level performance attribution focuses on ““property property levellevel”” investment performance, i.e., the total return achieved investment performance, i.e., the total return achieved within a given property or a static (fixed) portfolio of within a given property or a static (fixed) portfolio of properties (that is, apart from the effect of investment properties (that is, apart from the effect of investment allocation decisions, as if holding allocation among categories allocation decisions, as if holding allocation among categories constant).constant).Property level attribution should be designed to break out Property level attribution should be designed to break out the property level total return performance in a manner the property level total return performance in a manner useful for shedding light on the four major property level useful for shedding light on the four major property level investment management functions:investment management functions:•• Property selectionProperty selection (picking (picking ““goodgood”” properties as found);properties as found);•• Acquisition transaction executionAcquisition transaction execution;;•• Operational managementOperational management during the holding period (e.g., during the holding period (e.g., marketing, leasing, expense mgt, capital expenditure mgt);marketing, leasing, expense mgt, capital expenditure mgt);•• Disposition transaction executionDisposition transaction execution..



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These propertyThese property--level management functions are related level management functions are related generally to three attributes (components) of the propertygenerally to three attributes (components) of the property--level level sincesince--acquisition IRRacquisition IRR, essentially as indicated below, essentially as indicated below……

Initial Yield

(IY)

Cash Flow Change

(CFC)

Yield Change

(YC)

Property Selection

Acquisition Transaction Execution

Operational Management

Disposition Transaction Execution



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Conventional property level performance attribution is Conventional property level performance attribution is based on periodic returns, or on timebased on periodic returns, or on time--weighted multiweighted multi--period period returns (returns (TWRRsTWRRs, e.g., as implemented by IPD in England , e.g., as implemented by IPD in England and PCA in Australia).and PCA in Australia).

But But IRRIRR--based performance attribution is arguably more based performance attribution is arguably more useful for property level management diagnostic purposes, useful for property level management diagnostic purposes, because:because:

•• At the property level, the investment manager is typically At the property level, the investment manager is typically responsible for the major cash flow responsible for the major cash flow timingtiming decisions that can decisions that can significantly effect property level (static portfolio) returns, significantly effect property level (static portfolio) returns, e.g., e.g., leasing decisions, capital expenditure decisions.leasing decisions, capital expenditure decisions.•• The IRR is sensitive to the effect of cash flow timing, the TWRThe IRR is sensitive to the effect of cash flow timing, the TWRR is R is not.not.•• The The IRR is cash flow basedIRR is cash flow based (net of capital improvement (net of capital improvement expenditures), therefore, more accurately reflecting the investmexpenditures), therefore, more accurately reflecting the investment ent return effect of capital improvement decisions.return effect of capital improvement decisions.




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Useful IRRUseful IRR--Based property level performance attribution Based property level performance attribution benchmarking requires the use of:benchmarking requires the use of:

SinceSince--acquisition IRRacquisition IRR

•• IRR is computed IRR is computed since acquisitionsince acquisition of property (or portfolio):of property (or portfolio):•• In order to reflect investment operational performance In order to reflect investment operational performance during entire holding period since acquisition;during entire holding period since acquisition;

•• Property investment holding periods are typically multiProperty investment holding periods are typically multi--year (single period or periodic returns do not reflect effectiveyear (single period or periodic returns do not reflect effectiveinvestment management holding period).investment management holding period).

•• IRR is computed for appropriate IRR is computed for appropriate benchmark cohortbenchmark cohort, , defined as universe of similar investments by competing defined as universe of similar investments by competing managers, measured from same inception date (equal to managers, measured from same inception date (equal to property acquisition date).property acquisition date).




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Simple Numerical Example:Simple Numerical Example:

•• Property (or static portfolio) bought at initial cash Property (or static portfolio) bought at initial cash yield of 9%.yield of 9%.

•• Net cash flow grew at 2% per year.Net cash flow grew at 2% per year.

•• Property (or properties) sold (or appraised) after 10 Property (or properties) sold (or appraised) after 10 years at a terminal yield of 10%, based on yr.11 years at a terminal yield of 10%, based on yr.11 projected cash flow (also 2% more than yr.10).projected cash flow (also 2% more than yr.10).

•• IRR is 10.30%.IRR is 10.30%.

•• How much of this IRR is due to 3 components: How much of this IRR is due to 3 components: Initial Yield Initial Yield ((IYIY),), Cash Flow Change Cash Flow Change ((CFCCFC),), and and Yield Change Yield Change ((YCYC))??……




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Yr IRRs: 0 1 2 3 4 5 6 7 8 9 10 11(1) Actual Oper.CF 1.0000 1.0200 1.0404 1.0612 1.0824 1.1041 1.1262 1.1487 1.1717 1.1951 1.2190(2) Actual Capital CF -11.1111 12.1899(3) Actual Total CF (=1+2) 10.30% -11.1111 1.0000 1.0200 1.0404 1.0612 1.0824 1.1041 1.1262 1.1487 1.1717 13.3850(4) Init.Oper.CF constant 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000(5) Capital CF @ Init.Yld.on(4) -11.1111 11.1111(6) Init.CF @ Init.Yld (=4+5) 9.00% -11.1111 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 12.1111(7) Capital CF @ Init.Yld.on(1) -11.1111 13.5444(8) Actual Oper. CF @ Init.Yld (=1+7) 11.00% -11.1111 1.0000 1.0200 1.0404 1.0612 1.0824 1.1041 1.1262 1.1487 1.1717 14.7395(9) Capital CF @ ActualYld.on(4) -11.1111 10.0000(10) Init.CF @ Actual Yld (=4+9) 8.32% -11.1111 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 11.0000

There are several ways one might answer this question. The approThere are several ways one might answer this question. The approach that ach that seems most intuitively related to the 4 basic mgt seems most intuitively related to the 4 basic mgt fcnsfcns is presented hereis presented here……

•• Initial yield = 9.00%,Initial yield = 9.00%, computed from line (6) IRR.computed from line (6) IRR.•• Cash flow change component = 2.00%Cash flow change component = 2.00% = 11%= 11%--9%, computed as the line (8) IRR 9%, computed as the line (8) IRR less the line (6) IRR: = IRR with actual CF less the line (6) IRR: = IRR with actual CF –– IRR with no CF growth, (with constant IRR with no CF growth, (with constant yldyld at initial rate).at initial rate).•• Yield change component = Yield change component = --0.68%0.68% = 8.32%= 8.32%--9.00%, computed as the line (10) IRR 9.00%, computed as the line (10) IRR less the line (6) IRR: = IRR with actual less the line (6) IRR: = IRR with actual yldyld chg chg –– IRR with no IRR with no yldyld chg, (with constant chg, (with constant CF at initial level).CF at initial level).•• InterractionInterraction effect = effect = --0.02%,0.02%, the difference the difference bertweenbertween the line (3) overall IRR and the line (3) overall IRR and the sum of the three other attributes [10.3%the sum of the three other attributes [10.3%--(9%+2%(9%+2%--0.68%)].0.68%)].



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Subject Property: IRR & Component Breakout

-4%-2%0%2%4%6%8%

10%12%14%

IRR InitYld CFchg YldChg Interaction

IRR & Components

Here is a graphical presentation of the IRRHere is a graphical presentation of the IRR--Based propertyBased property--level level performance attribution we just performed:performance attribution we just performed:

Suppose we computed the same type of IRR component breakdown Suppose we computed the same type of IRR component breakdown for an appropriate benchmark, that is, a NCREIF subfor an appropriate benchmark, that is, a NCREIF sub--index cohort index cohort spanning the same period of timespanning the same period of time……www.bsscommunitycollege.in www.bssnewgeneration.in www.bsslifeskillscollege.in


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PropertyProperty--Level Performance Attribution Level Performance Attribution . . .. . .We could compare our subject performance with that achieved by aWe could compare our subject performance with that achieved by apeer universe of managers, for similar properties (e.g., Calif. peer universe of managers, for similar properties (e.g., Calif. IndustrIndustr. . bldgsbldgs):):

Subject vs NCREIF Cohort Performance Comparison: IRR & Component Breakout

-5%

0%

5%

10%

15%


IRR & Components

Subject NPI Cohort



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PropertyProperty--Level Performance Attribution Level Performance Attribution . . .. . .Here is the Here is the relative performancerelative performance, the , the differencedifference between our subject between our subject property and its benchmark, by attribute:property and its benchmark, by attribute:

The above pattern could be plausibly interpreted as tentative evThe above pattern could be plausibly interpreted as tentative evidence for idence for the following hypothesis: Subject performed relatively poorly duthe following hypothesis: Subject performed relatively poorly due largely to e largely to some combination of poor selection, acquisition, and operationalsome combination of poor selection, acquisition, and operational mgt, mgt, partially offset by some combination of good disposition executipartially offset by some combination of good disposition execution (or on (or optimistic terminal appraisal), futureoptimistic terminal appraisal), future--oriented capital improvements, &/or oriented capital improvements, &/or market movements during the holding period.market movements during the holding period.

Subject - NCREIF Cohort Relative Performance: IRR & Component Breakout

-2.50%-2.00%-1.50%-1.00%-0.50%0.00%0.50%1.00%1.50%


IRR & Components



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PropertyProperty--Level Performance Attribution Level Performance Attribution . . .. . .Here is the Here is the relative performancerelative performance, the , the differencedifference between our subject between our subject property and its benchmark, by attribute:property and its benchmark, by attribute:

Now suppose we computed these relative performance differentialsNow suppose we computed these relative performance differentials across a across a number of different properties (or portfolios) we have invested number of different properties (or portfolios) we have invested inin……

Subject - NCREIF Cohort Relative Performance: IRR & Component Breakout

-2.50%-2.00%-1.50%-1.00%-0.50%0.00%0.50%1.00%1.50%


IRR & Components



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PropertyProperty--Level Performance Attribution Level Performance Attribution . . .. . .We might gain some insights about our propertyWe might gain some insights about our property--level investment and level investment and management performance:management performance:

In this case Subject Properties #1 & 3 have similarly poor perfoIn this case Subject Properties #1 & 3 have similarly poor performance (rmance (relrel to to benchmkbenchmk), due to poor initial yield & poor CF change, suggesting poor a), due to poor initial yield & poor CF change, suggesting poor acquisition & cquisition & poor operational mgt. Property #2 did better, with good poor operational mgt. Property #2 did better, with good InitYldInitYld & & CFchgCFchg, but poor , but poor YldChgYldChg (suggesting good acquisition, but poor disposition or mgt actio(suggesting good acquisition, but poor disposition or mgt actions that hurt ns that hurt future outlook (e.g., inadequate Cap.Improvement). future outlook (e.g., inadequate Cap.Improvement). MktMkt movements can also affect movements can also affect these results (less so the longer the holding period).these results (less so the longer the holding period).

Three Properties Comparison:Subject - NCREIF Cohort Relative Performance

-5.00%-4.00%-3.00%-2.00%-1.00%0.00%1.00%2.00%3.00%


Subject 1 Subject 2 Subject 3



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Appendix 10C: “Certainty-Equivalent Valuation”…

Consider the fundamental element of our valuation model:

][1][

0

100 rE

VEV+

=

Here we are accounting for both time and risk in the discount rate in the denominator, as , where rf is riskless and accounts for the time value of money, and RP is the market’s required risk premium in the expected return for the investment.

[ ] ][0 RPErrE f +=

But we can easily expand and algebraically manipulate this formula so that the denominator purely reflects the time value of money (the discounting is done risklessly) and the risk is completely and purely accounted for in the numerator, by reducing the cash flow amount in the numerator to a “Certainty Equivalent Value” . . .



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][1][

][1][ 10

0

100 RPEr

VErE

VEVf ++

=+

=

( )fr

VRPEVEV+

−=

1][][ 010

0

( ) ( ) 0100 ][][1 VRPEVEVrf −=+

( ) ( ) ][][1 1000 VEVRPEVrf =++

( ) ][][1 100 VEVRPErf =++

A little algebra . . .




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][1][ 10

0 RPErVEV

f ++=

( )fr

VRPEVEV+

−=

1][][ 010

0

( ) 010 ][][ VRPEVE − is the “Certainty Equivalent” value of . 1V

The risk-adjusted discount rate formulation accounts for both time and risk simultaneously in the denominator:

The certainty-equivalence formulation accounts for time only in the denominator, and risk only in the numerator, discounting the certainty-equivalent cash flow amount risklessly back to the present:




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( ) 010 ][][ VRPEVE −

The investment market is indifferent between a claim on the actual risky amount of V1 one period in the future (with the actual amount of risk involved in that), versus a claim on the lesser amount of

one period in the future with no risk at all.




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Why do we care about this? . . .

The certainty-equivalent approach will be quite convenient later on when we develop the “real options” (or “decision tree analysis”) method for evaluating investments in real estate developmentprojects.

Consider a simple example . . .




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Suppose:

Riskfree interest rate = 3%

Stock market total return risk premium = 6%

Stock Mkt expected total return is:

E[rS] = rf + E[RPS] = 3% + 6% = 9%

“Binomial World”…

A stock mkt total return index that today has value 1.00 will next year have a value of either:

1.13 (with 70% probability), or

0.79 (with 30% probability).

Therefore, expected value of index next yr is:

E[S1] = (0.70)1.13 + (0.30)0.79 = 1.03




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S = 1.13

S = 0.79

Prob = 70%

Prob = 30%

S0

Here is the situation in the stock market…

Today

Next Year




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Suppose:

We could build an office building that upon completion next yearwill be worth either $113 or $79, correlated with the stock market.

In other words, if the stock market goes up next year, our building will be worth $113, if the stock mkt goes down next yr, our building will be worth $79.

How much is this building worth today? . . .




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94$09.1

103$%6%31

79)$30(.113)$70(.][1

][ 100 ==

+++

=++

=Vf RPEr

VEV

Risk-adjusted discount rate valuation:

94$03.197$

%3194)$06(.103$

1][][ 010

0 ==+−

=+−

=f

V

rVRPEVEV

Certainty-equivalant valuation:

$97 is the certainty-equivalent value of V1 whose expected value is $103.

In general we can determine the certainty-equivalent value if we know the expected future value and the riskfree and risk-adjusted discount rates:

103$09.103.1103$

06.03.103.197$

..],[][1

1][][

,][1

1][

][][

,][1

][1

][][

10010

10

010

10010

=++

+=

++

+=−

⇒++

+=

−

⇒++

=+−

geVERPEr

rVRPEVE

RPErr

VEVRPEVE

RPErVE

rVRPEVE

f

fV

f

fV

ff

V




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Notice that the difference between the expected future value and the certainty-equivalent value is E[RPV]V0:

6$)100($06.97$103$:..,][][ 0110 ==−=− geVRPECEQVE V

The general formula for this difference is:

( )

( )

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛=

⎟⎟⎠

⎞⎜⎜⎝

⎛=

⎟⎟⎠

⎞⎜⎜⎝

⎛=

%%$

%%

$

%%

%][ 00

returninriskMktreturninRPMktinriskV

returninRPMktreturninriskMktinriskV

VreturninRPMktreturninriskMkt

returninriskVVRPE V

( )

( ) ( ) ( ) 6$)17.0)(34($%36%634$

%84%120%3%934$

947994113%3%979$113$][

:.,.

%%][

][

0

0

==⎟⎠⎞

⎜⎝⎛=⎟

⎠⎞

⎜⎝⎛

−−

=⎟⎟⎠

⎞⎜⎜⎝

⎛−−

−=

⎟⎟⎠

⎞⎜⎜⎝

⎛

−

−−=

VRPE

exampleouringe

MktMktrrE

VVVRPE

V

downup

fMktdownupV

In the “binomial world” this formula becomes:




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64

⎟⎟⎠

⎞⎜⎜⎝

⎛==⎟⎟

⎠

⎞⎜⎜⎝

⎛=

][],[""

%%

][][

Mkt

MktV

Mkt

V

rVARrrCOVBeta

returninriskMktreturninriskV

RPERPE

In the “CAPM”:

(Don’t worry about this in this class.)

Three asides (see notes for further explanation) . . .

The “binomial world” is much more realistic and useful than you might think, in part because we can define the temporal length of a period to be as short as we want, and we can link and branch individual binomial elements together to make a “tree” of asset value possibilities over time.

, Thus:

( ) ( ) ( )( ))][(1][

1)][(][

],[][1)][(][

10

1100100

fMktf

ffMktMkt

MktffMkt

rrErVE

rrrErVAR

rVCOVVErVrrEVEV

−++=

+⎟⎟⎠

⎞⎜⎜⎝

⎛−−=+−−=

β

β

More generally for a cash flow T periods in the future with expected value E0[VT], define the certainty-equivalent amount CEQ[VT]. We have:

( ) ( )( )

( ) ][][1

1][,

1][

][1][

00

0 T

T

Vf

fTT

f

TT

Vf

T VERPEr

rVCEQ

rVCEQ

RPErVEV ⎟

⎟⎠

⎞⎜⎜⎝

⎛

+++

=⇒+

=++

=

A Technical Digression for PhD students…



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65

Let’s go back to our office building example…

Suppose the office building does not exist yet,

but we could build it in 1 year

by paying $90 of construction cost upon completion of construction next year. (Construction is instantaneous: We can decide next year whether to build or not.)

Suppose our option to build this project expires in 1 year: We either build then or we lose the right to ever build.

How much is this option worth?




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66

Vup = $113

K = $90

Do dvlpt, get:

$113 - $90 = $23

= Cup

Vdown = $79

K = $90

Don’t build, get:

$0 = Cdown

Prob = 70%

Prob = 30%

C0

Label the value of the option today C0.

Here is the situation we face…

Today

Next Year

In general: Cup = MAX[Vup-K, 0], Cdown = MAX[Vdown-K, 0].




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67

Use our certainty-equivalent valuation formula to value the option…

( )

( ) ( )

( ) ( )( )

12$03.1

2.12$03.1

9.3$1.16$03.1

17.23$1.16$03.1

%36%623$1.16$

%31%84%120

%3%90$23$0)30(.23)$70(.

:.,.

1%%

][][

0

10

0

==−

=

−=

⎟⎠⎞

⎜⎝⎛−

=

+

⎟⎠⎞

⎜⎝⎛

−−

−−+=

+

⎟⎟⎠

⎞⎜⎜⎝

⎛

−−

−−

=

C

exampleouringe

rMktMkt

rrECCCE

Cf

downup

fMktdownup




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68

12$34.1

1.16$%31%31

0)$30(.23)$70(.][1

][ 100 ==

+++

=++

=Cf RPEr

CEC

The equivalent valuation using the risk-adjusted discount rate approach is:

Which implies that the option has 31/6 = 5.2 times the investment risk that the office building has (and that the stock market has), as:

RPC = 31% = 5.2*6% = 5.2*RPV (= 5.2*RPS).

However, if we didn’t already know the option’s risk premium (31%), or hadn’t already done the certainty-equivalent approach, we wouldn’t be able to use the risk-adjusted discount rate approach.

The certainty-equivalent approach does not require prior knowledge of RPC. It only requires knowledge of Cup , Cdown , and the “up”probability (70% in our example).

This makes the certainty-equivalent approach very useful for option valuation. Most development projects are essentially “options”.




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69

( ) ( ) 17.0%36%6

%)16(%)20(%3%9

%%][$$94$79$113$%3%9

11111

==−−+

−=

−=

−=

−−

downupV

downupV

VVRP

VPVVVRP

( )

Fundamentally, what we are doing here is making sure that the expected return risk premium per unit of risk is the same between an investment in the development option, and an investment in already-build (stabilized) property. For example, for stabilized property:


( ) 17.0%190%31

%)100(%)90(%3%34

%%][$$12$0$23$%3%34

11111

==−−+

−=

−=

−=

−−

downupC

downupC

CCRP

CPVCCRP

For the development option:

Thus, this procedure for the valuation of the development option is equivalent to a cross-market equilibrium condition: that the expected return risk premium per unit of risk (or the “risk-adjusted return”) presented by the investments should be the same between the market for development options and the market for stabilized built property. Otherwise, investors will buy one type of asset and sell the other type until prices equilibrate the risk-adjusted returns across the two markets.



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Chapter 11: Chapter 11:

Real Estate Cash Flow Pro Formas & Opportunity Cost of Capital (OCC)



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"PROFORMA" "PROFORMA" = a multi-year cash flow forecast

(Typically 10 years.)

Show to: Lenders, Investors

But the proforma can be more useful than just “window dressing”, if done properly.

It is the basic vehicle to implement the DCF valuation and analysis procedure discussed in the previous chapter.

The CF proforma presents the numerators in the RHS of the DCF valuation equation.



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2 types of 2 types of CFsCFs::

• Operating• Reversion (Sale of Property, Sometimes

partial sales)



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2 ways of defining "bottom line". . .1) Property level (PBTCF, most common in practice):

• Net CF produced by property, before subtracting debt svc pmts (DS) and inc. taxes.

• CFs to Govt, Debt investors (mortgagees), equity owners.

• CFs due purely to underlying productive physical asset, not based on financing or income tax effects.

• Relatively easy to observe empirically.

• Focus of Chapter 11.

2) Equity ownership after-tax level (EATCF):• Net CF avail. to equity owner after DS & taxes.

• Determines value of equity only (not value to lenders).

• Sensitive to financing and income tax effects.

• Usually difficult to observe empirically (differs across investors).

• Will be addressed in Chapter 14.www.bsscommunitycollege.in www.bssnewgeneration.in www.bsslifeskillscollege.in


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Typical proforma line items...Exhibit 11-1:

At Property, Before-tax Level:

Operating (all years):Potential Gross Income = (Rent*SF) = PGI- Vacancy Allowance = -(vac.rate)*(PGI) = - v+ Other Income = (eg, parking, laundry) = +OI- Operating Expenses = - OE_____________________ _______Net Operating Income = NOI- Capital Improvement Expenditures = - CI_____________________ _______Property Before-tax Cash Flow = PBTCF

Reversion (last year & yrs of partial sales only):Property Value at time of sale = V- Selling Expenses = -(eg, broker) = - SE__________________ ______Property Before-tax Cash Flow = PBTCF



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Questions…

How forecast vacancy (v)?• Vac = (vac months)/(vac months + rented months) in typical cycle.• Look at typical vac rate in rental mkt; adjust for non-stabilized bldgs (e.g., gross vacancy in mkt typically > typical stabilized vac).• History of vac. in subject bldg.• Project for each space/lease: Probability of renewal & Expected vacant period if not renewed.

How forecast resale value (“reversion”, V at end)?• Divide Yr.11 NOI by “going-out” (terminal) cap rate.

What should be the typical relationship between the going-in cap rate and the going-out cap rate?. . .• Usually going-out ≥ going-in (older bldgs have less growth & more risk), esp. if little capital imprvmt expdtrs have been projected.



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-600

-500

-400

-300

-200

-100

0

100

200

300

400

1987

.4

1988

.3

1989

.2

1990

.1

1990

.4

1991

.3

1992

.2

1993

.1

1993

.4

1994

.3

1995

.2

1996

.1

1996

.4

1997

.3

1998

.2

1999

.1

1999

.4

2000

.3

2001

.2

2002

.1

2002

.4

2003

.3

Mid 70s vintage Early 80s vintage

Basis Point Spread

Exhibit 11-2: As New Competitors Enter the Market, Spread Between Building and Submarket Vacancy Increases for Older Buildings(Source: Torto-Wheaton Research; “TWR Overview &Outlook”, Winter 2004.)



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Operating Expenses Operating Expenses include:include:

Fixed:• Property Taxes• Property Insurance• Security• Management

Variable:• Maintenance & Repairs• Utilities (not paid by tenants)



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Operating ExpensesOperating ExpensesNOTE:OE do NOT include:

Income taxes,Depreciation expense.

Must include mgt expense even if self-managed.

Why? . . .Opportunity cost, “apples-to-apples” comparison with alternative investments that you don’t have to manage yourself.



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Capital Expenditures Capital Expenditures include:include:

Leasing costs:• Tenant build-outs or improvement expenditures (“TIs”)• Leasing commissions to brokers

Property Improvements:• Major repairs• Replacement of major equipment• Major remodeling of building, ground & fixtures• Expansion of rentable area



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Two truths often not reflected proformas used in practice in the real world . . .

• Realistic long-term rental growth projections in most commercial properties in most areas of the U.S. should average slightly less than realistic expectations about general (CPI) inflation.

• Realistic long-term capital expenditure projections for most types of commercial property should average at least 10% to 20% of the NOI, or an annual average of about 1% to 2% of the property value.



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Exhibit 11-2: The Noname Building: Cash Flow Projection Year: 1 2 3 4 5 6 7 8 9 10 11

Item: Market Rent/SF: $10.00 $10.10 $10.20 $10.30 $10.41 $10.51 $10.62 $10.72 $10.83 $10.94 $11.05 Potential Revenue: Gross Rent Space 1 (10000SF) $105,000 $105,000 $105,000 $103,030 $103,030 $103,030 $103,030 $103,030 $108,286 $108,286 $108,286 Gross Rent Space 2 (10000SF) $100,000 $100,000 $100,000 $100,000 $100,000 $105,101 $105,101 $105,101 $105,101 $105,101 $110,462 Gross Rent Space 3 (10000SF) $100,000 $101,000 $101,000 $101,000 $101,000 $101,000 $106,152 $106,152 $106,152 $106,152 $106,152 Total PGI $305,000 $306,000 $306,000 $304,030 $304,030 $309,131 $314,283 $314,283 $319,539 $319,539 $324,900 Vacancy allowance: Space 1 $0 $0 $0 $51,515 $0 $0 $0 $0 $54,143 $0 $0 Space 2 $0 $0 $0 $0 $0 $52,551 $0 $0 $0 $0 $55,231 Space 3 $100,000 $0 $0 $0 $0 $0 $53,076 $0 $0 $0 $0 Total vacancy allowance $100,000 $0 $0 $51,515 $0 $52,551 $53,076 $0 $54,143 $0 $55,231 Total EGI $205,000 $306,000 $306,000 $252,515 $304,030 $256,581 $261,207 $314,283 $265,396 $319,539 $269,669 Other Income $30,000 $30,300 $30,603 $30,909 $31,218 $31,530 $31,846 $32,164 $32,486 $32,811 $33,139 Expense Reimbursements Space 1 $0 $1,833 $2,003 $0 $1,651 $964 $1,118 $2,870 $0 $1,823 $329 Space 2 $0 $2,944 $3,114 $1,814 $3,465 $0 $153 $1,905 $469 $2,292 $0 Space 3 $0 $0 $170 $0 $260 $0 $0 $1,752 $316 $2,139 $645 Total Revenue $235,000 $341,078 $341,891 $285,238 $340,624 $289,075 $294,324 $352,974 $298,667 $358,602 $303,781 Reimbursable Operating Expenses

Property Taxes $35,000 $35,000 $35,000 $35,000 $35,000 $36,750 $36,750 $36,750 $36,750 $36,750 $36,750 Insurance $5,000 $5,000 $5,000 $5,000 $5,000 $5,250 $5,250 $5,250 $5,250 $5,250 $5,250 Utilities $16,667 $25,500 $26,010 $22,109 $27,061 $23,002 $23,462 $28,717 $24,410 $29,877 $25,396 Total Reimbursable Expenses $56,667 $65,500 $66,010 $62,109 $67,061 $65,002 $65,462 $70,717 $66,410 $71,877 $67,396 Management Expense $6,150 $9,180 $9,180 $7,575 $9,121 $7,697 $7,836 $9,428 $7,962 $9,586 $8,090 Total Operating Expenses $62,817 $74,680 $75,190 $69,684 $76,182 $72,699 $73,298 $80,146 $74,371 $81,463 $75,486

NOI $172,183 $266,398 $266,701 $215,554 $264,442 $216,376 $221,026 $272,828 $224,295 $277,139 $228,295 Capital Expenditures TI $50,000 $50,000 $55,000 $55,000 $55,000 $55,000 Leasing Commissions $15,150 $15,455 $15,765 $15,923 $16,243 $16,569 Common physical improvements

$100,000

Net Cash Flow (operations) $172,183 $201,248 $266,701 $150,100 $164,442 $145,611 $150,103 $272,828 $153,053 $277,139 Net Cash Flow (reversion) $2,282,951 IRR @ $2,000,000 price: 10.51%

Simple numerical example Simple numerical example (in book, Sect.11.1.8: (in book, Sect.11.1.8: Exh.11Exh.11--33))



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Real world example...The R.R. Donnelly

Bldg, Chicago

$280 million (1999),945000 SF, 50-story Office Tower



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Location:In “The Loop” (CBD) at W.Wacker Dr & N.Clark St,

On the Chicago River...



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Donnelley Bldg Pro Forma...Donnelley Bldg Pro Forma...RR Donnelley Bldg Annual Cash Flow Projection

Year: 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010POTENTIAL GROSS REVENUE Base Rental Revenue 24033811 24991054 25635350 26383811 27922939 28654131 29373663 30057496 29525448 29850252 30742749Absorptn & Turnover Vac. 0 -122098 -45383 -284864 -538960 -64691 -280794 -98390 -3542566 -468748 -133817Scheduled Base Rent Rev. 24033811 24868956 25589967 26098947 27383979 28589440 29092869 29959106 25982882 29381504 30608932CPI & Other Adjustmt Rev. 1295978 1489696 1688258 1891784 2100397 2314227 2533401 2758056 465942 0 0Expense Reimbursmt Rev. 13830780 14359735 14886942 15215378 15588172 16665170 17028629 17626489 16203409 18857047 19661109Miscellaneous Income 270931 279059 287430 296054 304935 314082 323505 333212 343207 353504 364108TOTAL PGR 39431500 40997446 42452597 43502163 45377483 47882919 48978404 50676863 42995440 48592055 50634149Collection Loss -561044 -592080 -625946 -638690 -681665 -759463 -770676 -811778 -827703 -867105 -921832EFFECTIVE GROSS REVENUE 38870456 40405366 41826651 42863473 44695818 47123456 48207728 49865085 42167737 47724950 49712317OPERATING EXPENSES Repairs & Maintenance 1723900 1775613 1829188 1883220 1938829 1998749 2057947 2120365 2171717 2248204 2316872Contract Cleaning 1033459 1064415 1100189 1122605 1145141 1201526 1227982 1273344 1157614 1334681 1390062Security 738946 761114 783949 807466 831690 856640 882340 908811 936075 964158 993081Utilities 1076597 1108856 1145319 1170863 1196712 1250955 1280500 1326010 1237641 1393269 1447839General & Administrative 741398 763639 786549 810146 834450 859483 885267 911825 939179 967355 996376Insurance 144503 148838 153303 157902 162639 167518 172544 177720 183052 188543 194200Real Estate Taxes 7943834 8182149 8427614 8680442 8940855 9209081 9485 9769914 10063012 10364902 10675849Management Fee 971761 1010134 1045666 1071587 1117395 1178086 1205193 1246627 1054193 1193124 1242808Non-Reimbursable 118890 122456 126131 129915 133812 137826 141961 146220 150607 155124 159778TOTAL OPERATING EXPENSES 14493288 14937 15397908 15834146 16301523 16859864 17339088 17880836 17893090 18809360 19416865NET OPERATING INCOME 24377168 25468152 26428743 27029327 28394295 30263592 30868640 31984249 24274647 28915590 30295452LEASING & CAPITAL COSTS Tenant Improvements 272920 390507 138182 870713 1239057 621936 864411 233947 10949093 1439521Leasing Commissions 83615 121036 44684 456082 396166 289709 371606 74189 6473182 461531Structural Reserves 95281 98139 101084 104116 134759 220920 227548 234374 241405 248648RR Donnelley TI 0 0 0 100000 0 0 0 0 0 0TOTAL CAPITAL COSTS 451816 609682 283950 1530911 1769982 1132565 1463565 542510 17663680 2149700OPERATING NET CASH FLOW 23925352 24858470 26144793 25498416 26624313 29131027 29405075 31441739 6610967 26765890Reversion @8.75%, 1%Cost 342771400TOTAL NET CASH FLOW 23925352 24858470 26144793 25498416 26624313 29131027 29405075 31441739 6610967 369537290

This was the actual proforma used in the investment decision.

How realistic was it (at the time)? . . .www.bsscommunitycollege.in www.bssnewgeneration.in www.bsslifeskillscollege.in


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Evidence of rental growth rates: Leases signed in this building . . .



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Rentt = (Rent0)etg

Ln(Rentt) = Ln(Rent0) + tg(Rent12/Rent0) – 1 = e12g – 1 = (2.7183)12*(-0.00093) -1 = -1.1% per year = Ann. rent trend, 92-98.Infla (92-98) = 2.4%/yr.

Real rent trend = -1.1% - 2.4% = -3.5%/yr.www.bsscommunitycollege.in www.bssnewgeneration.in www.bsslifeskillscollege.in


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NCREIF Office Properties NOI Level

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

781 801 821 841 861 881 901 921 941 961 981

YYQ

NO

I Lev

el In

dex

NOI Gro Rate = 0.9%/yrInfla = 4.6%/yrReal NOI Gro Rate = 0.9-4.6 = -3.6%/yr



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Index of Office Property Values (NCREIF)

0.0

0.5

1.0

1.5

2.0

2.5

78 80 82 84 86 88 90 92 94 96 98

Year

Office Values Inflation (CPI)

Avg Off Val Gro = 2.6%/yrAvg Infla = 4.6%/yr==> Avg Real Gro = -2.0%/yr



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Section 11.2:Section 11.2:

“Opportunity Cost of Capital” (OCC) at the Property Levelor: WHERE DO DISCOUNT RATES COME

FROM?...



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Broad Answer: Broad Answer: THE CAPITAL MARKETSTHE CAPITAL MARKETS

That is, competing investment opportunities.(This is so, whether we are talking about IV

or MV.)



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IN DCF APPLICATIONS, KEEP IN MIND IN DCF APPLICATIONS, KEEP IN MIND WHAT THE DISCOUNT RATE IS...WHAT THE DISCOUNT RATE IS...

Disc. Rate = Required Return= Oppty. Cost of Capital = Expected total return= r = rf + RP = y + g,

among investors in the market todayfor assets similar in risk to the property in

question.www.bsscommunitycollege.in www.bssnewgeneration.in www.bsslifeskillscollege.in


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Take the r = r = rrff + RP+ RP approach . . .

• For typical 10 yr horizon investment:

• rrff = Expected average short-term T-Bill yield over life of R.E. investment, well approximated by 10 yr T-Bond yld – 100 bps (“yield curve effect”). (Bond mkt’sexpectation of avg future short-term T-Bill yields over the next 10 years.)

• e.g., if T-Bond yld = 5%, then rrff = T-Bond yld – 150 bps = 5% - 1.5% = 3.5%.

•• RPRP = 250 to 400 bps for “institutional” investment property (based on NCREIF historical avg, ≈ ½ Stk MktRP), OCC = 3.5% + (2.5%OCC = 3.5% + (2.5%--4%) = 6%4%) = 6%--7.5% (or so)7.5% (or so);

• RPRP = 500 to 700 bps for “non-institutional”investment property (smaller, higher risk, less liquid),

OCC = 8% OCC = 8% -- 11%11%. www.bsscommunitycollege.in www.bssnewgeneration.in www.bsslifeskillscollege.in


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Take the r = y + gr = y + g approach . . .

• yy = “cap rate” (less CapEx) = e.g., in 2005 in the U.S. this was about 5% - 6% for “institutional” investment property, more like 7% - 9% for “non-institutional”investment property.

• Realistic growth rate gg = Historical rental mkt growth rate – Historical inflation + Realistic projected future inflation (Bond mkt T-Bond yld – Infla-adjusted T-Bond yld “TIP”) – Property real depreciation rate (≈1%- 2%/yr)

• Typically gg = 0% to 2% in most markets.

• rr = y + gy + g = e.g., in 2005 in U.S. ≈ 6% to 7% “institutional”, 8% to 10% “non-institutional”.

(Remember: This is meant to be applied to property-level CFs.)www.bsscommunitycollege.in www.bssnewgeneration.in www.bsslifeskillscollege.in


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Exhibit 11-4: Historical return, risk, and risk premia, 1970-2003 Asset Class Total Return Volatility Risk PremiumT Bills 6.30% 2.83% NAG Bonds 9.74% 11.76% 3.44%Real Estate 9.91% 9.02% 3.61%Stocks (S&P500) 12.72% 17.48% 6.42%Source: NCREIF, Ibbotson data as modified by authors in Exhibit 7-9 (see Sect.7.2.2 in Ch.7).

11.2.3 Historical Evidence about R.E. OCC in the U.S.11.2.3 Historical Evidence about R.E. OCC in the U.S.



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Survey avg ≈ 200 bps > Hist.avg.

1992

1994

1996

1998

2000

2002

2004

0%

2%

4%

6%

8%

10%

12%

14%

Exhibit 11-4: Backward-looking vs Forward-looking Total Returns in the Property Market: NCREIF vs Korpacz.

Inflation 3.01% 2.99% 2.61% 2.78% 2.96% 2.07% 1.48% 2.54% 3.41% 2.11% 2.02% 2.03% 3.16%

LT Bond 6.95% 5.98% 6.92% 6.86% 6.33% 6.48% 5.34% 5.45% 6.10% 4.96% 4.71% 3.86% 4.21%

NCREIF(Hist)* 9.67% 9.15% 8.99% 8.91% 8.98% 9.23% 9.56% 9.64% 9.76% 9.66% 9.54% 9.53% 9.71%

Korpacz IRR 12.15% 12.25% 12.18% 11.96% 11.82% 11.59% 11.35% 11.28% 11.29% 11.54% 11.56% 11.00% 10.28%

1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004

Exhibit 11-5:11.2.4 Survey Evidence about R.E. OCC in the U.S.11.2.4 Survey Evidence about R.E. OCC in the U.S.

What to make of the difference between the red and the green bars?...

Perhaps a little tinting in the shades?...



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1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

0%

2%

4%

6%

8%

10%

12%

14%

Exhibit 11-5: Stated going-in IRRs, Cap Rates, and Inflation

IRR - OAR 3.06% 2.97% 2.89% 2.65% 2.43% 2.24% 2.27% 2.15% 2.15% 2.12% 2.01% 1.77% 1.66%

Inflation 3.01% 2.99% 2.61% 2.78% 2.96% 2.07% 1.48% 2.54% 3.41% 2.11% 2.02% 2.03% 3.16%

Korpacz OAR 9.09% 9.28% 9.29% 9.31% 9.39% 9.35% 9.08% 9.13% 9.14% 9.42% 9.55% 9.23% 8.62%

Korpacz IRR 12.15 12.25 12.18 11.96 11.82 11.59 11.35 11.28 11.29 11.54 11.56 11.00 10.28

1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004

Exhibit 11-6:



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How to How to "back out""back out" implied discount rates from "cap rates" implied discount rates from "cap rates" (OAR) observed from (OAR) observed from transaction pricestransaction prices in the in the property property

marketmarket......

Cap rate = NOI / V ≈ CF / V = y.

Therefore, from market transaction data...1) Observe prices (V)2) Observe NOI of sold properties.3) Therefore, observe "cap rates" = NOI / V.4) Compute: r = y + g ≈ cap rate + g.

11.2.511.2.5



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So we can get an idea what the market's expected total So we can get an idea what the market's expected total

return (discount rate) is for different types of properties by:return (discount rate) is for different types of properties by:

1. observing the cap rates at which they are sold,

2. and then making reasonable assumptions about growth expectations (g).



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But, watch out for But, watch out for capital expenditurescapital expenditures::

y = CF / Vcap rate = NOI / VCF = NOI - CI,

(unless NOI is already net of a "reserve" for CI)CI / V ≈ 1% - 2% on avg in long run (usually).

Therefore:r = y + g

= (cap rate) + g - (CI/V), unless cap rate already net of CI.



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Watch out for terminology: Watch out for terminology:

In Brealey-Myers “capitalization rate” is often used to refer to “r”, the total cost of capital (especially in corporate finance). “r” is also sometimes called the “total yield” (especially in the appraisal profession).



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Typical per annum OCC (Typical per annum OCC (““goinggoing--in IRRin IRR””) rates ) rates (late 1990s) . . .(late 1990s) . . .

For high quality ("class A", "institutional quality") income property:• 10% - 12%, stated.• 8% - 10%, realistic.

Lower quality or more risky income property (e.g., hotels, class B commercial, turnarounds, "mom & pops"):• 12% - 15%

Raw land (speculation):• 15% - 30%



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Typical per annum OCC (Typical per annum OCC (““goinggoing--in IRRin IRR””) rates ) rates ((cercacerca 2005) . . .2005) . . .

For high quality ("class A", "institutional quality") income property:• 7% - 9%, stated.• 5% - 7%, realistic.

Lower quality or more risky income property (e.g., hotels, class B commercial, turnarounds, "mom & pops"):• 8% - 10%

Raw land (speculation):• 12% - 25%



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Mal

ls

Strip

Ctrs

Indu

st.

Apts

CBD

Offi

ce

Subu

rb.O

ff.

Hou

.Off

Man

h O

ff

0%

2%

4%

6%

8%

10%

12%

14%


Exh.11-6a: Investor Total Return Expectations (IRR) for Various Property Types*

Institutional 9.27% 9.35% 9.28% 9.31% 9.56% 10.03% 10.58% 9.11%


Malls Strip Ctrs


Suburb.Off.

Hou.Off Manh Off

Exhibit 11-7a:

11.2.6 Variation in Return Expectations Across Property Types11.2.6 Variation in Return Expectations Across Property Types



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Mal

ls

Strip

Ctrs

Indu

st.

Apts

CBD

Offi

ce

Subu

rb.O

ff.

Hou

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0%

2%

4%

6%

8%

10%

12%


Exh.11-6b: Investor Cap Rate Expectations for Various Property Types*

Institutional 7.33% 7.86% 7.88% 6.74% 8.26% 8.63% 9.19% 7.45%


Malls Strip Ctrs


Suburb.Off.

Hou.Off Manh Off

Exhibit 11-7b:



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Note that the difference in OCC tends to be much greater between “institutional” vs “non-institutional” quality real estate, than between most usage types of property (office, retail, industrial, residential) within either of those two categories.

Why do you suppose this is? . . .



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CHAPTER 13: CHAPTER 13: LEVERAGE.LEVERAGE.

(The use of debt)



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The analogy of physical leverage & financial leverage...The analogy of physical leverage & financial leverage...

““Give me a place to stand,Give me a place to stand, and I will move the earth.and I will move the earth.””-- Archimedes (287Archimedes (287--212 BC)212 BC)

500 lbs

200 lbs

A Physical Lever...

"Leverage Ratio" = 500/200 = 2.5

LIFTS

5 feet

2 feet



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Financial Leverage...Financial Leverage...

$4,000,000EQUITY

INVESTMENTBUYS

$10,000,000PROPERTY

"Leverage Ratio" = $10,000,000 / $4,000,000 = 2.5Equity = $4,000,000Debt = $6,000,000



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Terminology...Terminology...

“Leverage”“Debt Value”, “Loan Value” (L) (or “D”).“Equity Value” (E)“Underlying Asset Value” (V = E+L):"Leverage Ratio“ = LR = V / E = V / (V-L) = 1/(1-L/V)(Not the same as the “Loan/Value Ratio”: L / V,or “LTV” .)

“Risk”The RISK that matters to investors is the risk in their totalreturn, related to the standard deviation (or range or spread) in that return.



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Leverage Ratio & Loan-to-Value Ratio

0

5

10

15

20

25

0% 10% 20% 30% 40% 50% 60% 70% 80% 90%

LTV

LR

LTVLR −= 11



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Leverage Ratio & Loan-to-Value Ratio

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00 20.00

LR

LTV

LRLTV 11−=



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Effect of Leverage on Risk & Return Effect of Leverage on Risk & Return (Numerical Example)(Numerical Example)……

Example Property & Scenario Characteristics:

Current (t=0) values (known for certain):E0[CF1] = $800,000V0 = $10,000,000

Possible Future Outcomes are risky (next year, t=1):"Pessimistic" scenario (1/2 chance):CF1 = $700,000; V1 = $9,200,000.

"Optimistic" scenario (1/2 chance):CF1 = $900,000; V1 = $11,200,000. $10.0M

$11.2M+ 0.9M

$9.2M+0.7M

50%

50%

Property:

Loan:

$6.0M $6.0M+0.48M

100100%%



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Case I: All-Equity (No Debt: Leverage Ratio=1, L/V=0)...Item Pessimistic OptimisticInc. Ret. (y): Ex Ante:RISK:App. Ret. (g):Ex Ante: RISK:

Case II: Borrow $6 M @ 8%, with DS=$480,000/yr (Leverage Ratio=2.5, L/V=60%)...Item Pessimistic OptimisticInc. Ret.:Ex Ante: RISK:App. Ret.:Ex Ante: RISK:

700/10000= 7% 900/10000= 9%(1/2)7% + (1/2)9% = 8%

±1%(9.2-10)/10 = -8% (11.2-10)/10=+12%

(1/2)(-8) + (1/2)(12) = +2%±10%

(0.7-0.48)/4.0= 5.5% (0.9-0.48)/4.0= 10.5%(1/2)5.5 + (1/2)10.5 = 8%

±2.5%(3.2-4.0)/4.0 = -20% (5.2-4.0)/4.0 = +30%

(1/2)(-20) + (1/2)(30) = +5%±25%



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Exhibit 13-2: Typical Effect of Leverage on Expected Investment Returns Property Levered Equity Debt Initial Value $10,000,000 $4,000,000 $6,000,000Cash Flow $800,000 $320,000 $480,000Ending Value $10,200,000 $4,200,000 $6,000,000 Income Return 8% 8% 8% Apprec.Return 2% 5% 0% Total Return 10% 13% 8%

Exhibit 13-3: Sensitivity Analysis of Effect of Leverage on Risk in Equity Return Components, as Measured by Percentage Range in Possible Return Outcomes. ($ Values in millions) Property (LR=1) Levered Equity (LR=2.5) Debt (LR=0) OPT PES RANGE OPT PES RANGE OPT PES RANGE Initial Value $10.00 $10.00 NA $4.0 $4.0 NA $6.0 $6.0 NA Cash Flow $0.9 $0.7 ±$0.1 $0.42 $0.22 ±$0.1 $0.48 $0.48 0 Ending Value $11.2 $9.2 ±$1.0 $5.2 $3.2 ±$1.0 $6.0 $6.0 0 Income Return 9% 7% ±1% 10.5% 5.5% ±2.5% 8% 8% 0 Apprec.Return 12% -8% ±10% 30% -20% ±25% 0% 0% 0 Total Return 21% -1% ±11% 40.5% -14.5% ±27.5% 8% 8% 0 OPT = Outcome if "Optimistic" Scenario occurs. PES = Outcome if "Pessimistic" Scenario occurs. RANGE = Half the difference between "Optimistic" Scenario outcome and "Pessimistic" Scenario outcome. Note: Initial values are known deterministically, as they are in present, not future, time, so there is no range.

Return risk (y,g,r) directly proportional to Levg Ratio (not L/V).E[g] directly proportional to Leverage Ratio.E[r] increases with Leverage, but not proportionately.E[y] does not increase with leverage (here).E[RP] = E[r]-rf is directly proportional to Leverage Ratio (here)…



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Exhibit 13Exhibit 13--4: Effect of Leverage on Investment Risk and Return: 4: Effect of Leverage on Investment Risk and Return: The Case of The Case of RisklessRiskless Debt...Debt...

Expected Total Return

1 2.5 Leverage Ratio (LR) Risk

13%

10%

8% RP

RP

rf

2%

5%

8%

Levered Equity: 60% LTV

Unlevered Equity: Underlying Property

Riskless Mortgage

0



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Exhibit 13Exhibit 13--5: Effect of Leverage on Investment Risk and Return: 5: Effect of Leverage on Investment Risk and Return: The Case of Risky Debt...The Case of Risky Debt...

10%

Expected Total Return

0 2.5 Leverage Ratio (LR)

Risk

13%

8%

rf=6% RP

RP

rf

2%

7%

6%

Levered Equity: 60% LTV

Unlevered Equity: Property

Risky Mortgage

0

1

RP 4%



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The "Weighted Average Cost of Capital" (WACC) Formula . . .rP = (L/V)rD + [1-(L/V)]rE

A A reallyreally useful formula. . .useful formula. . .

Derivation of the WACC Formula:Derivation of the WACC Formula: V = E+D

DD

VD

EE

VDV

DD

VD

EE

VE

DD

VD

EE

VE

VD

VE

VV Δ

+Δ

⎟⎠⎞

⎜⎝⎛ −

=Δ

+Δ

=Δ

+Δ

=Δ

+Δ

=Δ

⇒

DD

VD

EE

VD

VV Δ

+Δ

⎟⎠⎞

⎜⎝⎛ −=

Δ⇒ 1

DEP rLTVrLTVrWACC

)()1(:

+−=⇒

Where: rE = Levered Equity Return,

rP = Property Return,

rD = Debt Return,

LTV=Loan-to-Value Ratio (D/V).

)1()(

LTVrLTVr

EDPr −

−=Invert for equity formula:

Section 13.3



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Or, equivalently, if you prefer . . .Or, equivalently, if you prefer . . .

E = V-D

DD

ED

VV

EV

DD

ED

VV

EV

ED

EV

EE Δ

−Δ

=Δ

−Δ

=Δ

−Δ

=Δ

⇒

⎟⎠⎞

⎜⎝⎛ Δ

−Δ

+Δ

=Δ

⎟⎠⎞

⎜⎝⎛ −−

Δ=

Δ−−

Δ=

Δ⇒

DD

VV

EV

DD

DD

EV

VV

EV

DD

EEV

VV

EV

EE 1)(

( )LRrrrrLRrLRrWACC

DPDDPE −+=−+=⇒

)1()(:



rD = Debt Return,

LR=Leverage Ratio (V/E).



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The "Weighted Average Cost of Capital" (WACC) Formula . . .rP = (L/V)rD + [1-(L/V)]rE

(L/V) = Loan/value ratio rD = Lender's return (return to the debt) rE = Equity investor's return. Apply to r, y, or g. . .E.g., in previous numerical example:

E[r] = (.60)(.08) + (.40)(.13) = 10%E[y] = (.60)(.08) + (.40)(.08) = 8%E[g] = (.60)(0) + (.40)(.05) = 2%

(Can also apply to RP.)In real estate, Difficult to directly and reliably observe levered return,But can observe return on loans,and can observe return on property (underlying asset). So, "invert" WACC Formula:Solve for unobservable parameter as a function of the observable parameters:

rE = {rP - (L/V)rD} / [1 - (L/V)](Or in y or in g.)(In y it’s “cash-on-cash” or “equity cash yield”)

Using the WACC formula in real estate:Using the WACC formula in real estate:



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Note:Note:

WACC based on accounting identities: Assets = Liabilities + Owners Equity, Property Cash Flow = Debt Cash Flow + Equity Cash Flow

WACC is approximation, Less accurate over longer time interval return horizons.



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Using WACC to avoid a common mistake. . .Using WACC to avoid a common mistake. . .

Suppose REIT A can borrow @ 6%, and REIT B @ no less than 8%. Then doesn’t REIT A have a lower cost of capital than REIT B?

Answer: Not necessarily. Suppose (for example):REIT A: D/E = 3/7. D/V = L/V = 30%.REIT B: D/E = 1. D/V = L/V = 50%.& suppose both A & B have cost of equity = E[rE] = 15%.Then:WACC(A) =(0.3)6% + (0.7)15% = 1.8% + 10.5% = 12.3%WACC(B) =(0.5)8% + (0.5)15% = 4% + 7.5% = 11.5%So in this example REIT A has a higher cost of capital than B, even though A can borrow at a lower rate. (Note, this same argument applies whether or not either or both investors are REITs.) You have to consider the cost of your equity as well as the cost of your debt to determine your cost of capital.



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““POSITIVEPOSITIVE”” & & ““NEGATIVENEGATIVE”” LEVERAGELEVERAGE

“Positive leverage” = When more debt will increase the equity investor’s (borrower’s) return.

“Negative leverage” = When more debt will decrease the equity investor’s (borrower’s) return.

13.413.4



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Whenever the Return Component is higher in the underlying property than it is in the mortgage loan, there will be "Positive Leverage" in that Return Component...

See this via The “leverage ratio” version of the WACC. . .

rE = rD + LR*(rP-rD)

““POSITIVEPOSITIVE”” & & ““NEGATIVENEGATIVE”” LEVERAGELEVERAGE



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Derivation of the Leverage Ratio Version of the WACC:Derivation of the Leverage Ratio Version of the WACC:

E = V-D

DD

ED

VV

EV

DD

ED

VV

EV

ED

EV

EE Δ

−Δ

=Δ

−Δ

=Δ

−Δ

=Δ

⇒

⎟⎠⎞

⎜⎝⎛ Δ

−Δ

+Δ

=Δ

⎟⎠⎞

⎜⎝⎛ −−

Δ=

Δ−−

Δ=

Δ⇒

DD

VV

EV

DD

DD

EV

VV

EV

DD

EEV

VV

EV

EE 1)(

( )LRrrrrLRrLRrWACC

DPDDPE −+=−+=⇒

)1()(:



rD = Debt Return,

LR=Leverage Ratio (V/E).



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Exhibit 13-6: Typical relative effect of leverage on income and growth components of investment return (numerical example)... Property total return (rP): 10.00% Cap rate (yP): 8.00% Positive cash-on-cash leverage... Loan Interest rate (rD): 6.00% Mortgage Constant (yD): 7.00%

Equity return component: LR LTV yE gE rE 1 0% 8.00% 2.00% 10.00% 2 50% 9.00% 5.00% 14.00% 3 67% 10.00% 8.00% 18.00% 4 75% 11.00% 11.00% 22.00% 5 80% 12.00% 14.00% 26.00% Negative cash-on-cash leverage... Loan Interest Rate (rD): 8.00% Mortgage Constant (yD): 9.00%

Equity return component: LR LTV yE gE rE 1 0% 8.00% 2.00% 10.00% 2 50% 7.00% 5.00% 12.00% 3 67% 6.00% 8.00% 14.00% 4 75% 5.00% 11.00% 16.00% 5 80% 4.00% 14.00% 18.00%

e.g.:e.g.:

Total: 10% =Total: 10% =(67%)*6%+(33%)*18%(67%)*6%+(33%)*18%

Yield: 8% = Yield: 8% = (67%)*7% + (33%)*10%(67%)*7% + (33%)*10%

Growth: 2% =Growth: 2% =(67%)*((67%)*(--1%)+(33%)*8%1%)+(33%)*8%

Leverage skews total Leverage skews total return relatively toward return relatively toward growth component, growth component, away from current away from current income yield.income yield.

Section 13.5



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SUMMARY OF LEVERAGE EFFECTS...SUMMARY OF LEVERAGE EFFECTS...(1) Under the typical assumption that the loan is less risky

than the underlying property, leverage will increase the ex ante total return on the equity investment, by increasing the risk premium in that return.

(2) Under the same relative risk assumption, leverage will increase the risk of the equity investment, normally proportionately with the increase in the risk premium noted in (1).

(3) Under the typical situation of non-negative price appreciation in the property and non-negative amortization in the loan, leverage will usually shift the expected return for the equity investor relatively away from the current income component and towards the growth or capital appreciation component.



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Real world example:Recall…The R.R. Donnelly

Bldg, Chicago

$280 million,945000 SF, 50-story Office Tower



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Location:In “The Loop” (CBD) at W.Wacker Dr & N.Clark St,

On the Chicago River...



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Donnelley Bldg Pro Forma...Donnelley Bldg Pro Forma...RR Donnelley Bldg Annual Cash Flow Projection

Year: 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010POTENTIAL GROSS REVENUE Base Rental Revenue 24033811 24991054 25635350 26383811 27922939 28654131 29373663 30057496 29525448 29850252 30742749Absorptn & Turnover Vac. 0 -122098 -45383 -284864 -538960 -64691 -280794 -98390 -3542566 -468748 -133817Scheduled Base Rent Rev. 24033811 24868956 25589967 26098947 27383979 28589440 29092869 29959106 25982882 29381504 30608932CPI & Other Adjustmt Rev. 1295978 1489696 1688258 1891784 2100397 2314227 2533401 2758056 465942 0 0Expense Reimbursmt Rev. 13830780 14359735 14886942 15215378 15588172 16665170 17028629 17626489 16203409 18857047 19661109Miscellaneous Income 270931 279059 287430 296054 304935 314082 323505 333212 343207 353504 364108TOTAL PGR 39431500 40997446 42452597 43502163 45377483 47882919 48978404 50676863 42995440 48592055 50634149Collection Loss -561044 -592080 -625946 -638690 -681665 -759463 -770676 -811778 -827703 -867105 -921832EFFECTIVE GROSS REVENUE 38870456 40405366 41826651 42863473 44695818 47123456 48207728 49865085 42167737 47724950 49712317OPERATING EXPENSES Repairs & Maintenance 1723900 1775613 1829188 1883220 1938829 1998749 2057947 2120365 2171717 2248204 2316872Contract Cleaning 1033459 1064415 1100189 1122605 1145141 1201526 1227982 1273344 1157614 1334681 1390062Security 738946 761114 783949 807466 831690 856640 882340 908811 936075 964158 993081Utilities 1076597 1108856 1145319 1170863 1196712 1250955 1280500 1326010 1237641 1393269 1447839General & Administrative 741398 763639 786549 810146 834450 859483 885267 911825 939179 967355 996376Insurance 144503 148838 153303 157902 162639 167518 172544 177720 183052 188543 194200Real Estate Taxes 7943834 8182149 8427614 8680442 8940855 9209081 9485 9769914 10063012 10364902 10675849Management Fee 971761 1010134 1045666 1071587 1117395 1178086 1205193 1246627 1054193 1193124 1242808Non-Reimbursable 118890 122456 126131 129915 133812 137826 141961 146220 150607 155124 159778TOTAL OPERATING EXPENSES 14493288 14937 15397908 15834146 16301523 16859864 17339088 17880836 17893090 18809360 19416865NET OPERATING INCOME 24377168 25468152 26428743 27029327 28394295 30263592 30868640 31984249 24274647 28915590 30295452LEASING & CAPITAL COSTS Tenant Improvements 272920 390507 138182 870713 1239057 621936 864411 233947 10949093 1439521Leasing Commissions 83615 121036 44684 456082 396166 289709 371606 74189 6473182 461531Structural Reserves 95281 98139 101084 104116 134759 220920 227548 234374 241405 248648RR Donnelley TI 0 0 0 100000 0 0 0 0 0 0TOTAL CAPITAL COSTS 451816 609682 283950 1530911 1769982 1132565 1463565 542510 17663680 2149700OPERATING NET CASH FLOW 23925352 24858470 26144793 25498416 26624313 29131027 29405075 31441739 6610967 26765890Reversion @8.75%, 1%Cost 342771400TOTAL NET CASH FLOW 23925352 24858470 26144793 25498416 26624313 29131027 29405075 31441739 6610967 369537290



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25www.bsscommunitycollege.in www.bssnewgeneration.in www.bsslifeskillscollege.in


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Rentt = (Rent0)etg

Ln(Rentt) = Ln(Rent0) + tg(Rent12/Rent0) – 1 = e12g – 1 = (2.7183)12*(-0.00093) -1 = -1.1% per year = Ann. rent trend, 92-98.Infla (92-98) = 2.4%/yr.

Real rent trend = -1.1% - 2.4% = -3.5%/yr.www.bsscommunitycollege.in www.bssnewgeneration.in www.bsslifeskillscollege.in


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NCREIF Office Properties NOI Level

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

781 801 821 841 861 881 901 921 941 961 981

YYQ

NO

I Lev

el In

dex

NOI Gro Rate = 0.9%/yrInfla = 4.6%/yrReal NOI Gro Rate = 0.9-4.6 = -3.6%/yr



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Index of Office Property Values (NCREIF)

0.0

0.5

1.0

1.5

2.0

2.5

78 80 82 84 86 88 90 92 94 96 98

Year

Office Values Inflation (CPI)

Avg Off Val Gro = 2.6%/yrAvg Infla = 4.6%/yr==> Avg Real Gro = -2.0%/yr



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Exhibit 1: Presentation cash flow pro-forma for sale purposes Assumptions (Staff's): Implied Returns: Price 280000 Going-inCap 8.71% Terminal Cap Rate 8.75% IRRs: CFGroRate Adjustment 0.00% Property (Unlevered) 10.40% Cap.Imp.Adjustmt Factor 1 Levered (Undifferentiated) 14.36% OTR (overall levered) 12.76%

Prime (levered) 19.24% Cash flow computations, Yr: IRRs: 0 1 2 3 4 5 6 7 8 9 10 11 End Jun 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 Staff NOI 24377 25468 26429 27029 28394 30264 30869 31984 24275 28916 30295 Staff CI 452 610 284 1531 1770 1133 1464 543 17664 2150 752 Adjstd NOI 24377 25468 26429 27029 28394 30264 30869 31984 24275 28916 30295 Adjstd CI 452 610 284 1531 1770 1133 1464 543 17664 2150 752 Unlevered Property Level: CF 23925 24858 26145 25498 26624 29131 29405 31441 6611 26766 29543 Reversion 342766 PBTCFs 10.40% -280000 23925 24858 26145 25498 26624 29131 29405 31441 6611 369532 DS 14588 14588 14588 14588 14588 14588 14588 14588 14588 14588 OLB 132864 DebtCFs 7.00% -170000 14588 14588 14588 14588 14588 14588 14588 14588 14588 147452 AfterDS: Levrd(Undiff)… Operating 9337 10270 11557 10910 12036 14543 14817 16853 -7977 12178 ECFs 14.36% -110000 9337 10270 11557 10910 12036 14543 14817 16853 -7977 222080 OTR Positions… Preferred 9.50% -66000 6270 6270 6270 6270 6270 6270 6270 6270 6270 72270 OTRprorata 19.24% -22000 1534 2000 2644 2320 2883 4137 4274 5292 -7124 74905 OTRTotal 12.76% -88000 7804 8270 8914 8590 9153 10407 10544 11562 -854 147175 Prime Position: PrimeTotal 19.24% -22000 1534 2000 2644 2320 2883 4137 4274 5292 -7124 74905



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Exhibit 2: More realstic cash flow projections Assumptions (Geltner's): Implied Returns: Price 280000 Going-inCap 8.71% Terminal Cap Rate 8.75% IRRs: CFGroRate Adjustment -1.60% Property (Unlevered) 8.29% Cap.Imp.Adjustmt Factor 1.5 Levered (Undifferentiated) 10.02% OTR (overall levered) 9.83%

Prime (levered) 10.68% Cash flow computations, Yr: IRRs: 0 1 2 3 4 5 6 7 8 9 10 11 End Jun 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 Staff NOI 24377 25468 26429 27029 28394 30264 30869 31984 24275 28916 30295 Staff CI 452 610 284 1531 1770 1133 1464 543 17664 2150 752 Adjstd NOI 24377 25061 25590 25752 26620 27919 28022 28569 21336 25009 25782 Adjstd CI 678 915 426 2297 2655 1700 2196 815 26496 3225 1128 Unlevered Property Level: CF 23699 24146 25164 23456 23965 26220 25826 27755 -5160 21784 24654 Reversion 291708 PBTCFs 8.29% -280000 23699 24146 25164 23456 23965 26220 25826 27755 -5160 313492 DS 14588 14588 14588 14588 14588 14588 14588 14588 14588 14588 OLB 132864 DebtCFs 7.00% -170000 14588 14588 14588 14588 14588 14588 14588 14588 14588 147452 AfterDS: Levrd(Undiff)… Operating 9111 9558 10576 8868 9377 11632 11238 13167 -19748 7196 ECFs 10.02% -110000 9111 9558 10576 8868 9377 11632 11238 13167 -19748 166040 OTR Positions… Preferred 9.50% -66000 6270 6270 6270 6270 6270 6270 6270 6270 6270 72270 OTRprorata 10.68% -22000 1421 1644 2153 1299 1553 2681 2484 3448 -13009 46885 OTRTotal 9.83% -88000 7691 7914 8423 7569 7823 8951 8754 9718 -6739 119155 Prime Position: PrimeTotal 10.68% -22000 1421 1644 2153 1299 1553 2681 2484 3448 -13009 46885



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Exhibit 2: Cash flow adjustments (Optmistic) Assumptions (Geltner's): Implied Returns: Price 280000 Going-inCap 8.71% Terminal Cap Rate 7.50% IRRs: CFGroRate Adjustment 0.0150 Property (Unlevered) 13.14% Cap.Imp.Adjustmt Factor 1 Levered (Undifferentiated) 19.12% OTR (overall levered) 16.30%

Prime (levered) 26.73% Cash flow computations, Yr: IRRs: 0 1 2 3 4 5 6 7 8 9 10 11 End Jun 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 Staff NOI 24377 25468 26429 27029 28394 30264 30869 31984 24275 28916 30295 Staff CI 452 610 284 1531 1770 1133 1464 543 17664 2150 752 Adjstd NOI 24377 25850 27228 28264 30136 32603 33754 35497 27346 33062 35159 Adjstd CI 452 610 284 1531 1770 1133 1464 543 17664 2150 752 Unlevered Property Level: CF 23925 25240 26944 26733 28366 31470 32290 34954 9682 30912 34407 Reversion 464093 PBTCFs 13.14% -280000 23925 25240 26944 26733 28366 31470 32290 34954 9682 495006 DS 14588 14588 14588 14588 14588 14588 14588 14588 14588 14588 OLB 132864 DebtCFs 7.00% -170000 14588 14588 14588 14588 14588 14588 14588 14588 14588 147452 AfterDS: Levrd(Undiff)… Operating 9337 10652 12356 12145 13778 16882 17702 20366 -4906 16324 ECFs 19.12% -110000 9337 10652 12356 12145 13778 16882 17702 20366 -4906 347554 OTR Positions… Preferred 9.50% -66000 6270 6270 6270 6270 6270 6270 6270 6270 6270 72270 OTRprorata 26.73% -22000 1534 2191 3043 2937 3754 5306 5716 7048 -5588 137642 OTRTotal 16.30% -88000 7804 8461 9313 9207 10024 11576 11986 13318 682 209912 Prime Position: PrimeTotal 26.73% -22000 1534 2191 3043 2937 3754 5306 5716 7048 -5588 137642



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Exhibit 2: Cash flow adjustments(Pesimistic) Assumptions (Geltner's): Implied Returns: Price 280000 Going-inCap 8.71% Terminal Cap Rate 10.00% IRRs: CFGroRate Adjustment -0.0450 Property (Unlevered) 3.60% Cap.Imp.Adjustmt Factor 2 Levered (Undifferentiated) -4.38% OTR (overall levered) 2.56%

Prime (levered) #NUM! Cash flow computations, Yr: IRRs: 0 1 2 3 4 5 6 7 8 9 10 11 End Jun 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 Staff NOI 24377 25468 26429 27029 28394 30264 30869 31984 24275 28916 30295 Staff CI 452 610 284 1531 1770 1133 1464 543 17664 2150 752 Adjstd NOI 24377 24322 24104 23542 23618 24040 23418 23172 16795 19106 19116 Adjstd CI 904 1220 568 3062 3540 2266 2928 1086 35328 4300 1504 Unlevered Property Level: CF 23473 23102 23536 20480 20078 21774 20490 22086 -18533 14806 17612 Reversion 189252 PBTCFs 3.60% -280000 23473 23102 23536 20480 20078 21774 20490 22086 -18533 204058 DS 14588 14588 14588 14588 14588 14588 14588 14588 14588 14588 OLB 132864 DebtCFs 7.00% -170000 14588 14588 14588 14588 14588 14588 14588 14588 14588 147452 AfterDS: Levrd(Undiff)… Operating 8885 8514 8948 5892 5490 7186 5902 7498 -33121 218 ECFs -4.38% -110000 8885 8514 8948 5892 5490 7186 5902 7498 -33121 56606 OTR Positions… Preferred 9.50% -66000 6270 6270 6270 6270 6270 6270 6270 6270 6270 72270 OTRprorata #NUM! -22000 1308 1122 1339 -189 -390 458 -184 614 -19695 -7832 OTRTotal 2.56% -88000 7578 7392 7609 6081 5880 6728 6086 6884 -13425 64438 Prime Position: PrimeTotal #NUM! -22000 1308 1122 1339 -189 -390 458 -184 614 -19695 -7832



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Summary of Sensitivity AnalysisSummary of Sensitivity Analysis

& Risk/Return Analysis& Risk/Return Analysis

Presentn Realistic Optimist Pessimist RANGE RP* RP/RANGEAssumptions:NOI Gro 2.20% 0.56% 3.73% -2.40% 6.13%CI/NOI 10.00% 15.00% 10.00% 20.00% 10.00%Term Cap 8.75% 8.75% 7.50% 10.00% 2.50%Expected Returns (Going-in IRR):Property 10.40% 8.29% 13.14% 3.60% 9.54% 1.54% 0.16Levrd Eq (Undiff) 14.36% 10.02% 19.12% -4.38% 23.50% 3.27% 0.14Teachers 12.76% 9.83% 16.30% -4.38% 20.68% 3.08% 0.15Prime 19.24% 10.68% 26.73% -100.00% 126.73% 3.93% 0.03*Realistic Exptd Going-in IRR Minus 6.75% prevailing T-Bill Yield



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AfterAfter--Tax Investment AnalysisTax Investment Analysis



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Going from the Going from the ““property beforeproperty before--tax tax cash flowscash flows”” (PBTCF), (PBTCF), to the to the ““equity afterequity after--taxtax cash flowscash flows”” (EATCF). . .(EATCF). . .

1) Property level (PBTCF):1) Property level (PBTCF):•• Net CF produced by property, before subtracting debt svc pmts (Net CF produced by property, before subtracting debt svc pmts (DS) DS) and inc. taxes.and inc. taxes.•• CFsCFs to to GovtGovt, Debt investors (mortgagees), equity owners. , Debt investors (mortgagees), equity owners. •• CFsCFs due purely to underlying productive physical asset, not based odue purely to underlying productive physical asset, not based on n financing or income tax effects. financing or income tax effects. •• Relatively easy to observe empirically.Relatively easy to observe empirically.

2) Equity ownership after2) Equity ownership after--tax level (EATCF):tax level (EATCF):•• Net CF avail. to equity owner after DS & taxes.Net CF avail. to equity owner after DS & taxes.•• Determines value of equity only (not value to lenders).Determines value of equity only (not value to lenders).•• Sensitive to financing and income tax effects.Sensitive to financing and income tax effects.•• Usually difficult to observe empirically (differs across investUsually difficult to observe empirically (differs across investors). ors).



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3 MAJOR DIFFERENCES between PBTCF & EATCF levels:3 MAJOR DIFFERENCES between PBTCF & EATCF levels:

Depreciation: An expense that reduces income tax cash outflows, but not itself a cash outflow at the before-tax level. (IRS income tax rules for property income based on accrual accounting, not cash flow accounting.)Capital expenditures: Not an accrual “expense”(because adds to asset value, “asset” life > 1 yr), hence not deducted from taxable income, even though they are a cash outflow.Debt principal amortization: Like capex, a cash outflow, but not deductible from taxable income.



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Exhibit 14-1a: Equity After-Tax Cash Flows from Operations PGI - vacancy = EGI

- OEs =NOI Cash Flow Taxes - Capital Improvements Exp. Net Operating Income (NOI) = PBTCF -Interest (I) - Debt Service (Int. & Principal) -Depreciation expense (DE) - Income Tax = Taxable Income = EATCF x Investor’s income tax rate

= Income Tax Due



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Exhibit 14-1b: Computation of CGT in Reversion Cash Flow Net Sale Proceeds (NSP) - Adjusted Basis = Taxable Gain on Sale x CGT Rate = Taxes Due on Sale where the Adjusted Basis or Net Book Value is calculated as: Original Basis (Total Initial Cost) + Capital Improvement Expenditures - Accumulated Depreciation = Adjusted Basis



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From PBTCF to EATCF. . . Operating: PBTCF IE - DS <---- +PP _______ EBTCF τ(NOI) - tax <---- -τ(DE) <---"Tax Shield" (DTS) _______ -τ(IE) <---"Tax Shield" (ITS) offset

EATCF by tax expense to lender Reversion: PBTCF - OLB ______ EBTCF - CGT = τG[VT – SE – (V0 + AccCI)] + τR(AccDE) ______ EATCF

Another perspective: Another perspective:



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Depreciation Expense:Depreciation Expense:

Straight-line– 39 years, commercial– 27.5 years, residential (apts)

Land not depreciable:– (typic. 20% in Midwest, South)– (often 50% in big E. & W. Coast cities)



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Exhibit 14-2: Example After-Tax Income & Cash Flow Proformas . . .

Property Purchase Price (Year 0): $1,000,000 Unlevered: Levered:Depreciable Cost Basis: $800,000 Before-tax IRR: 6.04% 7.40%Ordinary Income Tax Rate: 35.00% After-tax IRR: 4.34% 6.44%Capital Gains Tax Rate: 15.00% Ratio AT/BT: 0.719 0.870Depreciation Recaptur___________ 25.00% ____________________ ______________________________ ________________________________________________________________

Year: Oper. Reversion Rever. TotalOperating: 1 2 3 4 5 6 7 8 9 Yr.10 Item: Yr.10 Yr.10Accrual Items:

NOI $60,000 $60,600 $61,206 $61,818 $62,436 $63,061 $63,691 $64,328 $64,971 $65,621 Sale Price $1,104,622- Depr.Exp. $29,091 $29,091 $29,091 $29,091 $29,091 $29,091 $29,091 $29,091 $29,091 $29,091 - Book Val $809,091

- Int.Exp. $41,250 $41,140 $41,030 $40,920 $40,810 $40,700 $40,590 $40,480 $40,370 $40,260=Net Income (BT) ($10,341) ($9,631) ($8,915) ($8,193) ($7,465) ($6,730) ($5,990) ($5,243) ($4,490) ($3,730) =Book Gain $295,531 $291,801

- IncTax ($3,619) ($3,371) ($3,120) ($2,867) ($2,613) ($2,356) ($2,096) ($1,835) ($1,571) ($1,305) - CGT $73,421=Net Income (AT) ($6,722) ($6,260) ($5,795) ($5,325) ($4,852) ($4,375) ($3,893) ($3,408) ($2,918) ($2,424) =Gain (AT) $222,111 $219,686

Adjusting Accrual to Reflect Cash Flow:- Cap. Imprv. Expdtr. $0 $0 $50,000 $0 $0 $0 $0 $50,000 $0 $0

+ Depr.Exp. $29,091 $29,091 $29,091 $29,091 $29,091 $29,091 $29,091 $29,091 $29,091 $29,091 + Book Val $809,091-DebtAmort $2,000 $2,000 $2,000 $2,000 $2,000 $2,000 $2,000 $2,000 $2,000 $2,000 -LoanBal $730,000

=EATCF $20,369 $20,831 ($28,704) $21,766 $22,239 $22,716 $23,198 ($26,317) $24,173 $24,667 =EATCF $301,202 $325,868

+ IncTax ($3,619) ($3,371) ($3,120) ($2,867) ($2,613) ($2,356) ($2,096) ($1,835) ($1,571) ($1,305) + CGT $73,421=EBTCF $16,750 $17,460 ($31,824) $18,898 $19,626 $20,361 $21,101 ($28,152) $22,601 $23,361 =EBTCF $374,622 $397,983

___________________________________________________________ ______________________________ ________________________________________________________________CASH FLOW COMPONENTS FORMAT

Year: Oper. Reversion Rever. TotalOperating: 1 2 3 4 5 6 7 8 9 Yr.10 Item Yr.10 Yr.10Accrual Items:

NOI $60,000 $60,600 $61,206 $61,818 $62,436 $63,061 $63,691 $64,328 $64,971 $65,621 Sale Price $1,104,622- Cap. Imprv. Expdtr. $0 $0 $50,000 $0 $0 $0 $0 $50,000 $0 $0

=PBTCF $60,000 $60,600 $11,206 $61,818 $62,436 $63,061 $63,691 $14,328 $64,971 $65,621 =PBTCF $1,104,622 $1,170,243- Debt Svc $43,250 $43,140 $43,030 $42,920 $42,810 $42,700 $42,590 $42,480 $42,370 $42,260 - LoanBal $730,000

=EBTCF $16,750 $17,460 ($31,824) $18,898 $19,626 $20,361 $21,101 ($28,152) $22,601 $23,361 =EBTCF $374,622 $397,983-taxNOI $21,000 $21,210 $21,422 $21,636 $21,853 $22,071 $22,292 $22,515 $22,740 $22,967 taxMktGain $693 $23,661

+ DTS $10,182 $10,182 $10,182 $10,182 $10,182 $10,182 $10,182 $10,182 $10,182 $10,182 - AccDTS ($72,727) ($62,545)+ ITS $14,438 $14,399 $14,361 $14,322 $14,284 $14,245 $14,207 $14,168 $14,130 $14,091 $14,091

=EATCF $20,369 $20,831 ($28,704) $21,766 $22,239 $22,716 $23,198 ($26,317) $24,173 $24,667 EATCF $301,202 $325,868

Exhibit 14-2



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NOI = $60,000, 1st yr.

- Depr.Exp. = $800,000/27.5 = $29,091, ea. yr.

- Int.Exp. = $750,000*5.5% = $41,250, 1st yr.

=Net Income (BT) = 60000 - 29091- 41250 = -$10,341.

- IncTax = (.35)(-10341) = - $3,619, 1st yr.

=Net Income (AT) = -10341 - (-3619) = - $6,722, 1st yr.

Adjusting Accrual to Reflect Cash Flow:- Cap. Imprv. Expdtr. = - $0, 1st yr.

+ Depr.Exp. = + $29,091, ea. yr.

-DebtAmort = - $2,000, ea. yr (this loan).

=EATCF = (-6722-0+29091-2000) = $20,369, 1st yr.

+ IncTax = +(-$3,619) = -$3,619, 1st y r.

=EBTCF = 20369 - 3619 = $16,750, 1st yr.

Year 1 projection, Operating Cash Flow (details):Year 1 projection, Operating Cash Flow (details):



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Sale Price = VT - SE= NOI11/.06 - SE = 1.01*$65,621/0.06 – 0 = $1,104,620

- Book Val = - (V0 + AccCI - AccDE)= - (1000000 + 100000 – 290910) = - $809,091

=Book Gain = 1104620 – 809091 = $295,531 Inclu 1104620 – (1000000+100000) = 4620 Gain, + 290910 Recapture

- CGT = (.15)(4620) + (.25)(290910) = -$73,421

=Gain (AT) = 295531 – 73421 = $222,111

Adjusting Accrual to Reflect Cash Flow:

+ Book Val = + $809,091

-LoanBal = - (750000 – 10*2000) = -$730,000

=EATCF = 222111 + 809091 – 730000 = $301,202

+ CGT = + $73,421

=EBTCF = 301202 + 73421 = $374,622

Reversion Cash Flow, Year 10 (details):Reversion Cash Flow, Year 10 (details):



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Cash Flow Components Format… Operating: PBTCF = NOI – CI = $90,000 - $0 = $90,000, 1st yr. IE = $750,000 * 10% = $75,000, 1st yr. - DS <---- +PP = + $2,000 = $77,000, 1st yr. _______ _______ EBTCF = $90,000 - $77,000 = $13,000 τ(NOI) = - (.4)$90,000 = $36,000, 1st yr. - tax <---- -τ(DE) <---(“DTS”) = + (.4)$29,091 = $11,636, ea.yr. -τ(IE) <---(“ITS”) = + (.4)$75,000 = $30,000, 1st yr. _______ _______ EATCF = $13,000 - $36,000 + $11,636 + $30,000 = $18,636, 1st yr. Reversion (Yr.10): PBTCF = 1.025*$112,398/0.09 = $1,280,085. - OLB = $750,000 – (10*$2,000) = $730,000. ______ ________ EBTCF = 1280085 – 730000 = $550,085 - CGT Mkt Gain Component = τG[VT – SE – (V0 + AccCI)] = - (0.20)(1280085-0-(1000000+100000) = - (0.20)(1280085 – 1100000) = $36,017. - CGT DTS Recapture Comp. = - τR(AccDE) = - (0.25)($290,910) = - $72,728. ______ ________ EATCF = 550085 – (36017 + 72728) = 550085 - 108744 = $441,340.

Exercise: For 2005 numbers, replace: $90000 with $60000; 10% with 5.5% & $75000 with $41250; $1280085 with $1104620; .4 with .35; .20 with .15, . . .

You should get: EATCF=$20,369 (oper) & $301,202 (rever)…



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Property Purchase Price (Year 0): $1,000,000 Unlevered: Levered:Depreciable Cost Basis: $800,000 Before-tax IRR: 6.04% 7.40%Ordinary Income Tax Rate: 35.00% After-tax IRR: 4.34% 6.44%Capital Gains Tax Rate: 15.00% Ratio AT/BT: 0.719 0.870Depreciation Recaptur___________ 25.00% ____________________ ______________________________ ________________________________________________________________







=EATCF $20,369 $20,831 ($28,704) $21,766 $22,239 $22,716 $23,198 ($26,317) $24,173 $24,667 =EATCF $301,202 $325,868


___________________________________________________________ ______________________________ ________________________________________________________________CASH FLOW COMPONENTS FORMAT





+ DTS $10,182 $10,182 $10,182 $10,182 $10,182 $10,182 $10,182 $10,182 $10,182 $10,182 - AccDTS ($72,727) ($62,545)+ ITS $14,438 $14,399 $14,361 $14,322 $14,284 $14,245 $14,207 $14,168 $14,130 $14,091 $14,091

=EATCF $20,369 $20,831 ($28,704) $21,766 $22,239 $22,716 $23,198 ($26,317) $24,173 $24,667 EATCF $301,202 $325,868

14.2.5: Cash Flow Components:14.2.5: Cash Flow Components:Recall our previous apt property Recall our previous apt property investmentinvestment……

Exhibit 14-2



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Apprec.Rate = 1.00% Bldg.Val/Prop.Val= 80.00% Loan= $750,000Yield = 6.00% Depreciable Life= 27.5 years Int= 5.50%Income Tax Rate = 35.00% CGTax Rate = 15.00% Amort/yr $2,000

DepRecapture Rate= 25.00%(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)

tax w/out (4)-(5)+(6) Loan (4)-(9) (7)-(9)+(10) (9)-(10)Year Prop.Val NOI CI PBTCF shields DTS PATCF LoanBal DS ITS EBTCF EATCF LoanATCFs

0 $1,000,000 ($1,000,000) ($1,000,000) $750,000 ($750,000) ($250,000) ($250,000) ($750,000)1 $1,010,000 $60,000 $0 $60,000 $21,000 $10,182 $49,182 $748,000 $43,250 $14,438 $16,750 $20,369 $28,8132 $1,020,100 $60,600 $0 $60,600 $21,210 $10,182 $49,572 $746,000 $43,140 $14,399 $17,460 $20,831 $28,7413 $1,030,301 $61,206 $50,000 $11,206 $21,422 $10,182 ($34) $744,000 $43,030 $14,361 ($31,824) ($28,704) $28,6704 $1,040,604 $61,818 $0 $61,818 $21,636 $10,182 $50,364 $742,000 $42,920 $14,322 $18,898 $21,766 $28,5985 $1,051,010 $62,436 $0 $62,436 $21,853 $10,182 $50,765 $740,000 $42,810 $14,284 $19,626 $22,239 $28,5276 $1,061,520 $63,061 $0 $63,061 $22,071 $10,182 $51,171 $738,000 $42,700 $14,245 $20,361 $22,716 $28,4557 $1,072,135 $63,691 $0 $63,691 $22,292 $10,182 $51,581 $736,000 $42,590 $14,207 $21,101 $23,198 $28,3848 $1,082,857 $64,328 $50,000 $14,328 $22,515 $10,182 $1,995 $734,000 $42,480 $14,168 ($28,152) ($26,317) $28,3129 $1,093,685 $64,971 $0 $64,971 $22,740 $10,182 $52,413 $732,000 $42,370 $14,130 $22,601 $24,173 $28,241

10 $1,104,622 $65,621 $0 $1,170,243 $23,661 ($62,545) $1,084,037 $730,000 $772,260 $14,091 $397,983 $325,868 $758,169

IRR of above CF Stream = 6.04% 4.34% 5.50% 7.40% 6.44% 3.58%

Here are the example property’s cash flows by component…

Exhibit 14-3:



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10-yr Going-in IRR:

Property (Unlvd) Equity (Levd)

Before-tax 6.04% 7.40%

After-tax 4.34% 6.44%

AT/BT 434/604 = 72% 644/740 = 87%

Effective Tax RateWith ord inc=35%, CGT=15%, Recapt=25%.

100% – 72% = 28% 100% - 87% = 13%

Projected Total Return Calculations:Projected Total Return Calculations:(Based on $1,000,000 price…)



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In equilibrium,In equilibrium,

the linear the linear relationship (RP relationship (RP proportional to proportional to risk)risk)

must hold must hold afterafter--taxtax for for marginalmarginalinvestors in the investors in the relevant asset relevant asset market.market.(See Ch.12, sect.12.1.)

Lower effective tax rate on levered equity does not imply any Lower effective tax rate on levered equity does not imply any ““free lunchfree lunch”” . . .. . .

Risk & Return, AT

0%

1%

2%

3%

4%

5%

6%

7%

8%

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80

AT Risk Units

Expe

cted

Ret

urns

(Goi

ng-in

IRR

)

AT Returns

rf

RP



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Using these Using these returns from returns from our apartment our apartment bldg example, bldg example, we could have we could have this linear this linear relationshiprelationship

Lower Lower effective tax effective tax rate in levered rate in levered return does return does not imply that not imply that risk premium risk premium per unit of risk per unit of risk is greater with is greater with leverage than leverage than without.without.

After-Tax Risk & Return: In Equilibrium the Risk Premium is Proportional to Risk After-Tax for the Marginal Investors

0%

1%

2%

3%

4%

5%

6%

7%

8%

0.00 0.17 0.34 0.51 0.68 0.85 1.02 1.19 1.36 1.52 1.69

Risk Units (after-tax) as Measured by the Capital Market

Expe

cted

Ret

urns

(Goi

ng-in

IRR

) 6.4%= rL AT

4.3% = rU AT

2% = rf AT

RP



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14.3 After14.3 After--Tax Equity Valuation & Capital BudgetingTax Equity Valuation & Capital Budgeting

14.3.1 After14.3.1 After--Tax DCF in General:Tax DCF in General:•• Discount Equity AfterDiscount Equity After--Tax Cash Flows (EATCF),Tax Cash Flows (EATCF),

•• At Equity AfterAt Equity After--Tax Discount Rate (Levered),Tax Discount Rate (Levered),

•• To arrive at PV of Equity.To arrive at PV of Equity.

•• Add PV of Loan (cash borrower obtains),Add PV of Loan (cash borrower obtains),

•• To arrive at Investment Value (IV) of property:To arrive at Investment Value (IV) of property:

•• Max price investor should pay (if they must):Max price investor should pay (if they must):

•• DonDon’’t forget injunction against paying more than MV t forget injunction against paying more than MV (regardless of IV):(regardless of IV):

Always consider MV, not just IV.Always consider MV, not just IV.

AfterAfter--Tax (AT) analysis generally applies to Tax (AT) analysis generally applies to ““Investment ValueInvestment Value”” (IV), (IV), while beforewhile before--tax (BT) analysis applies to tax (BT) analysis applies to ““Market ValueMarket Value”” (MV).(MV).



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Although it makes theoretical sense, there is a major practical Although it makes theoretical sense, there is a major practical problem with the EATCF/EATOCC approach described problem with the EATCF/EATOCC approach described above:above:

It is very difficult to empirically observe or to accurately It is very difficult to empirically observe or to accurately estimate the appropriate levered equity afterestimate the appropriate levered equity after--tax opportunity tax opportunity

cost of capital, cost of capital, E[rE[r], the appropriate hurdle going], the appropriate hurdle going--in IRR.in IRR.

•• Can observe marketCan observe market--based based unleveredunlevered (property) going(property) going--in IRR, and adjust in IRR, and adjust for leverage using WACC, butfor leverage using WACC, but

•• WACC not accurate for longWACC not accurate for long--term term IRRsIRRs,,

•• And we still must account for the effective tax rate on the marAnd we still must account for the effective tax rate on the marginal ginal investor (recall that discount rate OCC even for investment valuinvestor (recall that discount rate OCC even for investment value is market e is market OCC, reflecting marginal investorOCC, reflecting marginal investor’’s afters after--tax OCC).tax OCC).

•• This is a function not only of tax rates, but holding period anThis is a function not only of tax rates, but holding period and degree of d degree of leverage (recall Exh.14leverage (recall Exh.14--2 apartment example: Effective tax rate went from 2 apartment example: Effective tax rate went from 28% to 13% in that case, with that particular bldg, holding peri28% to 13% in that case, with that particular bldg, holding period, & loan).od, & loan).



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e.g., In apartment building example, e.g., In apartment building example, If we did not already (somehow) know that $1,000,000 was the maIf we did not already (somehow) know that $1,000,000 was the market rket value of the property,value of the property,

What would be the meaning of the 6.44% equity afterWhat would be the meaning of the 6.44% equity after--tax IRR expectation tax IRR expectation that we calculated?that we calculated?

But if we already know the property market value, then what doesBut if we already know the property market value, then what does the the 6.44% equity after6.44% equity after--tax IRR tell us, that matters? . . .tax IRR tell us, that matters? . . .

How can we compare it to that offered by other alternative invesHow can we compare it to that offered by other alternative investments tments unless we know they are of the same risk (or we can quantify theunless we know they are of the same risk (or we can quantify the risk risk difference in a way that can be meaningfully related to the requdifference in a way that can be meaningfully related to the required goingired going--in IRR risk premium)?in IRR risk premium)?

Have we gone to a lot of trouble to calculate a number (the equiHave we gone to a lot of trouble to calculate a number (the equity afterty after--tax tax goinggoing--in IRR) that has no rigorous use in decision making? . . .in IRR) that has no rigorous use in decision making? . . .

Fasten your seatbelts…The latter part of Chapter 14 is an attempt to bring some rigor into micro-level real estate investment valuation based on fundamental economic principles.



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14.3.2 Shortcut for Marginal Investors (& for Market Value):14.3.2 Shortcut for Marginal Investors (& for Market Value):

Ignore the equity afterIgnore the equity after--tax level!tax level!Work with the Property BeforeWork with the Property Before--Tax (PBT) level cash flows and Tax (PBT) level cash flows and OCC.OCC.

This always works for Market Value (MV) analysis, This always works for Market Value (MV) analysis,

And also works for Investment Value (IV) analysis for And also works for Investment Value (IV) analysis for marginalmarginalinvestors (those who are typically about equally on both the buyinvestors (those who are typically about equally on both the buyand sell side of the relevant asset market and sell side of the relevant asset market –– recall Ch.12).recall Ch.12).

In the above circumstances, In the above circumstances,

The PBT approach is not only simpler,The PBT approach is not only simpler,

It is more accurate (fewer parameters to be estimated It is more accurate (fewer parameters to be estimated less less chance of estimation error).chance of estimation error).



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Example:Example:

Recall the apartment property with the 6.04% PBTCFRecall the apartment property with the 6.04% PBTCF--based goingbased going--in IRRin IRR……

The 6.04% PBT goingThe 6.04% PBT going--in IRR would presumably be empirically observable in IRR would presumably be empirically observable in the manner described in Section 11.2 of Chapter 11:in the manner described in Section 11.2 of Chapter 11:

•• Based on analysis of ex post return performance (e.g., NCREIF IBased on analysis of ex post return performance (e.g., NCREIF Index);ndex);

•• Based on current market survey information (&/or brokersBased on current market survey information (&/or brokers’’ knowledge);knowledge);

•• Backed out from observable recent transaction prices in the marBacked out from observable recent transaction prices in the market (cap rates ket (cap rates + realistic growth, accounting for CI).+ realistic growth, accounting for CI).

Then apply the 6.04% market PBT discount rate to derive the $1,0Then apply the 6.04% market PBT discount rate to derive the $1,000,000 00,000 MV of the property (based on the PBTCF).MV of the property (based on the PBTCF).

Recognize that this MV also equals IV for marginal investors, thRecognize that this MV also equals IV for marginal investors, those typical ose typical on both the buyon both the buy--side and sellside and sell--side of the market.side of the market.

As noted in Ch.12, itAs noted in Ch.12, it’’s probably best to assume you are a marginal investor s probably best to assume you are a marginal investor unless you can clearly document how you differ (e.g., in tax staunless you can clearly document how you differ (e.g., in tax status) from tus) from typical investors in the market.typical investors in the market.



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Example (cont.):Example (cont.):As a next step (after youAs a next step (after you’’ve estimated the $1,000,000 market value from market ve estimated the $1,000,000 market value from market evidence), you can develop an EATCF for a typical marginal invesevidence), you can develop an EATCF for a typical marginal investor in the market tor in the market for this type of property, and derive the levered equity afterfor this type of property, and derive the levered equity after--tax OCC for the tax OCC for the property, based on the typical property, based on the typical EATCFsEATCFs and the $1,000,000 MV and the fact that MV and the $1,000,000 MV and the fact that MV = IV for marginal investors.= IV for marginal investors.

In our previous example, if the investor subject to the 35% ordiIn our previous example, if the investor subject to the 35% ordinary income tax rate nary income tax rate (& 15% capital gains & 25% recapture rates) were typical, then w(& 15% capital gains & 25% recapture rates) were typical, then we would derive the e would derive the 6.44% rate noted previously, for the given amount of leverage. (6.44% rate noted previously, for the given amount of leverage. (In most markets, In most markets, such taxable investors are probably typical marginal investors.)such taxable investors are probably typical marginal investors.)

This 6.44% afterThis 6.44% after--tax, levered equity market OCC could then be used as the discountax, levered equity market OCC could then be used as the discount t rate in an analysis of rate in an analysis of youryour investment value (based on investment value (based on your ownyour own EATCF projection), EATCF projection), assuming a similar holding period and similar degree of leverageassuming a similar holding period and similar degree of leverage. (Don. (Don’’t forget to t forget to add the loan amount to the equity value.) add the loan amount to the equity value.) (See Section 14.3.4.)(See Section 14.3.4.)



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Example (cont.):Example (cont.):Obviously, if you are similar to the typical marginal investor iObviously, if you are similar to the typical marginal investor in the market, you will n the market, you will get the same $1,000,000 PV again, as you should (when you discouget the same $1,000,000 PV again, as you should (when you discount the same nt the same EATCFsEATCFs @ the 6.44% IRR that was based on that price and those @ the 6.44% IRR that was based on that price and those EATCFsEATCFs, and , and add the loan amount). Your IV will equal MV, by construction (deadd the loan amount). Your IV will equal MV, by construction (defining your fining your EATCFsEATCFs as typical of marginal investors). Hence, the validity of the Pas typical of marginal investors). Hence, the validity of the PBT shortcut. BT shortcut.

But if you are not similar (i.e., your But if you are not similar (i.e., your EATCFsEATCFs differ from the typical investordiffer from the typical investor’’s), s), then (using the 6.44% discount rate) you may get a personal IV fthen (using the 6.44% discount rate) you may get a personal IV for yourself that or yourself that differs from the MV (and marginal IV) of the property (i.e., difdiffers from the MV (and marginal IV) of the property (i.e., different from ferent from $1,000,000).$1,000,000).

But still, remember that you should not generally pay more than But still, remember that you should not generally pay more than MV (or sell for less MV (or sell for less than MV), even if your IV differs from MV. (Recall Section 12.1 than MV), even if your IV differs from MV. (Recall Section 12.1 in Chapter 12.)in Chapter 12.)

Use the PBT shortcut to estimate MV (based on as much market priUse the PBT shortcut to estimate MV (based on as much market price evidence as ce evidence as you can get).you can get).

Corollary: If you are not a marginal investor, then the after-tax levered equity IRR you calculate based on the property’s current market value and your CFs will not equal the opportunity cost of capital relevant for evaluating your investment value of that levered equity, and will therefore not be relevant for quantifying the risk in that position.



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Apprec.Rate = 1.00% Bldg.Val/Prop.Val= 80.00% Loan= $750,000Yield = 6.00% Depreciable Life= 27.5 years Int= 5.50%Income Tax Rate = 35.00% CGTax Rate = 15.00% Amort/yr $2,000

DepRecapture Rate= 25.00%(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)


0 $1,000,000 ($1,000,000) ($1,000,000) $750,000 ($750,000) ($250,000) ($250,000) ($750,000)1 $1,010,000 $60,000 $0 $60,000 $21,000 $10,182 $49,182 $748,000 $43,250 $14,438 $16,750 $20,369 $28,8132 $1,020,100 $60,600 $0 $60,600 $21,210 $10,182 $49,572 $746,000 $43,140 $14,399 $17,460 $20,831 $28,7413 $1,030,301 $61,206 $50,000 $11,206 $21,422 $10,182 ($34) $744,000 $43,030 $14,361 ($31,824) ($28,704) $28,6704 $1,040,604 $61,818 $0 $61,818 $21,636 $10,182 $50,364 $742,000 $42,920 $14,322 $18,898 $21,766 $28,5985 $1,051,010 $62,436 $0 $62,436 $21,853 $10,182 $50,765 $740,000 $42,810 $14,284 $19,626 $22,239 $28,5276 $1,061,520 $63,061 $0 $63,061 $22,071 $10,182 $51,171 $738,000 $42,700 $14,245 $20,361 $22,716 $28,4557 $1,072,135 $63,691 $0 $63,691 $22,292 $10,182 $51,581 $736,000 $42,590 $14,207 $21,101 $23,198 $28,3848 $1,082,857 $64,328 $50,000 $14,328 $22,515 $10,182 $1,995 $734,000 $42,480 $14,168 ($28,152) ($26,317) $28,3129 $1,093,685 $64,971 $0 $64,971 $22,740 $10,182 $52,413 $732,000 $42,370 $14,130 $22,601 $24,173 $28,241

10 $1,104,622 $65,621 $0 $1,170,243 $23,661 ($62,545) $1,084,037 $730,000 $772,260 $14,091 $397,983 $325,868 $758,169


Suppose $1,000,000 = MV of property = $750,000 loan val + $250,000 eq. val.

Then we know that $1,000,000 = IVM = IV of property for marginal investor.

Suppose the modeled investor (tax rates = 35%, 15%, 25%) is typical of marginal investors in mkt for this type of property.

Suppose modeled leverage & holding period (75% LTV, 10-yr hold) is typical of marginal investors in mkt for this type of property.

Then 6.44% = mkt after-tax levered OCC for this type of investment.

IRR(EATCF) = 6.44%



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Now consider a different type of investor, making the same type of investment (75% LTV, 10-yr hold), in the same type of property.Suppose it is a pension fund, facing effectively zero income tax. The cash flows for such an investor are different, as seen below…

Applying the mkt after-tax levered OCC of 6.44% to the P.F.’s EATCF:IVA(equity) = $270,548 > $250,000 = MV(equity) = IVM(equity).

Add to this the $750,000 loan amt, P.F. has max ability to pay for the property [for NPV(IVA) ≥ 0] equal to:

IVA(prop) = $1,020,548 > $1,000,000 = MV(prop) = IVM(prop).

PV @ 6.44% = $270,548.

Apprec.Rate = 1.00% Bldg.Val/Prop.Val= 80.00% Loan= $750,000Yield = 6.00% Depreciable Life= 27.5 years Int= 5.50%Income Tax Rate = 0.00% CGTax Rate = 0.00% Amort/yr $2,000 PV @6.44%=

DepRecapture Rate= 0.00% $270,548.47(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)


0 $1,000,000 ($1,000,000) ($1,000,000) $750,000 ($750,000) ($250,000) ($250,000) ($750,000)1 $1,010,000 $60,000 $0 $60,000 $0 $0 $60,000 $748,000 $43,250 $0 $16,750 $16,750 $43,2502 $1,020,100 $60,600 $0 $60,600 $0 $0 $60,600 $746,000 $43,140 $0 $17,460 $17,460 $43,1403 $1,030,301 $61,206 $50,000 $11,206 $0 $0 $11,206 $744,000 $43,030 $0 ($31,824) ($31,824) $43,0304 $1,040,604 $61,818 $0 $61,818 $0 $0 $61,818 $742,000 $42,920 $0 $18,898 $18,898 $42,9205 $1,051,010 $62,436 $0 $62,436 $0 $0 $62,436 $740,000 $42,810 $0 $19,626 $19,626 $42,8106 $1,061,520 $63,061 $0 $63,061 $0 $0 $63,061 $738,000 $42,700 $0 $20,361 $20,361 $42,7007 $1,072,135 $63,691 $0 $63,691 $0 $0 $63,691 $736,000 $42,590 $0 $21,101 $21,101 $42,5908 $1,082,857 $64,328 $50,000 $14,328 $0 $0 $14,328 $734,000 $42,480 $0 ($28,152) ($28,152) $42,4809 $1,093,685 $64,971 $0 $64,971 $0 $0 $64,971 $732,000 $42,370 $0 $22,601 $22,601 $42,370

10 $1,104,622 $65,621 $0 $1,170,243 $0 $0 $1,170,243 $730,000 $772,260 $0 $397,983 $397,983 $772,260


14.3.3 Evaluating Intra14.3.3 Evaluating Intra--Marginal Investment ValueMarginal Investment Value

Exhibit 14Exhibit 14--5:5:



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IVA = $1,020,548 = PV(eatcfA @ 6.44%)+loan amt

MV = $1,000,000 = PV(pbtcf @ 6.04%) = PV(eatcfM @ 6.44%)+loan amt = IVM

D

QQuantity of Trading

Q*

SP

Q0

Market for Apt Properties:

Mkt going-in IRR = 6.04%

Pension fund is an intra-marginal buyer.

Representing this as in Ch.12 market model (see Exh.12-1) ,

we have . . .




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This approach can be refined by breaking the investment cash flows into components of different risk categories, and computing the PV of each component using a discount rate appropriate for the risk in each component.

(Recall Ch.10.)

This can be viewed as motivating a useful analytical procedure known as “Adjusted Present Value (APV), or “Value Additivity”. . .



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14.3.4 Value 14.3.4 Value AdditivityAdditivity & the APV Decision Rule& the APV Decision RuleThe PBT approach is an example of use of the principle of The PBT approach is an example of use of the principle of ““Value Value AdditivityAdditivity””::

Value Value AdditivityAdditivity““The value of the whole equals the sum of the values of the partsThe value of the whole equals the sum of the values of the parts, i.e., the , i.e., the sum of the values of all the marketable (private sector) claims sum of the values of all the marketable (private sector) claims on the asset.on the asset.””

Prop.Val = Equity Val + Dbt Val

V = E + D

Where: V = Value of the property, E = Value of the equity, D = Value of the debt.

Therefore:Therefore: E = V E = V –– D D

““DD”” is usually straightforward to compute (unless loan is subsidizeis usually straightforward to compute (unless loan is subsidized, MV of d, MV of loan equals loan amount).loan equals loan amount).

So, use PBT to compute MV of So, use PBT to compute MV of ““VV””, then subtract MV of , then subtract MV of ““DD”” to arrive at to arrive at MV of MV of ““EE””, rather than trying to estimate , rather than trying to estimate ““EE”” directly.directly.



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““Adjusted Present ValueAdjusted Present Value”” (APV) Decision Rule(APV) Decision Rule……Like NPV, only accounts for financingLike NPV, only accounts for financing……

APV(equityAPV(equity) = ) = NPV(propertyNPV(property) + ) + NPV(financingNPV(financing))

Based on the Value Based on the Value AdditivityAdditivity Principle:Principle:Prop.Val = Equity Val + Dbt Val

V = E + DWhere: V = Value of the property,

E = Value of the equity, D = Value of the debt.

Define: P = Price paid for the property, L = Amount of the loan…V-P = E+D – P

= E+D – ((P-L)+L)= E-(P-L) + D-L= E-(P-L) – (L-D)

Thus: E-(P-L) = (V-P) + (L-D)Or: APV(Equity) = NPV(Prop)+ NPV(Fin)

Note: Arbitrage basis of Value Additivity applies to MV, but the common sense of Value Additivity can be applied to IV as well.



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““Adjusted Present ValueAdjusted Present Value”” (APV)(APV)……

APV Investment Decision Rule:APV Investment Decision Rule:

Analogous to that of NPVAnalogous to that of NPV……

1)1) Maximize APV over mutually exclusive alternatives;Maximize APV over mutually exclusive alternatives;

2)2) Never do a deal with APV < 0.Never do a deal with APV < 0.

(APV = 0 is OK.)(APV = 0 is OK.)

(APV = 0 is normal from a MV perspective.)(APV = 0 is normal from a MV perspective.)



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APV procedure can be expanded to any number of additive componenAPV procedure can be expanded to any number of additive components of a ts of a complex deal structure. e.g., complex deal structure. e.g.,

APV(equityAPV(equity) = ) = NPV(propertyNPV(property) + ) + NPV(preferredNPV(preferred) + ) + NPV(debtNPV(debt) + ) + NPV(taxNPV(tax credits)credits)

Try to use fundamental economic principles to help evaluate the Try to use fundamental economic principles to help evaluate the deal:deal:•• Market equilibrium (competition),Market equilibrium (competition),•• Rational behavior (Max NPV).Rational behavior (Max NPV).

For exampleFor example……•• If the deal structure is typical (e.g., of a If the deal structure is typical (e.g., of a ““classclass””), and sufficiently common that there ), and sufficiently common that there is a functioning is a functioning marketmarket for these types of deals, then for these types of deals, then market equilibriummarket equilibrium will tend to will tend to make it reasonable to expect: make it reasonable to expect: APV(equityAPV(equity)=0)=0. (You can use this as a working . (You can use this as a working assumption to help ascertain the MV of the individual deal compoassumption to help ascertain the MV of the individual deal components and positions.)nents and positions.)

•• Even if the overall deal structure is unique (such that there iEven if the overall deal structure is unique (such that there is not a market for the s not a market for the equity as structured), many (or even all) of the individual compequity as structured), many (or even all) of the individual components and positions onents and positions may be typical enough that there is a market for them. It shouldmay be typical enough that there is a market for them. It should then be assumed that then be assumed that rational behaviorrational behavior on the part of all the parties to the deal would tend to drive on the part of all the parties to the deal would tend to drive NPV NPV toward zero for each component of the deal. If all the componenttoward zero for each component of the deal. If all the components of the APV are s of the APV are zero, then so is the APV.zero, then so is the APV.

Note that the above refers to market value based analysis (MV), not IV. Do you recall why MV is important to the investor?. . .



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APV(equityAPV(equity) = ) = NPV(propertyNPV(property) + ) + NPV(financingNPV(financing))NPV(propertyNPV(property) = NPV of ) = NPV of unleveredunlevered (all equity) investment in the property (as (all equity) investment in the property (as if no debt).if no debt).

For MV based NPV, this can (should) be computed using the PBT apFor MV based NPV, this can (should) be computed using the PBT approach.proach.

NPV(financingNPV(financing) = NPV of loan transaction.) = NPV of loan transaction.

Debt market is relatively efficient & competitive (debt productsDebt market is relatively efficient & competitive (debt products are relatively are relatively homogeneous, often securitized in 2ndary homogeneous, often securitized in 2ndary mktmkt, relatively transparent and , relatively transparent and straightforward to evaluate).straightforward to evaluate).

Hence, in the absence of Hence, in the absence of subsidizedsubsidized (below market interest rate) financing:(below market interest rate) financing:

NPV(financingNPV(financing) = 0, normally (on an MV basis).) = 0, normally (on an MV basis).

Recall: Recall: NPVNPVMVMV(buyer(buyer) = ) = --NPVNPVMVMV(seller(seller). ).

So, for the loan transaction: So, for the loan transaction: NPVNPVMVMV(borrower(borrower) = ) = --NPVNPVMVMV(lender(lender))

In this (normal) situation (from an MV perspective): In this (normal) situation (from an MV perspective):

APV(equityAPV(equity) = ) = NPV(propertyNPV(property).).

i.e., i.e., Evaluate the deal without the loan. (Use the PBT shortcut).Evaluate the deal without the loan. (Use the PBT shortcut).



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Suppose a certain investor in bond mkt (call her Mary) faces effective income tax rate of 25% on her bond returns.

And faces an after-tax OCC (from the capital mkt) of 3%.

What will be the IV to this investor of a $100 (par) 4% perpetual bond (pays $4/yr forever)?

Answer:

Discount Mary’s after-tax cash flows, at the mkt-based after-tax OCC. . .

( ) ( ) 100$03.03

03.14)25.1(

03.14)25.1(

03.14)25.1(

32 ==+++= −−− LMIV

LetLet’’s now delve into more depth in the valuation of the debt compones now delve into more depth in the valuation of the debt component of the dealnt of the deal……

14.3.5 After14.3.5 After--Tax Valuation of Debt FinancingTax Valuation of Debt Financing



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Suppose Mary typifies the marginal investor in the bond mkt.

What will be the MV of this bond?

Answer:

MV = IV (marginal investor) = IVM = $100.

What will be the observed “mkt yield” in the bond mkt?

Answer:

Observable mkt returns are pre-tax, so:

Mkt yield = going-in IRR @ observed mkt price:

= IRR(-100, 4, 4, 4, . . .) = 4%.



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MV = $100 = $4/0.04 = $3/0.03 = IVM

Q*

D

S

Q

L Market for Taxed Debt Assets:

Mkt Int.Rate = 4%

Here is a picture of what we have just discovered about the bond market . . .

L = PV of a Loan (Debt Asset).



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Note: We started out with the assumption that Mary was the marginal investor.

Suppose we didn’t know that she was the marginal investor.

Or suppose that we didn’t know that the marginal investor faced an effective tax rate of 25%.

How could we derive (from empirically observable data) that the market’s after-tax OCC is 3%?

Answer:

If there is a simultaneous market for tax-exempt bonds, and investors can trade between the two markets, then we can directly observe the market’s after-tax OCC as the yield on tax-exempt (municipal) bonds.



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We can also compare the yields across the two types of bond mkts (taxed & tax-exempt) to derive what must be the effective tax rate of the marginal investor.

In the previously described situation (4% yield in bond mkt, marginal investors face 25% tax rate), what will be the observed mkt yield in the municipal (tax-exempt) bond mkt?

Answer: 3%, because 3% = (1-.25)4% = after-tax yield for marginal investors in bond mkt.

Otherwise, what?...



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If muni yield were > 3%, marginal investors in taxed bond mkt would sell bonds and buy munis, driving up muni price (driving down muni yield) until the 3/4 relationship in yields existed.

If muni yield were < 3%, marginal investors in muni bond mkt would sell munis and buy bonds, driving down muniprice (driving up muni yield) until the 3/4 relationship in yields existed.

Thus, ratio:

muni yld / taxable bond yld

= 1 – effective tax rate on margl investor in bond mkt.

Margl tax rate = 1 – muniYld/bondYld



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Suppose Abner is a tax-advantaged investor compared to the marginal investor (Mary).

Abner faces only 20% tax on bond returns.

What is the IV of the 4% perpetual bond to Abner?

Answer:

Discount Abner’s after-tax cash flows, at the mkt-based after-tax OCC. . .

( ) ( ) 107$03.020.3

03.14)20.1(

03.14)20.1(

03.14)20.1(

32 ==+++= −−− LAIV

Thus: IVA = $107 > $100 = MV = IVM .

Which makes sense, to reflect Abner’s tax advantage compared to the market’s marginal investor who determines the price in the mkt.



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Suppose Clarence is a tax-disadvantaged investor compared to the marginal investor (Mary).

Clarence faces 30% tax on bond returns.

What is the IV of the 4% perpetual bond to Clarence?

Answer:

Discount Clarence’s after-tax cash flows, at the mkt-based after-tax OCC. . .

( ) ( ) 93$03.080.2

03.14)30.1(

03.14)30.1(

03.14)30.1(

32 ==+++= −−− LCIV

Thus: IVC = $93 < $100 = MV = IVM .

Which makes sense, to reflect Clarence’s tax disadvantage compared to the market’s marginal investor who determines the price in the mkt.



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IVA = $107 = $3.20/0.03

MV = $100 = $4/0.04 = $3/0.03 = IVM

D

S

Q

L

Q*Q0

IVC = $93 = $2.80/0.03

Market for Taxed Debt Assets:

Mkt Int.Rate = 4%

Abner & Clarence are intra-marginal market participants in the bond mkt.Abner is an intra-marginal buyer. Clarence is an intra-marginal seller.




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IVA = $107 = $3.20/0.03

MV = $100 = $4/0.04 = $3/0.03 = IVM

D

S

Q

L

Q*Q0

IVC = $93 = $2.80/0.03

Market for Taxed Debt Assets:

Mkt Int.Rate = 4%

Trading occurs at the mkt price of $100 (4% yield).

NPV(for Abner buying, based on his IV) = $107 - $100 = +$7.

NPV(for Clarence selling, based on his IV) = $100 - $93 = +$7.Exhibit 14Exhibit 14--7:7:



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Relationship to value of “interest tax shields” (ITS) in borrowing money to finance real estate investment . . .

Borrowing money is like selling bonds (receive cash up front, pay back contractual periodic cash flows over time).

Mary, Abner, & Clarence are all considering making real estate investments, and taking out a mortgage to finance that investment.

The mkt interest rate on the mortgage is 4%, and the loan is perpetual, interest only.

What is the value of the ITS to Mary, Abner, & Clarence, in this mortgage?



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Value of the ITS:The amount of the ITS each year equals the income tax savings that year: the investor’s tax rate times the interest expense. The PV is found by discounting at the OCC…

( ) ( )

( ) ( )

( ) ( ) .40$)(

.27$)(

.33$)(

03.020.1

03.14)30(.

03.14)30(.

03.14)30(.

03.080.0

03.14)20(.

03.14)20(.

03.14)20(.

03.01

03.14)25(.

03.14)25(.

03.14)25(.

32

32

32

==+++=

==+++=

==+++=

L

L

L

C

A

M

ITSPV

ITSPV

ITSPV

The ITS are worth more to the more heavily-taxed investor (Clarence), and for everyone they are worth a large fraction of the loan amount ($100).

But what is the NPV of the borrowing transaction, to Mary, Abner, & Clarence? . . .



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NPVIV of borrowing to finance real estate investment (@ mkt interest rate, no subsidy):

( ) ( )( )( ) ( )( )( ) ( )( ) .7$93100100100

.7$107100100100

.0100100100100

03.080.2

03.14)30.1(

03.14)30.1(

03.14)30.1(

03.020.3

03.14)20.1(

03.14)20.1(

03.14)20.1(

03.03

03.14)25.1(

03.14)25.1(

03.14)25.1(

32

32

32

+=−=−=+++−=

−=−=−=+++−=

=−=−=+++−=

−−−

−−−

−−−

L

L

L

C

A

M

NPV

NPV

NPV

Even though the ITS have substantial value to all three investorEven though the ITS have substantial value to all three investors,s,

Borrowing is zero NPV for the marginal investor (Mary).Borrowing is zero NPV for the marginal investor (Mary).

Borrowing is negative NPV for the taxBorrowing is negative NPV for the tax--advantaged investor advantaged investor ((AbnerAbner).).

Borrowing is only positive NPV for the taxBorrowing is only positive NPV for the tax--disadvantaged investor disadvantaged investor (relative to the marginal investor in the bond (relative to the marginal investor in the bond mktmkt),),

And even for him (Clarence) the NPV of borrowing is much And even for him (Clarence) the NPV of borrowing is much smaller than the PV of his ITS ($7 smaller than the PV of his ITS ($7 vsvs $40).$40).

(Note: This is NPV based on IV. NPV based on MV is zero by defn in non-subsidized loan.)www.bsscommunitycollege.in www.bssnewgeneration.in www.bsslifeskillscollege.in


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Why might each of them (Clarence, Mary, Abner) borrow to finance their real estate investment?...

•• Clarence (alone) can justify the loan purely for the positive NClarence (alone) can justify the loan purely for the positive NPV in PV in its tax shelter (with the caveat that it is not a large positiveits tax shelter (with the caveat that it is not a large positive NPV).NPV).

•• Clarence and Mary can justify the loan if they want leverage (tClarence and Mary can justify the loan if they want leverage (to o magnify risk & return in their R.E. investment), but magnify risk & return in their R.E. investment), but AbnerAbner cancan’’t use t use this justification due to his NPV<0 (he should look for other wathis justification due to his NPV<0 (he should look for other ways to ys to increase risk & return).increase risk & return).

•• All three investors can justify the loan if they are capital coAll three investors can justify the loan if they are capital constrained nstrained and the R.E. investment has a sufficient positive NPV. (For Clarand the R.E. investment has a sufficient positive NPV. (For Clarence, ence, the R.E. NPV can even be a bit negative.) For the R.E. NPV can even be a bit negative.) For AbnerAbner, the positive R.E. , the positive R.E. NPV may result from his tax advantage (if he is also tax advantaNPV may result from his tax advantage (if he is also tax advantaged ged relative to the marginal investor in the R.E. asset relative to the marginal investor in the R.E. asset mktmkt, not just , not just relative to the marginal investor in the bond relative to the marginal investor in the bond mktmkt).).



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Now suppose the seller of the real estate offers below-marketfinancing (subsidized loan), an interest rate of 3% instead of the mkt rate of 4%, on the same (perpetual) loan.What would be the MV of this loan (if the seller sold it in the 2ndary mkt)?

Or (more fundamentally), discount the loan’s after-tax cash flows to the marginal investor in the bond mkt (Mary), at the mkt-based after-tax OCC. . .

( ) ( ) 75$03.025.2

03.13)25.1(

03.13)25.1(

03.13)25.1(

32 ==+++== −−− LMIVMV

( ) ( ) 75$04.03

04.13

04.13

04.13

32 ==+++= LMV

Answer:Discount the loan’s before-tax cash flows at the market interest rate . . .



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What is the IV based NPV of the subsidized loan offer to each of our investors? . . .

( ) ( )( )( ) ( )( )( ) ( )( ) .30$70100100100)(

.20$80100100100)(

.25$75100100100)(

03.010.2

03.13)30.1(

03.13)30.1(

03.13)30.1(

03.040.2

03.13)20.1(

03.13)20.1(

03.13)20.1(

03.025.2

03.13)25.1(

03.13)25.1(

03.13)25.1(

32

32

32

+=−=−=+++−=

+=−=−=+++−=

+=−=−=+++−=

−−−

−−−

−−−

L

L

L

C

A

M

loanNPV

loanNPV

loanNPV

How much more should each of the investors be willing to pay for the property (more than they think it is otherwise worth), as a result of the subsidized loan offer from the seller? . . .

Mary $25 more.

Abner $20 more.

Clarence $30 more.

(Note: These IV-based NPV effects of loan rate subsidies are reduced the shorter the loan term.)



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Preceding used perpetuity example. Suppose finite loan (extreme case 1-period).Compare for subsidized loan NPV(IV after-tax for marglinvestor: 25% tax rate) vs NPV(MV before-tax)…Perpetuity: NPV(loan @ MV) =

( ) ( )( ) .25$75100100100 04.03

04.13

04.13

04.13

32 +=−=−=+++− L

Perpetuity: NPV(loan @ IVM) =

( ) ( )( ) .25$75100100100 03.025.2

03.13)25.1(

03.13)25.1(

03.13)25.1(

32 +=−=−=+++− −−− L

It’s the same (as you would expect, for margl investor).1-period: NPV(loan @ MV) =

.96.0$04.99100100100 04.1103

04.11003 +=−=−=− +

1-period: NPV(loan @ IVM) =.73.0$27.99100100100 03.1

25.10203.1

1003)25.1( +=−=−=− +−

It’s different! NPV(loan @ IVM) ≈ (1 – T)NPV(loan @ MV):$0.73 ≈ (1 – 0.25)$0.96.

Recall Ch.12 (sect.12.1) rules about what to do when NPV differs from MV and IV perspectives: Use common sense!www.bsscommunitycollege.in www.bssnewgeneration.in www.bsslifeskillscollege.in


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Summarizing Summarizing NPV(loanNPV(loan) from borrower) from borrower’’s perspective:s perspective:•• Unsubsidized (Unsubsidized (mktmkt rate) loans:rate) loans:

•• NPV(loanNPV(loan) ) == 0 from 0 from MVMV (before(before--tax) perspective.tax) perspective.•• NPV(loanNPV(loan) ) >> 0 (but much less than PV(ITS)) for 0 (but much less than PV(ITS)) for highhigh taxtax--bracket bracket taxable investors from taxable investors from IVIV perspective.perspective.•• NPV(loanNPV(loan) ) << 0 for 0 for lowlow taxtax--bracket taxable investors from bracket taxable investors from IVIVperspective.perspective.

••Subsidized (below Subsidized (below mktmkt rate) loans:rate) loans:•• NPV(loanNPV(loan) ) >> 0 from 0 from MVMV perspective (by definition).perspective (by definition).•• NPV(loanNPV(loan) ) >> 0 from 0 from IVIV perspective for perspective for highhigh or or averageaverage tax bracket tax bracket investors, butinvestors, but•• NPV(loanNPV(loan) IV (after) IV (after--tax) tax) ≤≤ NPV(loanNPV(loan) MV (before) MV (before--tax):tax):•• NPV(loanNPV(loan) IV (after) IV (after--tax) converges to (1tax) converges to (1--T)NPV(loan) MV (beforeT)NPV(loan) MV (before--tax) as loantax) as loan--term approaches zero (where T is borrowerterm approaches zero (where T is borrower’’s tax rate);s tax rate);•• NPV(loanNPV(loan) IV (after) IV (after--tax) converges to exactly equal tax) converges to exactly equal NPV(loanNPV(loan) MV ) MV (before(before--tax) as loantax) as loan--term approaches infinity (perpetual debt).term approaches infinity (perpetual debt).



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Suppose $1,000,000 = MV of property, & 25% is tax rate of marginal investor in debt mkt, ATOCC dbt = (1-.25)*5.5% = 4.13%

Suppose the modeled investor (tax rates = 35%, 15%, 25%) is typical of marginal investors in mkt for this type of property, & modeled leverage & holding period (75% LTV, 10-yr hold) is typical of marginal investors in mkt for this type of property. IV-based APV = 0 for whole deal (inclu debt).Then we know margl invstr in prop mkt is intra-marginal in debt mkt on the sell (borrow) side: Debt part is pos-NPV, thus:APV = 0 (mkt equilibr) Property (unlevrd) is neg-NPV.

LetLet’’s now apply APV to dissect the valuation of our previous apartmes now apply APV to dissect the valuation of our previous apartment property . . .nt property . . .

14.3.6 Example Application of APV to a Marginal Investor14.3.6 Example Application of APV to a Marginal Investor

Apprec.Rate = 1.00% Bldg.Val/Prop.Val= 80.00% Loan= $750,000Yield = 6.00% Depreciable Life= 27.5 years Int= 5.50%Income Tax Rate = 35.00% CGTax Rate = 15.00% Amort/yr $2,000Debt Mkt Margl Tax Rate= 25.00% DepRecapture Rate= 25.00%

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)tax w/out (4)-(5)+(6) Loan (4)-(9) (7)-(9)+(10) (9)-(10)

Year Prop.Val NOI CI PBTCF shields DTS PATCF LoanBal DS ITS EBTCF EATCF LoanATCF&Val0 $1,000,000 ($1,000,000) ($967,119) $750,000 ($750,000) ($250,000) ($250,000) ($717,119)1 $1,010,000 $60,000 $0 $60,000 $21,000 $10,182 $49,182 $748,000 $43,250 $14,438 $16,750 $20,369 $28,8132 $1,020,100 $60,600 $0 $60,600 $21,210 $10,182 $49,572 $746,000 $43,140 $14,399 $17,460 $20,831 $28,7413 $1,030,301 $61,206 $50,000 $11,206 $21,422 $10,182 ($34) $744,000 $43,030 $14,361 ($31,824) ($28,704) $28,6704 $1,040,604 $61,818 $0 $61,818 $21,636 $10,182 $50,364 $742,000 $42,920 $14,322 $18,898 $21,766 $28,5985 $1,051,010 $62,436 $0 $62,436 $21,853 $10,182 $50,765 $740,000 $42,810 $14,284 $19,626 $22,239 $28,5276 $1,061,520 $63,061 $0 $63,061 $22,071 $10,182 $51,171 $738,000 $42,700 $14,245 $20,361 $22,716 $28,4557 $1,072,135 $63,691 $0 $63,691 $22,292 $10,182 $51,581 $736,000 $42,590 $14,207 $21,101 $23,198 $28,3848 $1,082,857 $64,328 $50,000 $14,328 $22,515 $10,182 $1,995 $734,000 $42,480 $14,168 ($28,152) ($26,317) $28,3129 $1,093,685 $64,971 $0 $64,971 $22,740 $10,182 $52,413 $732,000 $42,370 $14,130 $22,601 $24,173 $28,241

10 $1,104,622 $65,621 $0 $1,170,243 $23,661 ($62,545) $1,084,037 $730,000 $772,260 $14,091 $397,983 $325,868 $758,169

IRR of above CF Stream = 6.04% 4.76% 5.50% 7.40% 6.44% 4.13%www.bsscommunitycollege.in www.bssnewgeneration.in www.bsslifeskillscollege.in


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Suppose $1,000,000 = MV of property, & 25% is tax rate of marginal investor in debt mkt, ATOCC dbt = (1-.25)*5.5% = 4.13%

Suppose the modeled investor (tax rates = 35%, 15%, 25%) is typical of marginal investors in mkt for this type of property, & modeled leverage & holding period (75% LTV, 10-yr hold) is typical of marginal investors in mkt for this type of property. IV-based APV = 0 for whole deal (inclu debt).Then we know margl invstr in prop mkt is intra-marginal in debt mkt on the sell (borrow) side: Debt part is pos-NPV, thus:APV = 0 (mkt equilibr) Property (unlevrd) is neg-NPV.

0 = APV = NPV(prop) + NPV(loan) = (X - $1,000,000 ) + ($750,000 - $717,119); X = $967,119 = IV(prop); AT(unlevrd)OCC = 4.76%;

Therfore: NPV(prop) = $967,119 - $1,000,000 = -$32,881; NPV(loan) = $750,000 - $717,119 = +$32,881.

IV(loan liab) @ 4.13% = -$717,119


(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)tax w/out (4)-(5)+(6) Loan (4)-(9) (7)-(9)+(10) (9)-(10)


10 $1,104,622 $65,621 $0 $1,170,243 $23,661 ($62,545) $1,084,037 $730,000 $772,260 $14,091 $397,983 $325,868 $758,169





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(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)tax w/out (4)-(5)+(6) Loan (4)-(9) (7)-(9)+(10) (9)-(10)


10 $1,104,622 $65,621 $0 $1,170,243 $23,661 ($62,545) $1,084,037 $730,000 $772,260 $14,091 $397,983 $325,868 $758,169


IV(loan liab) @ 4.13% = -$717,119

0 = APV = NPV(prop) + NPV(loan) = (X - $1,000,000 ) + ($750,000 - $717,119); X = $967,119 = IV(prop); AT(unlevrd)OCC = 4.76%

Start with the known after-tax OCC of debt observable from muni bond market. (Here, 4.13%, based on 25% margl tax.)

Then back out the value of the property without debt using the APV = 0 equilibrium condition for marginal investor.




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HereHere’’s another way to use Value s another way to use Value AdditivityAdditivity to dissect the to dissect the apartment dealapartment deal……Consider the investment by a typical (taxed) marginal investor again (for whom IVM = MV, not now the intra-marginal P.F. for whom IVA > MV).Break the cash flows into components by risk class…

DTS & loan ATCF are relatively low risk (legally fixed): OCC = 4.13%.

PBTCF & tax w/out shields are relatively high risk: OCC = 4.76%.


(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)tax w/out (4)-(5)+(6) Loan (4)-(9) (7)-(9)+(10) (9)-(10)


10 $1,104,622 $65,621 $0 $1,170,243 $23,661 ($62,545) $1,084,037 $730,000 $772,260 $14,091 $397,983 $325,868 $758,169


Exhibit 14Exhibit 14--9a:9a:



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_ =

DTS - loan ATCF = Tot.FixedPBTCF - Tax w/out Shlds = Tot.Risky

_ =

+ =

Fixed + Risky = EATCF

PV(risky) = $250,000 – (-$683,592) = $933,592 ≈ $933,257

IRR(risky for PV $933,257) = 4.75% = Risky OCC

MV prop = IVMequity + loan amt = $250,000 + $750,000 = $1,000,000 = $966,473 val w/out taxshields + $33,000 IVM tax shields to margl investor .

Risky Val: $933,257

+ Fixed Val: -683,592

= Eq. Val: $249,664

DTS

$10,182$10,182$10,182$10,182$10,182$10,182$10,182$10,182$10,182

($62,545)

DS - ITS

$28,813$28,741$28,670$28,598$28,527$28,455$28,384$28,312$28,241

$758,169

Fixed

-$18,631-$18,559-$18,488-$18,416-$18,345-$18,273-$18,202-$18,130-$18,059

-$820,714

PBTCF

$60,000$60,600$11,206$61,818$62,436$63,061$63,691$14,328$64,971

$1,170,243

tax w/outshields

$21,000$21,210$21,422$21,636$21,853$22,071$22,292$22,515$22,740$23,661

Risky

$39,000$39,390

-$10,216$40,182$40,584$40,989$41,399-$8,187$42,231

$1,146,583

Fixed

-$18,631-$18,559-$18,488-$18,416-$18,345-$18,273-$18,202-$18,130-$18,059

-$820,714

Risky

$39,000$39,390

-$10,216$40,182$40,584$40,989$41,399-$8,187$42,231

$1,146,583

PV @ 4.13% = - $683,592 PV @ 4.76% = $933,257

PV @ 6.44% = $250,000

EATCF

$20,369$20,831

-$28,704$21,766$22,239$22,716$23,198

-$26,317$24,173

$325,868

Exhibit 14Exhibit 14--9b:9b:



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MV prop = IVMequity + loan amt = $250,000 + $750,000 = $1,000,000 = $966,473 val w/out taxshields + $33,527 IVM tax shields to margl investor .

This is consistent with PV of depreciation tax shields:PV(DTS @ 4.13%) = $33,527:

DTS

$10,182$10,182$10,182$10,182$10,182$10,182$10,182$10,182$10,182

($62,545)

And with there being no further component of MV (= IVM ) attributable to tax shields, given that we are here assuming that the loan is zero-NPV to the marginal investor: NPVM(loan) = $750,000 - $750,000 = 0.

For a more in-depth perspective on the effect debt financing can have given income tax considerations, see the following slides…



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Does the lower effective tax rate on levered equity imply that Does the lower effective tax rate on levered equity imply that borrowing is profitable (in the sense of NPV>0)?borrowing is profitable (in the sense of NPV>0)?

Recall from Chapter 13:Recall from Chapter 13:

•• Leverage increases expected total return,Leverage increases expected total return,

•• But it also increases risk.But it also increases risk.

•• Risk increases proportionately to Risk increases proportionately to risk premiumrisk premium in E[r].in E[r].

•• Hence E[RP] / Unit of Risk remains constant.Hence E[RP] / Unit of Risk remains constant.

•• Hence, NPV(borrowing)=0 (Hence, NPV(borrowing)=0 (No No ““free lunchfree lunch””).).

•• This holds true afterThis holds true after--tax as well as beforetax as well as before--tax (at least for tax (at least for marginal investors marginal investors –– those with tax rates typical of marginal those with tax rates typical of marginal investors in the debt market).investors in the debt market).

(Do you believe in a (Do you believe in a ““free lunchfree lunch””?...)?...)



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In equilibrium,In equilibrium,

the linear the linear relationship (RP relationship (RP proportional to proportional to risk)risk)

must hold must hold afterafter--taxtax for for marginalmarginalinvestors in the investors in the relevant asset relevant asset market.market.(See Ch.12, sect.12.1.)

Risk & Return, AT

0%

1%

2%

3%

4%

5%

6%

7%

8%

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80

AT Risk Units

Expe

cted

Ret

urns

(Goi

ng-in

IRR

)

AT Returns

rf

RP



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Using these Using these returns from returns from our apartment our apartment bldg example, bldg example, we could have we could have this linear this linear relationshiprelationship

Lower Lower effective tax effective tax rate in levered rate in levered return does return does not imply that not imply that risk premium risk premium per unit of risk per unit of risk is greater with is greater with leverage than leverage than without.without.

After-Tax Risk & Return: In Equilibrium the Risk Premium is Proportional to Risk After-Tax for the Marginal Investors

0%

1%

2%

3%

4%

5%

6%

7%

8%

0.00 0.17 0.34 0.51 0.68 0.85 1.02 1.19 1.36 1.52 1.69

Risk Units (after-tax) as Measured by the Capital Market

Expe

cted

Ret

urns

(Goi

ng-in

IRR

)6.4%

= rL AT

4.8% = rU AT

2% = rf AT

RP

4.1% = rD AT

DebtRisk

Prop.Risk

LevdProp.Risk



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Consider again the tax-exempt P.F.’s investment in our $1,000,000 apt property…

Working directly with the EATCF, recall that we computed:

NPV(IVA) = [PV(EATCFA @ 6.44%)+Loan] - $1,000,000

= $1,020,548 - $1,000,000

= + $20,548.

PV @ 6.44% = $270,548.Exhibit 14Exhibit 14--5:5:

14.3.7 Example Application of APV to an Intra14.3.7 Example Application of APV to an Intra-- Marginal InvestorMarginal Investor

Apprec.Rate = 1.00% Bldg.Val/Prop.Val= 80.00% Loan= $750,000Yield = 6.00% Depreciable Life= 27.5 years Int= 5.50%Income Tax Rate = 0.00% CGTax Rate = 0.00% Amort/yr $2,000 PV @6.44%=

DepRecapture Rate= 0.00% $270,548.47(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)


0 $1,000,000 ($1,000,000) ($1,000,000) $750,000 ($750,000) ($250,000) ($250,000) ($750,000)1 $1,010,000 $60,000 $0 $60,000 $0 $0 $60,000 $748,000 $43,250 $0 $16,750 $16,750 $43,2502 $1,020,100 $60,600 $0 $60,600 $0 $0 $60,600 $746,000 $43,140 $0 $17,460 $17,460 $43,1403 $1,030,301 $61,206 $50,000 $11,206 $0 $0 $11,206 $744,000 $43,030 $0 ($31,824) ($31,824) $43,0304 $1,040,604 $61,818 $0 $61,818 $0 $0 $61,818 $742,000 $42,920 $0 $18,898 $18,898 $42,9205 $1,051,010 $62,436 $0 $62,436 $0 $0 $62,436 $740,000 $42,810 $0 $19,626 $19,626 $42,8106 $1,061,520 $63,061 $0 $63,061 $0 $0 $63,061 $738,000 $42,700 $0 $20,361 $20,361 $42,7007 $1,072,135 $63,691 $0 $63,691 $0 $0 $63,691 $736,000 $42,590 $0 $21,101 $21,101 $42,5908 $1,082,857 $64,328 $50,000 $14,328 $0 $0 $14,328 $734,000 $42,480 $0 ($28,152) ($28,152) $42,4809 $1,093,685 $64,971 $0 $64,971 $0 $0 $64,971 $732,000 $42,370 $0 $22,601 $22,601 $42,370

10 $1,104,622 $65,621 $0 $1,170,243 $0 $0 $1,170,243 $730,000 $772,260 $0 $397,983 $397,983 $772,260




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Now let’s apply the APV approach to dissect the deal…APV(equity) = NPV(property) + NPV(financing)

From an IV perspective, the NPV(property) for the P.F. is:

NPV = IV(property) – Prop.Price

= PV(patcfA @ 4.76%) - $1,000,000

= PV(pbtcf @ 4.76%) - $1,000,000

= $1,104,714 - $1,000,000 = +$104,714.

= mkt unlevd AT OCC, from marginal investor’s AT IRR without leverage (@ MV = $1,000,000).

Because P.F. tax-exempt: PATCF = PBTCF.

From an IV perspective, the NPV(financing) for the P.F. is:

NPV = Loan Amt - IV(loan)

= $750,000 - PV(loan atcfA @ muni yld%)

= $750,000 - PV(loan btcf @ 4.13%)

= $750,000 - $832,202 = -$82,202.

Suppose muni yld = 4.13% = (1 - .25)5.5%.

APV(equity) = +104,714 - $82,202 = +$22,512 ≈ 20,548*.*In principle this equation should be exactly equal, otherwise there is some sort of “arbitrage” opportunity between the markets. But in reality valuations are not that precise.www.bsscommunitycollege.in www.bssnewgeneration.in www.bsslifeskillscollege.in


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PV @ 4.76% = $1,104,714 PV @ 4.13% = $832,202

PV @ 6.44% = $270,548.

Value Additivity:E = V - D

IV(equity) = $1,104,714 - $832,202 = $272,512 ≈ $270,548*.*In principle this equation should be exactly equal, otherwise there is some sort of “arbitrage”opportunity between the markets. But in reality valuations are not that precise.

Tax-exempt investor (e.g., pension fund) “Value Additivity”valuation of apartment investment by components . . .


(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)tax w/out (4)-(5)+(6) Loan (4)-(9) (7)-(9)+(10) (9)-(10)

Year Prop.Val NOI CI PBTCF shields DTS PATCF LoanBal DS ITS EBTCF EATCF LoanATCF&Val0 $1,000,000 ($1,000,000) ($1,104,714) $750,000 ($750,000) ($250,000) ($270,548) ($832,202)1 $1,010,000 $60,000 $0 $60,000 $0 $0 $60,000 $748,000 $43,250 $0 $16,750 $16,750 $43,2502 $1,020,100 $60,600 $0 $60,600 $0 $0 $60,600 $746,000 $43,140 $0 $17,460 $17,460 $43,1403 $1,030,301 $61,206 $50,000 $11,206 $0 $0 $11,206 $744,000 $43,030 $0 ($31,824) ($31,824) $43,0304 $1,040,604 $61,818 $0 $61,818 $0 $0 $61,818 $742,000 $42,920 $0 $18,898 $18,898 $42,9205 $1,051,010 $62,436 $0 $62,436 $0 $0 $62,436 $740,000 $42,810 $0 $19,626 $19,626 $42,8106 $1,061,520 $63,061 $0 $63,061 $0 $0 $63,061 $738,000 $42,700 $0 $20,361 $20,361 $42,7007 $1,072,135 $63,691 $0 $63,691 $0 $0 $63,691 $736,000 $42,590 $0 $21,101 $21,101 $42,5908 $1,082,857 $64,328 $50,000 $14,328 $0 $0 $14,328 $734,000 $42,480 $0 ($28,152) ($28,152) $42,4809 $1,093,685 $64,971 $0 $64,971 $0 $0 $64,971 $732,000 $42,370 $0 $22,601 $22,601 $42,370

10 $1,104,622 $65,621 $0 $1,170,243 $0 $0 $1,170,243 $730,000 $772,260 $0 $397,983 $397,983 $772,260





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63

APV(equity) = +104,714 - $82,202 = +$22,512.

From property investment From loan

P.F. has:• Positive NPV (+104,714) in property investment as intra-marginal buyer,• Negative NPV (-82,202) in loan borrowing transaction as its tax-exempt status makes it an intra-marginal lender (not borrower).• Net is still slightly positive (APV).

Would be better off not using debt to finance the investment (unless capital constrained).



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64

Pension Fund: IVA = $1,104,714 = PV(patcfA @ 4.76%)

MV = $1,000,000 = PV(pbtcf @ 6.04%) = PV(patcfM @ 4.76%)+loan amt –

PV(loanatcf @ 4.13%) = IVM

D


Q*

SP

Q0

Market for Apt Properties:

Mkt going-in IRR = 6.04%

Pension fund is an intra-marginal buyer.

Marginal investor (Marginal investor (MM) is ) is marginal in marginal in propertypropertymarket (faces 35% tax market (faces 35% tax rate).rate).

Representing this as in Ch.12 market model, we have for the property market . . .



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65

MV = $750,000 = PV(loanbtcf @ 5.5%) = PV(loanatcfM @ 4.13%) = IVM

Q*

D

S


P

Q0

Market for Mortgages:

Mkt Interest Rate = 5.5%

Representing this as in Ch.12 market model, we have for the mortgage market . . .

Pension fund is an intra-marginal buyer (lender, not borrower).

Pension Fund: IVA = $832,202 = PV(loanatcfA @ 4.13%)

Marginal investor (Marginal investor (MM) is ) is marginal in marginal in debtdebt market market (faces 25% tax rate).(faces 25% tax rate).



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Commercial Mortgage AnalysisCommercial Mortgage Analysis

& Underwriting& Underwriting



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Section 18.1:Section 18.1:

Expected Returns Expected Returns vsvs Stated YieldsStated Yields

Measuring the Impact of Default RiskMeasuring the Impact of Default Risk



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““Expected ReturnsExpected Returns”” versus versus ““Stated YieldsStated Yields”” . . .. . .

In a bond or mortgage (capital asset with contractual cash flowsIn a bond or mortgage (capital asset with contractual cash flows):):

Stated YieldStated Yield (aka (aka ““Contractual YieldContractual Yield””) = YTM based on ) = YTM based on contractual obligationcontractual obligation..

Expected ReturnExpected Return (aka (aka ““Expected YieldExpected Yield”” or or ““Ex Ante YieldEx Ante Yield””) ) = = EE[[rr] = Mean of probability distribution of future total ] = Mean of probability distribution of future total return on the bond or mortgage investment.return on the bond or mortgage investment.

••Quoted yields are always Quoted yields are always stated yieldsstated yields..••Contract yields are used in Contract yields are used in mortgage design and mortgage design and evaluation.evaluation.

••Expected return is more Expected return is more fundamentalfundamental measure for measure for mortgage investors,mortgage investors,•• For making investment For making investment decisions.decisions.

Difference: Difference: Stated Yield Stated Yield –– Expected Return Expected Return

Impact of Impact of Default RiskDefault Risk in in ex anteex ante return investor cares about.return investor cares about.www.bsscommunitycollege.in www.bssnewgeneration.in www.bsslifeskillscollege.in


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18.1.1 Yield Degradation & Conditional Cash Flows18.1.1 Yield Degradation & Conditional Cash Flows……

““Credit LossesCredit Losses”” = Shortfalls to the lender (mortgage investor) as a result = Shortfalls to the lender (mortgage investor) as a result of of defaultdefault and and foreclosureforeclosure..

““Realized YieldRealized Yield”” = What the lender (investor) actually receives (as an = What the lender (investor) actually receives (as an IRR).IRR).

““Yield DegradationYield Degradation”” = Impact of = Impact of credit lossescredit losses on the lenderon the lender’’s realized yield s realized yield as compared to the contractual yield (expressed in IRR units).as compared to the contractual yield (expressed in IRR units).

Contractual YieldContractual Yield

-- Yield Degradation Yield Degradation Due to Due to Credit LossesCredit Losses

----------------------------------------------------

= Realized Yield= Realized Yield

Yield DegradationYield Degradation ((““YDEGRYDEGR””) = Lender) = Lender’’s losses measured as a multis losses measured as a multi--period lifetime return on the original investment (IRR impact).period lifetime return on the original investment (IRR impact).



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Numerical example of Numerical example of Yield DegradationYield Degradation::

•• $100 loan.$100 loan.•• 3 years, annual payments in arrears.3 years, annual payments in arrears.•• 10% interest rate.10% interest rate.•• InterestInterest--only loan.only loan.

Here are the Here are the contractual contractual terms of the loan as an NPV equation:terms of the loan as an NPV equation:

( ) ( )32 )10.0(1110$

)10.0(110$

)10.0(110$100$0

++

++

++−=

Contractual YTM = 10.00%.Suppose:Suppose:

•• Loan defaults in 3Loan defaults in 3rdrd year.year.•• Bank takes property & sells in foreclosure, butBank takes property & sells in foreclosure, but•• Bank only gets 70% of OLB: $77.Bank only gets 70% of OLB: $77.

( ) ( )32 )0112.0(177$

)0112.0(110$

)0112.0(110$100$0

−++

−++

−++−=

Here are the Here are the realizedrealized cash flows of the loan as an NPV equation:cash flows of the loan as an NPV equation:

Realized IRR = -1.12% Yield Degradation = 11.12%:

Contract.YTM – Yld Degrad = Realized Yld:10.00%. – 11.12% = -1.12%.

• $33 = “Credit Losses”.• 70% = “Recovery Rate”.• 30% = “Loss Severity”.



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From an From an ex anteex ante perspective, this 11.12% yield degradation is a perspective, this 11.12% yield degradation is a ““conditionalconditional”” yield degradationyield degradation. .

It is the yield degradation that will occur It is the yield degradation that will occur ifif the loan defaults in the third the loan defaults in the third year, and year, and ifif the lender gets 70% of the OLB at that time. the lender gets 70% of the OLB at that time.

(Also, 70% is a (Also, 70% is a conditionalconditional recovery rate.)recovery rate.)

( )2)0711.0(177$

)0711.0(110$100$0

−++

−++−=

Suppose the default occurred in the 2Suppose the default occurred in the 2ndnd year instead of the 3year instead of the 3rdrd::

Yield Degradation = -17.11%.

Other things being equal (in particular, the conditional recoverOther things being equal (in particular, the conditional recovery y rate), rate), the conditional yield degradation is greater, the earlier the the conditional yield degradation is greater, the earlier the default occurs in the loan lifedefault occurs in the loan life. .

From a loan lifetime performance perspective, lenders are hit woFrom a loan lifetime performance perspective, lenders are hit worse when rse when default occurs early in the life of a mortgage.default occurs early in the life of a mortgage.



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Note: Note: ““YDEGRYDEGR”” as defined in the previous example was:as defined in the previous example was:•• The reduction in the IRR (yield to maturity) below the The reduction in the IRR (yield to maturity) below the contract rate, contract rate, •• ConditionalConditional on default occurring (in the 3on default occurring (in the 3rdrd year), and year), and •• Based on a specified conditional Based on a specified conditional recovery raterecovery rate (or (or loss loss severityseverity) in the event that default occurs.) in the event that default occurs.

tttt DEFseveritylossIRRYTMDEFYLDYTMYDEGR )(−=−=

( ) ( )32 )0287.0(188$

)0287.0(110$

)0287.0(110$100$0

++

++

++−=

For example, if the loss severity were 20% instead of 30%, For example, if the loss severity were 20% instead of 30%, then the conditional yield degradation would be 7.13% then the conditional yield degradation would be 7.13% instead of 11.12%:instead of 11.12%:

YDEGR3 = 10% - 2.87% = 7.13%.



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Relation between Relation between Contract YieldContract Yield, , Conditional Yield DegradationConditional Yield Degradation, , & the & the Expected ReturnExpected Return on the mortgageon the mortgage……

Expected return is an Expected return is an ex anteex ante measure.measure.To compute it we must specify:To compute it we must specify:

•• Ex anteEx ante probability of defaultprobability of default, & , & •• CConditional recovery rateonditional recovery rate (or the (or the conditional loss severityconditional loss severity) that will occur in ) that will occur in the event of default.the event of default.

Suppose that at the time the mortgage is issued, there is:Suppose that at the time the mortgage is issued, there is:•• 10% chance of default in 310% chance of default in 3rdrd year.year.•• 70% conditional recovery rate for such default.70% conditional recovery rate for such default.•• No chance of any other default event.No chance of any other default event.

Then at the time of mortgage issuance, the Then at the time of mortgage issuance, the expected returnexpected return is:is:EE[[rr] = 8.89%] = 8.89% = (0.9)10.00% + (0.1)(= (0.9)10.00% + (0.1)(--1.12%)1.12%)

= (0.9)10.00% + (0.1)(10.00%= (0.9)10.00% + (0.1)(10.00%--11.12%)11.12%)

= 10.00% = 10.00% -- (0.1)(11.12%) = 8.89%.(0.1)(11.12%) = 8.89%.In general: In general: Expected Return = Contract Yield – Prob. of Default * Yield Degradation.

EE[[rr] = YTM ] = YTM –– ((PrDEF)(YDEGRPrDEF)(YDEGR) ) www.bsscommunitycollege.in www.bssnewgeneration.in www.bsslifeskillscollege.in


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What would be the expected return if the ex ante default What would be the expected return if the ex ante default probability and conditional credit loss expectations were:probability and conditional credit loss expectations were:

•• 80% chance of no default;80% chance of no default;•• 10% chance of default in 210% chance of default in 2ndnd year with 70% conditional recovery;year with 70% conditional recovery;•• 10% chance of default in 310% chance of default in 3rdrd year with 70% conditional recovery.year with 70% conditional recovery.

??

Answer:Answer:EE[[rr] = YTM ] = YTM –– ΣΣ((PrDEF)(YDEGRPrDEF)(YDEGR))

EE[[rr] = 10% ] = 10% –– (.1)(11.12%) (.1)(11.12%) –– (.1)(17.11%) = 10% (.1)(17.11%) = 10% -- 2.82% = 7.18%.2.82% = 7.18%.



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Note: The probabilities we were working with in the previous Note: The probabilities we were working with in the previous example:example:

•• 80% chance of no default;80% chance of no default;•• 10% chance of default in 210% chance of default in 2ndnd year;year;•• 10% chance of default in 310% chance of default in 3rdrd year.year.

Were Were ““unconditionalunconditional probabilitiesprobabilities”” as of the time of mortgage as of the time of mortgage issuance:issuance:

•• They did not depend on any preThey did not depend on any pre--conditioning event;conditioning event;•• They describe an exhaustive and mutuallyThey describe an exhaustive and mutually--exclusive set of possible exclusive set of possible outcomes for the mortgage, i.e.,:outcomes for the mortgage, i.e.,:•• The probabilities sum to 100% across all the eventualities.The probabilities sum to 100% across all the eventualities.



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18.1.2 Hazard Functions and the Timing of Default18.1.2 Hazard Functions and the Timing of Default……

More realistic and detailed analysis of mortgage (or bond) defauMore realistic and detailed analysis of mortgage (or bond) default lt probability (and the resulting impact of credit losses on expectprobability (and the resulting impact of credit losses on expected returns) ed returns) usually works with usually works with conditionalconditional probabilitiesprobabilities of default, what is known as a:of default, what is known as a:

Hazard FunctionHazard Function

The hazard function tells the The hazard function tells the conditional probabilityconditional probability of default at each point of default at each point in time in time given thatgiven that default has not already occurred before then.default has not already occurred before then.

Year: Hazard:1 1%2 2%3 3%

Example: Suppose this is the Example: Suppose this is the hazard functionhazard function for the previous 3for the previous 3--yr loan:yr loan:

i.e., There is:i.e., There is:•• 1% chance loan will default in the 11% chance loan will default in the 1stst year (i.e., at the time of the first payment);year (i.e., at the time of the first payment);•• 2% chance loan will default in 22% chance loan will default in 2ndnd year year if it has not already defaulted in the 1if it has not already defaulted in the 1stst yearyear; &; &•• 3% chance loan will default in 33% chance loan will default in 3rdrd year year given that it has not already defaulted by thengiven that it has not already defaulted by then..



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Year

Hazard

ConditionalSurvival

CumulativeSurvival

UnconditionalPrDEF

CumulativePrDEF

1 0.01 1-.01 = 0.9900 0.99*1.0000 = 0.9900 .01*1.0000 = 0.0100 0.01002 0.02 1-.02 = 0.9800 0.98*0.9900 = 0.9702 .02*0.9900 = 0.0198 .0100+.0198 = 0.02983 0.03 1-.03 = 0.9700 0.97*0.9702 = 0.9411 .03*0.9702 = 0.0291 .0298+.0291 = 0.0589

Example: Suppose this is the Example: Suppose this is the hazard functionhazard function for the previous 3for the previous 3--yr loan:yr loan:Year: Hazard:

1 1%2 2%3 3%

Given the hazard function for a mortgage, we can compute the cumGiven the hazard function for a mortgage, we can compute the cumulative ulative and unconditional default and survival probabilities.and unconditional default and survival probabilities.

Then the table below computes the unconditional and cumulative dThen the table below computes the unconditional and cumulative default efault probabilities for this loan:probabilities for this loan:

• “Conditional Survival Probability” (for year t) = 1 – Hazard for year t.• “Cumulative Survival Prob.” (for year t) = Probability loan survives through that yr.• “Unconditional Default Prob.” (for year t) = Prob.(as of time of loan origination) that loan will default in the given year (t) = Hazard * Cumulative Survival (t-1) = Cumulative Survival (t) –Cumulative Survival (t-1).• “Cumulative Default Prob.” (yr.t) = Prob.(as of time of loan origination) that loan will default any time up through year t.

In this case: In this case: 5.89% unconditional probability5.89% unconditional probability (as of time of origination) that this (as of time of origination) that this loan will default (at some point in its life). loan will default (at some point in its life). 5.89% = 1.00% + 1.98% + 2.91% = 1 – 0.9411.www.bsscommunitycollege.in www.bssnewgeneration.in www.bsslifeskillscollege.in


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( )( )∑=

−=T

ttt YDEGRDEFYTMrE

1Pr][

For each year in the life of the loan, a conditional yield degraFor each year in the life of the loan, a conditional yield degradation can be computed, dation can be computed, conditional on default occurring in that year, and given an assuconditional on default occurring in that year, and given an assumption about the mption about the conditional recovery rate in that year. conditional recovery rate in that year.

For example, we saw that with previous 3For example, we saw that with previous 3--yr loan the conditional yield degradation was yr loan the conditional yield degradation was 11.12% if default occurs in year 3, and 17.11% if default occurr11.12% if default occurs in year 3, and 17.11% if default occurred in year 2, in both ed in year 2, in both cases assuming a 70% recovery rate. cases assuming a 70% recovery rate.

Similar calculations reveal that the conditional yield degradatiSimilar calculations reveal that the conditional yield degradation would be 22.00% if on would be 22.00% if default occurs in year 1 with an 80% recovery rate.* default occurs in year 1 with an 80% recovery rate.*

Defaults in each year of a loanDefaults in each year of a loan’’s life and no default at all in the life of the loan s life and no default at all in the life of the loan represent mutuallyrepresent mutually--exclusive events that together exhaust all of the possible defauexclusive events that together exhaust all of the possible default lt timing occurrences for any loan. timing occurrences for any loan.

For example, with the threeFor example, with the three--year loan, Borrower will either default in year 1, year 2, year loan, Borrower will either default in year 1, year 2, year 3, or never. year 3, or never.

Thus, the expected return on the loan can be computed as the conThus, the expected return on the loan can be computed as the contractual yield minus tractual yield minus the sum across all the years of the products of the the sum across all the years of the products of the unconditionalunconditional default probabilities default probabilities times the conditional yield degradations.times the conditional yield degradations.



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Example:Example:

•• Given previous hazard function (1%, 2%, and 3% for the successGiven previous hazard function (1%, 2%, and 3% for the successive years);ive years);

•• Given conditional recovery rates (80%, 70%, and 70% for the suGiven conditional recovery rates (80%, 70%, and 70% for the successive ccessive years);years);

•• Expected return on the 3Expected return on the 3--yr 10% mortgage at the time it is issued would be:yr 10% mortgage at the time it is issued would be:

E[rE[r]] =10.00%=10.00%--((.0100)(22.00%)+(.0198)(17.11%)+(.0291)(11.12%))((.0100)(22.00%)+(.0198)(17.11%)+(.0291)(11.12%))

=10.00% =10.00% -- 0.88% 0.88%

= 9.12%.= 9.12%.

The 88 basisThe 88 basis--point shortfall of the expected return below the contractual yiepoint shortfall of the expected return below the contractual yield ld is the is the ““ex ante yield degradationex ante yield degradation”” (aka: (aka: ““unconditional yield degradationunconditional yield degradation””).).

It reflects the ex ante credit loss expectation in the mortgage It reflects the ex ante credit loss expectation in the mortgage as of the time of as of the time of its issuance.its issuance.



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( )( )

( )( )

( ) ( )( )

( )( ) ( )( )∑ ∑

∑

∑

∑

= =

=

=

=

==

+=

−−=

−=

N

i

N

iiiii

T

ttt

T

ttt

T

ttt

CFIRRSCENYLDSCEN

DEFYLDDEFYTMNODEF

DEFYLDYTMDEFYTM

YDEGRDEFYTMrE

1 1

1

1

1

)(PrPr

PrPr

Pr

Pr][

( )( )⎟⎠

⎞⎜⎝

⎛= ∑

=

N

iii CFSCENIRRrE

1Pr][

““Method 2Method 2”” ““Expected CFExpected CF--basedbased””, or , or ““Pooled CFPooled CF--basedbased””, , IRR(EIRR(E[[CFCF]])) : : Take the expectation over the conditional cash flows and then coTake the expectation over the conditional cash flows and then compute the mpute the return on the expected cash flow stream:return on the expected cash flow stream:

Makes sense if investor preferences are based on the cash flows Makes sense if investor preferences are based on the cash flows achieved.achieved.

Two alternative ways to compute the Two alternative ways to compute the expected returnexpected return . . .. . .““Method 1Method 1”” ““ReturnReturn--basedbased”” (as previously described) (as previously described) EE[[IRR(CF)IRR(CF)] : ] : Take the expectation over the conditional returnsTake the expectation over the conditional returns……

Makes sense if investor preferences are based on the return achiMakes sense if investor preferences are based on the return achieved.eved.

Most commonly used.



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18.1.3 Yield Degradation in Typical Commercial Mortgages18.1.3 Yield Degradation in Typical Commercial Mortgages……

The most widely used empirical evidence on commercial mortgage hThe most widely used empirical evidence on commercial mortgage hazard azard rates in the U.S. is that of rates in the U.S. is that of SnydermanSnyderman and subsequent studies at Morganand subsequent studies at Morgan--Stanley.*Stanley.*

Typical Commercial Mortgage Hazard Rates*

0.0%

0.2%

0.4%

0.6%

0.8%

1.0%

1.2%

1.4%

1.6%

1.8%

2.0%

1 3 5 7 9 11 13 15 17 19 21 23 25

Loan Life Year *Source: Esaki et al (2002)

Con

ditio

nal D

efau

lt Pr

obab

ility



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The implied survival function and cumulative default probabilityThe implied survival function and cumulative default probability is shown is shown here:here:

Overall Average Default Probability = 16%.Overall Average Default Probability = 16%.

1 out of 6 commercial mortgages in the U.S. default at some poin1 out of 6 commercial mortgages in the U.S. default at some point in t in their lives.their lives.

Typical Commercial Mortgage Survival Rates*

0.80

0.82

0.84

0.86

0.88

0.90

0.92

0.94

0.96

0.98

1.00

1 3 5 7 9 11 13 15 17 19 21 23 25Loan Life Year

*Source: Esaki at al (2002)

Cum

ulat

ive

Surv

ival

Pro

babi

lity



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Loan lifetime default probabilities are strongly influenced by tLoan lifetime default probabilities are strongly influenced by the time he time (phase of the real estate market cycle) at which the loan was or(phase of the real estate market cycle) at which the loan was originated:iginated:

Why do you suppose this is so?Why do you suppose this is so?And what do you think about it?And what do you think about it?

Lifetime default rates & property values

0%

5%

10%

15%

20%

25%

30%

72 74 76 78 80 82 84 86 88 90 92 94 96

Year of loan origination *Esaki (2002), **NCREIF (unsmoothed)

Life

time

defa

ult r

ate*

0.0

0.5

1.0

1.5

2.0

Prop

erty

val

ue in

dex*

*www.bsscommunitycollege.in www.bssnewgeneration.in www.bsslifeskillscollege.in


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Combining empirical data on conditional recovery rates (typicallCombining empirical data on conditional recovery rates (typically assumed y assumed to be between 60% and 70%), we can estimate the typical ex ante to be between 60% and 70%), we can estimate the typical ex ante yield yield degradation in U.S. commercial mortgagesdegradation in U.S. commercial mortgages……

Typical Yield Degradation:Typical Yield Degradation:60 to 120 basis points.60 to 120 basis points.

Similar results are observed in the Similar results are observed in the GilibertoGiliberto--Levy Commercial Mortgage Levy Commercial Mortgage Index (GLCMI)Index (GLCMI), the major index of commercial mortgage (, the major index of commercial mortgage (““whole loanwhole loan””) ) periodic ex post returns (periodic ex post returns (HPRsHPRs).).

19721972--2004 2004 AvgAvg ==

62 basis points*62 basis points*

Commercial Mortgage Credit Loss as Fraction of Par Value*

0

50

100

150

200

250

300

72 74 76 78 80 82 84 86 88 90 92 94 96 98 00 02 04

Year *Source: GLCMPI (John B. Levy & Co.)

Bas

is P

oint

s



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Consider relation between:Consider relation between:•• LTV,LTV,•• Property Risk (volatility), Property Risk (volatility), •• Loan Default Probability.Loan Default Probability.

A simplified exampleA simplified example……(Text box p. 447)

SupposeSuppose……•• Initial Prop. Val = $100, Initial Prop. Val = $100, E[gE[g] = 2%/yr.] = 2%/yr.

•• 75% LTV (No 75% LTV (No amortamort OLB = $75 constant).OLB = $75 constant).

•Average loan default occurs in year 7 of loan life (Esaki).

• Individ. Prop. Ann. Volatility (Std.Dev[g]) = 15%.

• Prop. Val follows random walk (effic. mkt.).

• ( )VolatilityAnnTVolatilityyrT .=

Is 16% Is 16% avgavg lifetime default probability surprisingly high? . . .lifetime default probability surprisingly high? . . .



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A simplified exampleA simplified example……

Thus, After 7 years:

• E[Val] = 1.027(100) = 115

• Std.Dev[Val] =

• 1 Std.Dev below E[Val] = $115 - $40 = $75.• If Prob[Val] ~ Normal, 1/6 chance Val < OLB, Loan “under water” (large chance of default in that case).

( )( )( )

( ) .40100%40100%15*6.2

100%157

±=±==

Property value

1/6 Probability

1/6 Probability

Probability

7 Years

7575

100

Loan OLB

115

155

+40

-40

}}

Image by MIT OCW.



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Section 18.2:

Commercial Mortgage UnderwritingCommercial Mortgage Underwriting



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“Underwriting”= Process lenders go through to decide to issue = Process lenders go through to decide to issue

a commercial mortgage, and the terms of the a commercial mortgage, and the terms of the loan:loan:

Loan Origination (Loan Origination (““primaryprimary”” market)market)..

• Often a negotiation type process (esp. for large loans): Commercial Mortgage business is a “custom” shop.

• Standard criteria may sometimes be “bent”(esp. for large borrowers, or when the market is “hot”), but provide the basic guidelines.



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Basic Purpose of Underwriting:

To make default a rare event.But no one can operate But no one can operate ““outside the marketoutside the market”…”…

Supply & Demand:Supply & Demand:• Most borrowers cannot (or do not want to) conform to underwriting standards so tight as to eliminate default risk (even if that would get them T-Bond interest rates).

• Lenders must conform to the market in order to “play the game”: Modify loan terms so that E[r] is sufficient to compensate for default risk.



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Two Foci of Underwriting:Borrower & Property

1) Borrower:1) Borrower:

On the downside:i) Can “bleed” healthy property as “cash cow”.ii) Can use Ch.11 if they get in trouble (“cramdown”).iii) Financial health of borrower is important.iv) Check “parent” company.

On the upside:i) Potential “repeat customer”.ii) Consider size, track record, future potential.



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2) Property:2) Property:

Generally more important than borrower:Generally more important than borrower:i) Main source of CF to service loan.ii) Comm.Mtgs effectively “non-recourse”.iii) Careful lender w well-crafted loan: strong

property counts more than strong borrower.

Standard PropertyStandard Property--level Underwriting Criteria:level Underwriting Criteria:i) Asset value criteria...ii) Property income criteria...

Two Foci of Underwriting:Borrower & Property



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Asset Value Criterion:Initial Loan-to-Value Ratio (LTV)

LTV = L/VExh. 18-5: Typical relationship between initial LTV ratio and the ex ante

lifetime default probability on a commercial property mortgage:

LTV Ratio

Default Prob.



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Relation between:Relation between:•• LTV,LTV,•• Property Risk (volatility), Property Risk (volatility), •• Loan Default Probability.Loan Default Probability.

A simplified exampleA simplified example……(Text box p. 447)

SupposeSuppose……•• Initial Prop. Val = $100, Initial Prop. Val = $100, E[gE[g] = 2%/yr.] = 2%/yr.

•• 75% LTV (No 75% LTV (No amortamort OLB = $75 constant).OLB = $75 constant).

•Average loan default occurs in year 7 of loan life.

• Individ. Prop. Ann. Volatility (Std.Dev[g]) = 15%.

• Prop. Val follows random walk (effic. mkt.).

• ( )VolatilityAnnTVolatilityyrT .=



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Relation between:Relation between:•• LTV,LTV,•• Property Volatility, & Property Volatility, & •• Loan Default Probability.Loan Default Probability.

A simplified exampleA simplified example……

Thus, After 7 years:

• E[Val] = 1.027(100) = 115

• Std.Dev[Val] =

• 1 Std.Dev below E[Val] = $115 - $40 = $75.

• If Prob[Val] ~ Normal, 1/6 chance Val < OLB, Loan “under water” (large chance of default in that case).

( )( )( )

( ) .40100%40100%15*6.2

100%157

±=±==

Property value

1/6 Probability

1/6 Probability

Probability

7 Years

7575

100

Loan OLB

115

155

+40

-40

}}

Image by MIT OCW.



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Greater Property Volatility (Risk) Greater Property Volatility (Risk) Lower LTV corresponds to a given lifetime Lower LTV corresponds to a given lifetime default probability.default probability.Lower Max LTV Limit in underwriting Lower Max LTV Limit in underwriting criteria.criteria.

The point is . . .

Typical LTVLTV limit in commercial mortgages on good quality stabilized properties is 75%75%.

• Based on lower of appraisal or purchase price.• Based on lower of DCF or Direct Cap.• Sometimes “bent”, or fudged in appraisal, due to market pressure.



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Property Income Criteria…

1) 1) Debt Service Coverage Ratio (DCR):Debt Service Coverage Ratio (DCR):

DCR = NOI / DS

Typical: DCR >= 120%



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2) Break-even Ratio (BER):

BER = (DS+OE) / PGI

Occupancy ratio required for EBTCF > 0 (Occupancy ratio required for EBTCF > 0 (excluexclu CI)CI)

Lender usually requires BER < (100% Lender usually requires BER < (100% -- MktMkt VacVac))

Typical: BER <= 85%, or less than Typical: BER <= 85%, or less than mktmkt avgavgoccupanceoccupance minus some buffer (typically 5%).minus some buffer (typically 5%).



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3) Equity Before-Tax Cash Flow (EBTCF):

EBTCF = NOI – DS – CISimilar to DCR, only includes effect of CI.

Projection of EBTCF < 0 any year of loan “Red Flag”.



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4) Multi-year Pro-Forma Projection:

In principle, lenders project income ratios for all years of loan life.



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Variables and loan terms to negotiate:

•• Loan AmountLoan Amount•• Loan Term (maturity)Loan Term (maturity)•• Contract Interest RateContract Interest Rate•• Amortization rateAmortization rate•• UpUp--front fees and pointsfront fees and points•• Prepayment option and backPrepayment option and back--end penaltiesend penalties•• Recourse vs. NonRecourse vs. Non--recourse debtrecourse debt•• Collateral (e.g., crossCollateral (e.g., cross--collateralization)collateralization)•• Lender participation in property equityLender participation in property equity•• CramdownCramdown insurance insurance •• Etc. . . .Etc. . . .



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Underwriting Example

The Problem:The Problem:• Buyer (borrower) & seller claim property worth $12,222,000;• Buyer wants to borrow 75% ($9.167 Million, or $91.67/SF) from you (mortgage lender), for purchase-money 1st mortgage;• Wants non-recourse, 10-yr interest-only loan, monthly pmts;• Willing to accept “lock-out”.•• Should you do the deal?Should you do the deal?



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Current Capital Market Information:Current Capital Market Information:• In Bond Mkt: 10-yr US Govt Bonds yielding 6.00%.• In Mortg Mkt: 10-yr balloon lock-out commercial

mortgages require risk premium in contract total yield typically 200bp (CEY) spread over TBonds for good properties, non-recourse.

• Loan YTM = 6% + 2% = 8% CEY,• What EAY & MAY?• EAY = 8.16%, 7.87% MEY required YTM7.87% MEY required YTM.

Underwriting Example (cont.)



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Underwriting Criteria (from capital provider):Underwriting Criteria (from capital provider):1. Max Initial LTV = 75%.2. Max projected terminal LTV = 65%.3. In computing LTV, normally: (i) Apply direct

capitalization with going-in cap rate ≥ 9%, terminal cap rate ≥ 10%; (ii) Apply multi-yr DCF with Disc. Rate ≥ 10%; (iii) Use lower of (i) & (ii) to compute Initial LTV.

4. Min DCR = 120%.5. Max BER = 85%, or 5% less than mkt vac

(whichever is less).6. Consider need for CI, and avoid EBTCF < 0.


Loan must conform to these criteria, given capital market Loan must conform to these criteria, given capital market (yield requirement) and property markets (space & asset (yield requirement) and property markets (space & asset mktsmkts value & income criteria).value & income criteria).



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Property & R.E. Market Information (from Property & R.E. Market Information (from broker):broker):

• 100,000SF, fully occupied, single-tenant, off.bldg.• 10-yr lease signed 3 yrs ago.• $11/SF net (suppose EOY ann. pmts).• "Step-ups" of $0.50 in lease yr.5 & 8 (yrs 2 & 5).• Current mkt rents on new 10-yr leases are $12/SF

net.• Expect mkt rents to grow @ 3%/yr. (same age).




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Solution, General Procedure . . .

Step 1: Construct 10-yr "Proforma": 1) Forecast Property Cash Flows 2) Calculate Loan Debt Service Cash Flows for Requested Loan Step 2: Examine DCR, BER, EBTCF, @ Requested Loan: Is there Compliance with Income Underwriting Criteria?... Step 3: Estimate Property Value (Use Direct Capitalization &/or DCF): Is there Compliance with Value Underwriting Criterion?... Step 4: If Compliance Fails in either Step 2 or 3: How can loan be modified to meet underwriting criteria?... How much (and why) is lender willing to "bend" underwriting criteria to make loan?... --> What "yield enhancements" (e.g., "origination fee") would temp lender? --> What security enhancements (e.g., "recourse", "multi-collateral", “cramdown”

insur) would assuage lender?



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Underwriting Example (cont.)Broker’s pro-forma submitted with loan request. . . Assumes: 75% renewal probability 3 mo. Vacancy if non-renewal No provision for CI (inclu leasing expenses). Yr.10 cap rate = 9%.

Year: 1 2 3 4 5 6 7 8 9 10 Year 11Mkt Rent (net) /SF $12.36 $12.73 $13.11 $13.51 $13.91 $14.33 $14.76 $15.20 $15.66 $16.13 $16.61Property Rent(net) $11.00 $11.50 $11.50 $11.50 $12.00 $12.00 $12.00 $15.20 $15.20 $15.20 $15.20Vacancy Allow $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00NOI/SF $11.00 $11.50 $11.50 $11.50 $12.00 $12.00 $12.00 $15.20 $15.20 $15.20 $15.20NOI $1,100,000 $1,150,000 $1,150,000 $1,150,000 $1,200,000 $1,200,000 $1,200,000 $1,520,124 $1,520,124 $1,520,124 $1,520,124Reversion@9%Cap $16,890,268

So, you need to deal with the usual . . .So, you need to deal with the usual . . .You make following modified assumptions:You make following modified assumptions:• 1% Market rental growth for existing bldg (3%-2%depr).• Yr.8 Leasing expenses: $2/SF if renew, $5/SF not renew.• Yr.8 TI: $10/SF if renew, $20/SF if not renew.• Yr.10 cap rate = 10%.



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Your adjusted pro-forma (based on research): Assumes: 1% Market rental growth for existing bldg (3%-2%depr). Yr.8 Leasing expenses: $2/SF if renew, $5/SF not renew. Yr.8 TI: $10/SF if renew, $20/SF if not renew. Yr.10 cap rate = 10%.


Note income underwriting criteria for $9,167,000, 7.87% loan. DCR & BER look good. How were these computed?...

Year: 1 2 3 4 5 6 7 8 9 10 Year 11Mkt Rent (net) /SF $12.12 $12.24 $12.36 $12.49 $12.61 $12.74 $12.87 $12.99 $13.12 $13.26 $13.39Property Rent(net) $11.00 $11.50 $11.50 $11.50 $12.00 $12.00 $12.00 $12.99 $12.99 $12.99 $12.99Vacancy Allow $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.81 $0.00 $0.00 $0.00NOI/SF $11.00 $11.50 $11.50 $11.50 $12.00 $12.00 $12.00 $12.18 $12.99 $12.99 $12.99NOI $1,100,000 $1,150,000 $1,150,000 $1,150,000 $1,200,000 $1,200,000 $1,200,000 $1,218,214 $1,299,428 $1,299,428 $1,299,428Lease Comm $0 $0 $0 $0 $0 $0 $0 -$275,000 $0 $0Ten.Imprv $0 $0 $0 $0 $0 $0 $0 -$1,250,000 $0 $0Reversion@10%Cap $12,994,280Less OLB $9,167,000PBTCF $1,100,000 $1,150,000 $1,150,000 $1,150,000 $1,200,000 $1,200,000 $1,200,000 -$306,786 $1,299,428 $14,293,709Debt Svc -$721,443 -$721,443 -$721,443 -$721,443 -$721,443 -$721,443 -$721,443 -$721,443 -$721,443 -$9,888,443EBTCF $378,557 $428,557 $428,557 $428,557 $478,557 $478,557 $478,557 ($1,028,229) $577,985 $4,405,266DCR 152% 159% 159% 159% 166% 166% 166% 169% 180% 180%BER @ Mkt 60% 59% 58% 58% 57% 57% 56% 56% 55% 54%



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DCR (Yr.1) = NOI / DS = $1,100,000 / $721,443 = 1.52

BER (Yr.1) = (OE + DS) / PGI = ($0 + $7.214) / $12.12 = 0.60(Note use of current mkt rent in BER: Consistent with intent of that ratio.)

DS from: $9,167,000 X 7.87% = $721,443, in Interest-Only Loan.

Although standard income ratios look good, this loan Although standard income ratios look good, this loan does have some problems. does have some problems.




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One problem is in the income criteria. Can you spot it in the proforma?...

Another problem is in the initial LTV:Another problem is in the initial LTV:•• Based on direct capitalization, loan passes OK:Based on direct capitalization, loan passes OK:

•• $1,100,000 / 9% = $12.22 M, $1,100,000 / 9% = $12.22 M, LTV = 9.167 / 12.22 = 75%.LTV = 9.167 / 12.22 = 75%.

•• But the DCF @ 10% gives PV(PBTCF) = $11,557,000.But the DCF @ 10% gives PV(PBTCF) = $11,557,000.•• 9.167 / 11.557 = 79%.9.167 / 11.557 = 79%.


Negative EBTCF in Yr. 8

A similar problem is in the Terminal LTV:A similar problem is in the Terminal LTV:•• $9,167,000 / $12,994,280 = 71%, which is > the 65% limit.$9,167,000 / $12,994,280 = 71%, which is > the 65% limit.www.bsscommunitycollege.in www.bssnewgeneration.in www.bsslifeskillscollege.in


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Problems in the loan proposal: Income: Projected EBTCF (Yr.8) = -$1,028,229 < 0. Value: Initial LTV Ratio = 79% > 75% (in DCF @ 10%, OK in dir.cap) Terminal LTV Ratio = 71% > 65% (@ 10% cap rate). But EBTCF < 0 is:

Due mostly to cap impr (financing possible?). Far in future (when inflation will have improved default risk). After much previous positive cash flow. Not untypical in single-tenant bldg. And Value criteria are missed only slightly. So loan is “close” to passing criteria.


How good a future potential How good a future potential ““customercustomer”” is this borrower?is this borrower?How much pressure is there in the loan market?How much pressure is there in the loan market?

Try to negotiate a similar loan? . .Try to negotiate a similar loan? . . ..www.bsscommunitycollege.in www.bssnewgeneration.in www.bsslifeskillscollege.in


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Consider a $8,700,000 loan with 40Consider a $8,700,000 loan with 40--yr yr AmortAmort. 10. 10--yr balloon yr balloon (instead of $9,167,000, Interest(instead of $9,167,000, Interest--Only):Only):


$9,167,000 Int-Only $8,700,000 40-yr Amort PMT $721,443 $715,740 Initial OLB $9,167,000 $8,700,000 Initial LTV Ratio 79% 75% Terminal OLB $9,167,000 $8,230,047 Terminal LTV Ratio 71% 63%



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CHAPTER 17: CHAPTER 17:

MORTGAGE BASICS II:Payments, Yields, & Values



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The “Four Rules” of Loan Payment & Balance Computation. . .

• Rule 1: The interest owed in each payment equals the applicable interest rate times the outstanding principal balance (aka: “outstanding loan balance”, or “OLB” for short) at the end of the previous period: INTt = (OLBt-1)rt.

• Rule 2: The principal amortized (paid down) in each payment equals

the total payment (net of expenses and penalties) minus the interest owed: AMORTt = PMTt - INTt.

• Rule 3: The outstanding principal balance after each payment equals

the previous outstanding principal balance minus the principal paid down in the payment: OLBt = OLBt-1 - AMORTt.

• Rule 4: The initial outstanding principal balance equals the initial contract principal specified in the loan agreement: OLB0 = L.

Where: L = Initial contract principal amount (the “loan amount”); rt = Contract simple interest rate applicable for payment in Period "t"; INTt = Interest owed in Period "t"; AMORTt = Principal paid down in the Period "t" payment; OLBt = Outstanding principal balance after the Period "t" payment has been

made; PMTt = Amount of the loan payment in Period "t". Know how to apply these rules in a Computer Spreadsheet!



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Interest-only loan: PMTt=INTt (or equivalently: OLBt=L), for all t.

Exhibit 17-1a: Interest-only Mortgage Payments & Interest Component: $1,000,000, 12%, 30-yr, monthly pmts.

Rules 3&4: Rule 1: Rule 2: Rules 3&4:

Month#: OLB(Beg): PMT: INT: AMORT: OLB(End):0 $1,000,000.00 1 $1,000,000.00 $10,000.00 $10,000.00 $0.00 $1,000,000.00 2 $1,000,000.00 $10,000.00 $10,000.00 $0.00 $1,000,000.00 3 $1,000,000.00 $10,000.00 $10,000.00 $0.00 $1,000,000.00

... ... ... ... ... ...358 $1,000,000.00 $10,000.00 $10,000.00 $0.00 $1,000,000.00 359 $1,000,000.00 $10,000.00 $10,000.00 $0.00 $1,000,000.00 360 $1,000,000.00 $1,010,000.00 $10,000.00 $1,000,000.00 $0.00

Interest Only Mortgage

0

2000

4000

6000

8000

10000

12000

14000

1 33 65 97 129

161

193

225

257

289

321

353

PMT Number

$ PMT

INT

$1000000



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How do you construct the pmt & balance schedule in How do you construct the pmt & balance schedule in ExcelExcel?...?...Four columns are necessary:Four columns are necessary:

•• OLB, PMT, INT, AMORT.OLB, PMT, INT, AMORT.•• (OLB may be repeated at Beg & End of each pmt period to add a 5(OLB may be repeated at Beg & End of each pmt period to add a 5thth col.;)col.;)

•• First, First, ““Rule 4Rule 4”” is applied to the 1st row of the OLB column to set initial OLBis applied to the 1st row of the OLB column to set initial OLB00 = L = L = Initial principal owed;= Initial principal owed;•• Then, the remaining rows and columns are filled in by copy/pastThen, the remaining rows and columns are filled in by copy/pasting formulas ing formulas representing representing ““Rule 1Rule 1””, Rule 2, Rule 2””, and , and ““Rule 3Rule 3””, , •• Applying one of these rules to each of three of the four necessApplying one of these rules to each of three of the four necessary columns.ary columns.•• ““CircularityCircularity”” in the Excel formulas is avoided by placing in the remaining coin the Excel formulas is avoided by placing in the remaining column lumn (the 4(the 4thth column) a formula which reflects the definition of the type of column) a formula which reflects the definition of the type of loan:loan:

•• e.g., For the intereste.g., For the interest--only loan we could use the only loan we could use the PMTPMTtt==INTINTtt characteristic of characteristic of the interestthe interest--only mortgage to define the PMT column.only mortgage to define the PMT column.••Then:Then:

•• ““Rule 1Rule 1”” is employed in the INT column to derive the interest from the is employed in the INT column to derive the interest from the beginning OLB as: beginning OLB as: INTINTtt = OLB= OLBtt--11 * * rrtt ;;•• ““Rule 2Rule 2”” in the AMORT column to derive in the AMORT column to derive AMORTAMORTtt = = PMTPMTtt -- INTINTtt ; ; •• ““Rule 3Rule 3”” in the remainder of the OLB column (t > 0) to derive in the remainder of the OLB column (t > 0) to derive OLBOLBtt=OLB=OLBtt--11 –– AMORTAMORTtt ;;

•• (Alternatively, we could have used the (Alternatively, we could have used the AMORTAMORTtt=0 loan characteristic to =0 loan characteristic to define the AMORT column and then applied define the AMORT column and then applied ““Rule 2Rule 2”” to derive the PMT to derive the PMT column instead of the AMORT column.)column instead of the AMORT column.)



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What are some What are some advantagesadvantages of the of the interestinterest--only loanonly loan?...?...•• Low payments.Low payments.•• Payments entirely taxPayments entirely tax--deductible deductible (only marginally valuable for high tax-bracket borrowers)..•• If FRM, payments always the same (easy budgeting).If FRM, payments always the same (easy budgeting).•• Payments invariant with maturity.Payments invariant with maturity.•• Very simple, easy to understand loan.Very simple, easy to understand loan.

What are some What are some disadvantagesdisadvantages of the of the interestinterest--only loanonly loan?...?...•• Big Big ““balloonballoon”” payment due at end payment due at end (maximizes refinancing stress)(maximizes refinancing stress)..•• Maximizes total interest payments Maximizes total interest payments (but this is not really a cost or (but this is not really a cost or disadvantage from an NPV or OCC perspective)disadvantage from an NPV or OCC perspective)..•• Has slightly higher Has slightly higher ““durationduration”” than amortizing loan of same maturity than amortizing loan of same maturity (( greater interest rate risk for lender, possibly slightly highergreater interest rate risk for lender, possibly slightly higher interest interest rate when yield curve has normal positive slope)rate when yield curve has normal positive slope)..•• Lack of Lack of paydownpaydown of principle may increase default risk if property of principle may increase default risk if property value may decline in nominal terms.value may decline in nominal terms.



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Constant-amortization mortgage (CAM): AMORTt = L / N, all t.

Exhibit 17-2: Constant Amortization Mortgage (CAM) Payments & Interest Component: $1,000,000, 12%, 30-yr, monthly pmts.


Month#: OLB(Beg): PMT: INT: AMORT: OLB(End): 0 $1,000,000.00 1 $1,000,000.00 $12,777.78 $10,000.00 $2,777.78 $997,222.22 2 $997,222.22 $12,750.00 $9,972.22 $2,777.78 $994,444.44 3 $994,444.44 $12,722.22 $9,944.44 $2,777.78 $991,666.67

... ... ... ... ... ... 358 $8,333.33 $2,861.11 $83.33 $2,777.78 $5,555.56 359 $5,555.56 $2,833.33 $55.56 $2,777.78 $2,777.78 360 $2,777.78 $2,805.56 $27.78 $2,777.78 $0.00

Constant Amortization Mortgage (CAM)

0

2000

4000

6000

8000

10000

12000

14000

1 61 121 181 241 301

PMT Number

$

PMT

INT

AMORT = 1000000 / 360

In Excel, set:In Excel, set:

Then use Then use ““RulesRules”” to derive to derive other columns.other columns.



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What are some What are some advantagesadvantages of the of the CAMCAM?...?...•• No balloon No balloon (no refinancing stress)(no refinancing stress)..•• Declining payments may be appropriate to match a declining asseDeclining payments may be appropriate to match a declining asset, or t, or a a deflationarydeflationary environment (e.g., 1930s).environment (e.g., 1930s).•• Popular for consumer debt (installment loans) on shortPopular for consumer debt (installment loans) on short--lived assets, lived assets, but not common in real estate.but not common in real estate.

What are some What are some disadvantagesdisadvantages of the of the CAMCAM?...?...•• High initial payments.High initial payments.•• Declining payment pattern doesnDeclining payment pattern doesn’’t usually match property income t usually match property income available to service debt. available to service debt. •• Rapidly declining interest component of payments reduces PV of Rapidly declining interest component of payments reduces PV of interest tax shield for high taxinterest tax shield for high tax--bracket investors.bracket investors.•• Rapid Rapid paydownpaydown of principal reduces leverage faster than many of principal reduces leverage faster than many borrowers would like.borrowers would like.•• Constantly changing payment obligations are difficult to adminiConstantly changing payment obligations are difficult to administer ster and budget for.and budget for.



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The constant-payment mortgage (CPM): PMTt = PMT, a constant, for all t.

Exhibit 17-3: Constant Payment Mortgage (CPM) Payments & Interest Component: $1,000,000, 12%, 30-year, monthly payments.


Month#: OLB(Beg): PMT: INT: AMORT: OLB(End): 0 $1,000,000.00 1 $1,000,000.00 $10,286.13 $10,000.00 $286.13 $999,713.87 2 $999,713.87 $10,286.13 $9,997.14 $288.99 $999,424.89 3 $999,424.89 $10,286.13 $9,994.25 $291.88 $999,133.01

... ... ... ... ... ... 358 $30,251.34 $10,286.13 $302.51 $9,983.61 $20,267.73 359 $20,267.73 $10,286.13 $202.68 $10,083.45 $10,184.28 360 $10,184.28 $10,286.13 $101.84 $10,184.28 $0.00

Constant Payment Mortgage (CPM)

0

2000

4000

6000

8000

10000

12000

14000

1 61 121 181 241 301PMT Number

$

PMT

INT

Then use Then use ““RulesRules”” to derive to derive other columns.other columns.

=PMT(.01,360,1000000)

In Excel, set:In Excel, set:

Use Annuity Use Annuity Formula to Formula to determine determine constant PMTconstant PMT

Calculator:Calculator:360 = N12 = I/yr1000000 = PV0 = FVCpt PMT = 10,286

““The ClassicThe Classic””!!



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What are some What are some advantagesadvantages of the of the CPMCPM?...?...•• No balloon No balloon (no refinancing stress) (no refinancing stress) if fully amortizing.if fully amortizing.•• Low payments possible with long amortization Low payments possible with long amortization (e.g., $10286 in 30(e.g., $10286 in 30--yr yr CPM CPM vsvs $10000 in interest$10000 in interest--only)only)..•• If FRM, constant flat payments easy to budget and administer.If FRM, constant flat payments easy to budget and administer.•• Large initial interest portion in pmts improves PV of interest Large initial interest portion in pmts improves PV of interest tax tax shields (compared to CAM) for high tax borrowers.shields (compared to CAM) for high tax borrowers.•• Flexibly allows Flexibly allows tradetrade--offoff between pmts, amortization term, maturity, between pmts, amortization term, maturity, and balloon size.and balloon size.

What are some What are some disadvantagesdisadvantages of the of the CPMCPM?...?...•• Flat payment pattern may not conform to income pattern in some Flat payment pattern may not conform to income pattern in some properties or for some borrowers (e.g., in high growth or inflatproperties or for some borrowers (e.g., in high growth or inflationary ionary situations):situations):

•• 11stst--time homebuyers (especially in high inflation time).time homebuyers (especially in high inflation time).•• Turnaround property (needing leaseTurnaround property (needing lease--up phase).up phase).•• Income property in general in high inflation time.Income property in general in high inflation time.



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The tradeThe trade--off in the CPM among:off in the CPM among:•• Regular payment level,Regular payment level,•• Amortization term (how fast the principal is paid down),Amortization term (how fast the principal is paid down),•• Maturity & size of balloon paymentMaturity & size of balloon payment……

Example: Consider 12% $1,000,000 monthlyExample: Consider 12% $1,000,000 monthly--pmt loan:pmt loan:What is pmt for 30What is pmt for 30--yr amortization?yr amortization?

Answer: $10,286.13 Answer: $10,286.13 (END, 12 P/YR; N=360, I/YR=12, PV=1000000, FV=0, CPT PMT= )

What is balloon for 10What is balloon for 10--yr maturity?yr maturity?Answer: $934,180 Answer: $934,180 (N=120, CPT FV= )

What is pmt for 10What is pmt for 10--yr amortization (to eliminate balloon)?yr amortization (to eliminate balloon)?Answer: $14,347.09 Answer: $14,347.09 (FV=0, CPT PMT= )

Go back to 30Go back to 30--yr amortization, what is 15yr amortization, what is 15--yr maturity balloon (to reduce yr maturity balloon (to reduce 1010--yr balloon while retaining low pmts)?yr balloon while retaining low pmts)?

Answer: $857,057 Answer: $857,057 (N=360, FV=0, CPT PMT=10286.13, N=180, CPT FV= )



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The constant-payment mortgage (CPM): PMTt = PMT, a constant, for all t.

Exhibit 17-3: Constant Payment Mortgage (CPM) Payments & Interest Component: $1,000,000, 12%, 30-year, monthly payments.


Month#: OLB(Beg): PMT: INT: AMORT: OLB(End): 0 $1,000,000.00 1 $1,000,000.00 $10,286.13 $10,000.00 $286.13 $999,713.87 2 $999,713.87 $10,286.13 $9,997.14 $288.99 $999,424.89 3 $999,424.89 $10,286.13 $9,994.25 $291.88 $999,133.01

... ... ... ... ... ... 358 $30,251.34 $10,286.13 $302.51 $9,983.61 $20,267.73 359 $20,267.73 $10,286.13 $202.68 $10,083.45 $10,184.28 360 $10,184.28 $10,286.13 $101.84 $10,184.28 $0.00

Constant Payment Mortgage (CPM)

0

2000

4000

6000

8000

10000

12000

14000

1 61 121 181 241 301PMT Number

$

PMT

INT

1010--yr maturity:yr maturity:

3030--yr yr amortamort

10286 pmt, 10286 pmt,

934000 balloon934000 balloon

2020--yr yr amortamort

11010 pmt,11010 pmt,

770000 balloon.770000 balloon.

934

1028611010 770



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Graduated Payment Mortgage (GPM):

(PMTt+s > PMTt, for some positive value of s and t.)

Allows initial payments to be lower than they otherwise could be... Exhibit 17-4: Graduated Payment Mortgage (GPM) Payments & Interest Component: $1,000,000, 12%, 30-year, monthly payments; 4 Annual 7.5% steps.

Rules 3&4: Rule 1: Rule 2: Rules 3&4:Month#: OLB(Beg): PMT: INT: AMORT: OLB(End):

0 $1,000,000.00 1 $1,000,000.00 $8,255.76 $10,000.00 ($1,744.24) $1,001,744.24 2 $1,001,744.24 $8,255.76 $10,017.44 ($1,761.69) $1,003,505.93 3 $1,003,505.93 $8,255.76 $10,035.06 ($1,779.30) $1,005,285.23

... ... ... ... ... ...12 $1,020,175.38 $8,255.76 $10,201.75 ($1,946.00) $1,022,121.38 13 $1,022,121.38 $8,874.94 $10,221.21 ($1,346.28) $1,023,467.65 14 $1,023,467.65 $8,874.94 $10,234.68 ($1,359.74) $1,024,827.39 ... ... ... ... ... ...24 $1,037,693.53 $8,874.94 $10,376.94 ($1,502.00) $1,039,195.53 25 $1,039,195.53 $9,540.56 $10,391.96 ($851.40) $1,040,046.92 26 $1,040,046.92 $9,540.56 $10,400.47 ($859.91) $1,040,906.83 ... ... ... ... ... ...36 $1,049,043.49 $9,540.56 $10,490.43 ($949.88) $1,049,993.37 37 $1,049,993.37 $10,256.10 $10,499.93 ($243.83) $1,050,237.20 38 $1,050,237.20 $10,256.10 $10,502.37 ($246.27) $1,050,483.48 ... ... ... ... ... ...48 $1,052,813.75 $10,256.10 $10,528.14 ($272.04) $1,053,085.79 49 $1,053,085.79 $11,025.31 $10,530.86 $494.45 $1,052,591.34 50 $1,052,591.34 $11,025.31 $10,525.91 $499.39 $1,052,091.95 ... ... ... ... ... ...

358 $32,425.27 $11,025.31 $324.25 $10,701.05 $21,724.21 359 $21,724.21 $11,025.31 $217.24 $10,808.07 $10,916.15 360 $10,916.15 $11,025.31 $109.16 $10,916.15 $0.00

Graduated Payment Mortgage (GPM)

0

2000

4000

6000

8000

10000

12000

14000

1 61 121 181 241 301PMT Number

$

PMT

INT



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(PMTt+s > PMTt, for some positive value of s and t.)Allows initial payments to be lower than they otherwise could be...

Exhibit 17-4: Graduated Payment Mortgage (GPM) Payments & Interest Component: $1,000,000, 12%, 30-year, monthly payments; 4 Annual 7.5% steps.


0

2000

4000

6000

8000

10000

12000

14000

1 61 121 181 241 301PMT Number

$

PMT

INT

Graduated Payment Mortgage (GPM):Graduated Payment Mortgage (GPM):



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0 $1,000,000.00 1 $1,000,000.00 $8,255.76 $10,000.00 ($1,744.24) $1,001,744.24 2 $1,001,744.24 $8,255.76 $10,017.44 ($1,761.69) $1,003,505.93 3 $1,003,505.93 $8,255.76 $10,035.06 ($1,779.30) $1,005,285.23

... ... ... ... ... ...12 $1,020,175.38 $8,255.76 $10,201.75 ($1,946.00) $1,022,121.38 13 $1,022,121.38 $8,874.94 $10,221.21 ($1,346.28) $1,023,467.65 14 $1,023,467.65 $8,874.94 $10,234.68 ($1,359.74) $1,024,827.39 ... ... ... ... ... ...24 $1,037,693.53 $8,874.94 $10,376.94 ($1,502.00) $1,039,195.53 25 $1,039,195.53 $9,540.56 $10,391.96 ($851.40) $1,040,046.92 26 $1,040,046.92 $9,540.56 $10,400.47 ($859.91) $1,040,906.83 ... ... ... ... ... ...36 $1,049,043.49 $9,540.56 $10,490.43 ($949.88) $1,049,993.37 37 $1,049,993.37 $10,256.10 $10,499.93 ($243.83) $1,050,237.20 38 $1,050,237.20 $10,256.10 $10,502.37 ($246.27) $1,050,483.48 ... ... ... ... ... ...48 $1,052,813.75 $10,256.10 $10,528.14 ($272.04) $1,053,085.79 49 $1,053,085.79 $11,025.31 $10,530.86 $494.45 $1,052,591.34 50 $1,052,591.34 $11,025.31 $10,525.91 $499.39 $1,052,091.95 ... ... ... ... ... ...

358 $32,425.27 $11,025.31 $324.25 $10,701.05 $21,724.21 359 $21,724.21 $11,025.31 $217.24 $10,808.07 $10,916.15 360 $10,916.15 $11,025.31 $109.16 $10,916.15 $0.00

(PMTt+s > PMTt, for some positive value of s and t.)Allows initial payments to be lower than they otherwise could be...

Exhibit 17-4: Graduated Payment Mortgage (GPM) Payments & Interest Component: $1,000,000, 12%, 30-year, monthly payments; 4 Annual 7.5% steps.

Graduated Payment Mortgage (GPM):Graduated Payment Mortgage (GPM):

Graduation characteristicsGraduation characteristicsof loan used to derive of loan used to derive PMTsPMTsbased on Annuity Formula.based on Annuity Formula.

Then rest of table is derived Then rest of table is derived by applying the by applying the ““Four Four RulesRules”” as before.as before.

Once you know what the Once you know what the initial PMT is, everything initial PMT is, everything else follows. . .else follows. . .



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Mechanics: Mechanics: How to calculate the first payment in a GPM...How to calculate the first payment in a GPM...

In principle, we could use the constant-growth annuity formula:

But in practice, only a few (usually annual) “step ups” are made...

( ) ( )( )⎟⎟⎠

⎞⎜⎜⎝

⎛

−++−

=gr

rgLPMTN111

1



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For example,For example,

12%, monthly-pmt, 30-yr GPM with 4 annual step-ups of 7.5% each, then constant after year 4:

L =L = PMTPMT11((PV(0.01,12,1)PV(0.01,12,1)+ (1.075/1.01+ (1.075/1.011212)(PV(0.01,12,1))(PV(0.01,12,1)+ (1.075+ (1.07522/1.01/1.012424)(PV(0.01,12,1))(PV(0.01,12,1)+ (1.075+ (1.07533/1.01/1.013636)(PV(0.01,12,1))(PV(0.01,12,1)+ (1.075+ (1.07544/1.01/1.014848)(PV(0.01,312,1))(PV(0.01,312,1)))

Just invert this formula to solve for Just invert this formula to solve for ““PMTPMT11””..



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A potential problem with A potential problem with GPMsGPMs::“Negative Amortization”. . .

Whenever PMTt < INTt, AMORTt = PMTt – INTt < 0


0

2000

4000

6000

8000

10000

12000

14000

1 61 121 181 241 301PMT Number

$

PMT

INT

e.g., OLB peaks here e.g., OLB peaks here at $1053086 at $1053086

5.3% above original 5.3% above original principal amt.principal amt.



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What are some What are some advantagesadvantages of the of the GPMGPM?...?...•• Lower initial payments.Lower initial payments.•• Payment pattern that may better match that of income servicing Payment pattern that may better match that of income servicing the the debt (for turnaround properties, startdebt (for turnaround properties, start--up tenants, 1up tenants, 1stst--time homebuyers, time homebuyers, inflationary times).inflationary times).•• (Note: An alternative for inflationary times is the (Note: An alternative for inflationary times is the ““PLAMPLAM”” –– Price Level Price Level Adjusted Mortgage, where OLB is periodically adjusted to reflectAdjusted Mortgage, where OLB is periodically adjusted to reflect inflation, inflation, allows loan interest rate to include less allows loan interest rate to include less ““inflation premiuminflation premium””, more like a , more like a ““real interest ratereal interest rate””.).)

What are some What are some disadvantagesdisadvantages of the of the GPMGPM?...?...•• NonNon--constant payments difficult to budget and administer.constant payments difficult to budget and administer.•• Increased Increased default riskdefault risk due to due to negative amortizationnegative amortization and and growing debt growing debt serviceservice..



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Adajustable Rate Mortgage (ARM):

rt may differ from rt+s , for some t & s Exhibit 17-5: Adjustable Rate Mortgage (ARM) Payments & Interest Component: $1,000,000, 9% Initial Interest, 30-year, monthly payments; 1-year Adjustment interval, possible hypothetical history.


Month#: OLB(Beg): PMT: INT: AMORT: OLB(End):Applied

Rate0 10000001 1000000 8046.23 7500.00 546.23 999454 0.0900 2 999454 8046.23 7495.90 550.32 998903 0.0900 3 998903 8046.23 7491.78 554.45 998349 0.0900 ... ... ... ... ... ... ...

12 993761 8046.23 7453.21 593.02 993168 0.0900 13 993168 9493.49 9095.76 397.73 992770 0.1099 14 992770 9493.49 9092.12 401.37 992369 0.1099 ... ... ... ... ... ... ...

24 988587 9493.49 9053.81 439.68 988147 0.1099 25 988147 8788.72 8251.03 537.68 987610 0.1002 26 987610 8788.72 8246.54 542.17 987068 0.1002 ... ... ... ... ... ... ...

358 31100 10605.24 356.61 10248.63 20851 0.1376 359 20851 10605.24 239.09 10366.14 10485 0.1376 360 10485 10605.24 120.23 10485.01 0 0.1376

Adjustable Rate Mortgage

0

2000

4000

6000

8000

10000

12000

14000

1 61 121 181 241 301

PMT Number

$

PMT

INT

PMT varies over time PMT varies over time because market interest because market interest rates vary.rates vary.



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Adjustable Rate Mortgage

0

2000

4000

6000

8000

10000

12000

14000

1 61 121 181 241 301

PMT Number

$

PMT

INT

Adjustable Rate Mortgage (ARM):Adjustable Rate Mortgage (ARM):rt ≠ rt+s for some s and t.

Exhibit 17-5: Adjustable Rate Mortgage (ARM) Payments & Interest Component:$1,000,000, 9% Initial Interest, 30-year, monthly payments; 1-year Adjustment

interval, possible hypothetical history.



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AppliedRate

0 10000001 1000000 8046.23 7500.00 546.23 999454 0.0900 2 999454 8046.23 7495.90 550.32 998903 0.0900 3 998903 8046.23 7491.78 554.45 998349 0.0900 ... ... ... ... ... ... ...

12 993761 8046.23 7453.21 593.02 993168 0.0900 13 993168 9493.49 9095.76 397.73 992770 0.1099 14 992770 9493.49 9092.12 401.37 992369 0.1099 ... ... ... ... ... ... ...

24 988587 9493.49 9053.81 439.68 988147 0.1099 25 988147 8788.72 8251.03 537.68 987610 0.1002 26 987610 8788.72 8246.54 542.17 987068 0.1002 ... ... ... ... ... ... ...

358 31100 10605.24 356.61 10248.63 20851 0.1376 359 20851 10605.24 239.09 10366.14 10485 0.1376 360 10485 10605.24 120.23 10485.01 0 0.1376

Calculating ARM payments & balances:Calculating ARM payments & balances:

1.1. Determine the current applicable Determine the current applicable contract interest rate for each period or contract interest rate for each period or adjustment interval (adjustment interval (rrtt), based on ), based on current market interest ratescurrent market interest rates..

2.2. Determine the periodic payment for Determine the periodic payment for that period or adjustment interval that period or adjustment interval based on the OLB at the beginning of based on the OLB at the beginning of the period or adjustment interval, the the period or adjustment interval, the number of periods remaining in the number of periods remaining in the amortization term of the loan as of that amortization term of the loan as of that time, and the current applicable time, and the current applicable interest rate (interest rate (rrtt).).

3.3. Apply the Apply the ““Four RulesFour Rules”” of mortgage of mortgage payment & balance determination as payment & balance determination as always.always.

3030--year fullyyear fully--amortizing ARM with:amortizing ARM with:•• 11--year adjustment interval, year adjustment interval, •• 9% initial interest rate,9% initial interest rate,•• $1,000,000 initial principal loan $1,000,000 initial principal loan amount.amount.

PMTsPMTs 11--12:12:360 = N, 9 = I/yr, 1000000 = PV, 0 = FV, 360 = N, 9 = I/yr, 1000000 = PV, 0 = FV, CPT CPT PMT = PMT = --8046.238046.23..OLBOLB1212::348 = N, 348 = N, CPT PV = 993168CPT PV = 993168..

Example:Example:

PMTsPMTs 1313--24:24:Suppose applicable int. rate changes to Suppose applicable int. rate changes to 10.99%.10.99%.(with N = 348, PV = 993168, FV = 0, as (with N = 348, PV = 993168, FV = 0, as already):already):10.99 = I/yr, 10.99 = I/yr, CPT PMT = 9493.49CPT PMT = 9493.49..OLBOLB2424: 336 = N, : 336 = N, CPT PV = 988147CPT PV = 988147..



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ARM Features & Terminology. . . Adjustment Interval e.g., 1-yr, 3-yr, 5-yr: How frequently the contract interest rate changes Index The publicly-observable market yield on which the contract interest rate is based. Margin Contract interest rate increment above index: rt = indexyldt + margin Caps & Floors (in pmt, in contract rate) - Lifetime: Applies throughout life of loan. - Interval: Applies to any one adjustment. Initial Interest Rate - "Teaser": Initial contract rate less than index+margin r0 < indexyld0 + margin - "Fully-indexed Rate": r0 = indexyld0 + margin Prepayment Privilege Residential ARMs are required to allow prepayment w/out penalty. Conversion Option Allows conversion to fixed-rate loan (usu. At “prevailing rate”).



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Because of Because of capscaps, the applicable ARM interest rate will , the applicable ARM interest rate will generally be:generally be:

rrtt = = MINMIN(( Lifetime Cap, Interval Cap, Lifetime Cap, Interval Cap, Index+MarginIndex+Margin ))

Example of Example of ““teaser rateteaser rate””::Suppose:Suppose:•• Index = 8% (e.g., current 1Index = 8% (e.g., current 1--yr LIBOR)yr LIBOR)•• Margin = 200 bpsMargin = 200 bps•• Initial interest rate = 9%.Initial interest rate = 9%.

What is the amount of the “teaser”? 100 bps = (8%+2%) 100 bps = (8%+2%) –– 9%.9%.

What will the applicable interest rate be on the loan during What will the applicable interest rate be on the loan during the 2the 2ndnd year if market interest rates year if market interest rates remain the sameremain the same (1(1--yr yr LIBOR still 8%)?...LIBOR still 8%)?... 10% = Index + Margin = 8% + 2%,10% = Index + Margin = 8% + 2%,

A 100 A 100 bpbp jump from initial 9% rate.jump from initial 9% rate.www.bsscommunitycollege.in www.bssnewgeneration.in www.bsslifeskillscollege.in


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What are some What are some advantagesadvantages of the of the ARMARM?...?...•• Lower Lower initialinitial interest rate and payments (due to teaser).interest rate and payments (due to teaser).•• Probably Probably slightlyslightly lower lower averageaverage interest rate and payments over the interest rate and payments over the life of the loan, due to typical slight upward slope of bond life of the loan, due to typical slight upward slope of bond mktmkt yield yield curvecurve (which reflects (which reflects ““preferred habitatpreferred habitat”” & & ““interest rate riskinterest rate risk””).).•• Reduced interest rate risk for lender (reduces effective Reduced interest rate risk for lender (reduces effective ““durationduration””, , allows pricing off the short end of the yield curve).allows pricing off the short end of the yield curve).•• Some Some hedginghedging for borrower?... Interest rates tend to rise during for borrower?... Interest rates tend to rise during ““good good timestimes””, fall during , fall during ““bad timesbad times”” (even inflation can be relatively (even inflation can be relatively ““goodgood””for real estate), so bad news about your interest rate is likelyfor real estate), so bad news about your interest rate is likely to be to be somewhat offset by good news about your property or income.somewhat offset by good news about your property or income.

What are some What are some disadvantagesdisadvantages of the of the ARMARM?...?...•• NonNon--constant payments difficult to budget and administer.constant payments difficult to budget and administer.•• Increased Increased interest rate riskinterest rate risk for for borrowerborrower (interest rate risk is (interest rate risk is transferred from lender to borrower).transferred from lender to borrower).•• As a result of the above, possibly slightly greater As a result of the above, possibly slightly greater default riskdefault risk??•• All of the above are mitigated by use of:All of the above are mitigated by use of:

•• Adjustment intervals (longer intervals, less problems);Adjustment intervals (longer intervals, less problems);•• Interest rate (or payment) Interest rate (or payment) capscaps..www.bsscommunitycollege.in www.bssnewgeneration.in www.bsslifeskillscollege.in


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Yields on US Govt Bonds

-2%

0%

2%

4%

6%

8%

10%

12%

14%

16%

1926 1936 1946 1956 1966 1976 1986 1996Source: Ibbotson Assoc (SBBI Yearbook)

30-Day T-Bills 10-yr T-Bonds

Some economics behind Some economics behind ARMsARMs (See Chapter 19)

Interest rates are variable, not fully predictable, ST rates morInterest rates are variable, not fully predictable, ST rates more e variable than LT rates, more volatility in recent decades . . .variable than LT rates, more volatility in recent decades . . .

ST rates ST rates usuallyusually (but not always) lower than LT rates:(but not always) lower than LT rates:•• UpwardUpward--sloping sloping ““Yield CurveYield Curve”” ((avgavg 100100--200 bps).200 bps).



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Average (Average (““typicaltypical””) yield curve is ) yield curve is ““slightly upward slopingslightly upward sloping”” (100(100--200 bps) 200 bps) because:because:

•• Interest Rate Risk:Interest Rate Risk:•• Greater volatility in LT bond values and periodic returns Greater volatility in LT bond values and periodic returns (simple (simple HPRsHPRs) than in ST bond values and returns:) than in ST bond values and returns:•• LT bonds require greater ex ante risk premium (E[RP]).LT bonds require greater ex ante risk premium (E[RP]).

•• ““Preferred HabitatPreferred Habitat””::•• More borrowers would rather have LT debt,More borrowers would rather have LT debt,•• More lenders would rather make ST loans:More lenders would rather make ST loans:•• Equilibrium requires higher interest rates for LT debt.Equilibrium requires higher interest rates for LT debt.

This is the main fundamental reason why This is the main fundamental reason why ARMsARMs tend to have slightly tend to have slightly lower lower lifetime averagelifetime average interest rates than otherwise similar interest rates than otherwise similar FRMsFRMs, yet , yet not every borrower wants an ARM. Compared to similar FRM:not every borrower wants an ARM. Compared to similar FRM:

•• ARM borrower takes on more interest rate risk, ARM borrower takes on more interest rate risk,

•• ARM lender takes on less interest rate risk.ARM lender takes on less interest rate risk.



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The yield curve is The yield curve is not alwaysnot always slightly upwardslightly upward--sloping . . .sloping . . .

Exhibit 19-5: Typical yield curve shapes . . .

Steep "inverted" (high current inflation)

Shallow inverted (recession fear)

Flat

Slightly rising (normal)

Steeply rising (from recession to recovery)

Maturity (duration)

Yield



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Y ield Curv e: US Treas ury Str ips

0%

1%

2%

3%

4%

5%

6%

7%

8%

9%

0 1 2 3 4 5 6 7 8 9 10

M atu r ity (yr s )

Yie

ld

1993 1995 1998

The yield curve changes frequently:The yield curve changes frequently:



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Here is a more recent example:Here is a more recent example:

The Yield Curve

1.52

2.53

3.54

4.55

5.56

3 month 6 month 1 year 2 year 5 year 10 year 30 year

Maturity

Yiel

d (%

) 02-Jan-0131-Jul-0116-Oct-0119-Jan-02

Check out Check out ““The Living Yield CurveThe Living Yield Curve”” at:at:

http://http://www.smartmoney.com/onebond/index.cfm?storywww.smartmoney.com/onebond/index.cfm?story==yieldcurveyieldcurve



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When the yield curve is When the yield curve is steeply risingsteeply rising (e.g., 200(e.g., 200--400 bps from ST to LT 400 bps from ST to LT yields), ARM rates may appear yields), ARM rates may appear particularly favorableparticularly favorable (for borrowers) (for borrowers) relative to FRM rates.relative to FRM rates.

But what do borrowers need to watch out for during such times? .But what do borrowers need to watch out for during such times? . . .. .

For a longFor a long--term borrower, the FRMterm borrower, the FRM--ARM differential may be somewhat ARM differential may be somewhat misleading (ex ante) during such times:misleading (ex ante) during such times:

The steeply rising yield curve reflects the The steeply rising yield curve reflects the ““Expectations TheoryExpectations Theory”” of the of the determination of the yield curve:determination of the yield curve:

•• LT yields reflect current LT yields reflect current expectationsexpectations about about future shortfuture short--term yieldsterm yields..

Thus, ARM borrowers in such circumstances face greater than averThus, ARM borrowers in such circumstances face greater than average age risk that their rates will go up in the future. risk that their rates will go up in the future.



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Design your own custom loanDesign your own custom loan . . .. . .



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Section 17.2.1: Computing Mortgage Yields. . .Section 17.2.1: Computing Mortgage Yields. . .

““YieldYield”” = IRR of the loan.= IRR of the loan.

Most commonly, it is computed as the Most commonly, it is computed as the ““Yield to MaturityYield to Maturity”” (YTM), the IRR over (YTM), the IRR over the full contractual life of the loan...the full contractual life of the loan...



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Example:Example:L = $1,000,000; FullyL = $1,000,000; Fully--amortizing 30amortizing 30--yr monthlyyr monthly--pmt CPM; pmt CPM; 8%=interest rate8%=interest rate..

(with calculator set for: P/YR=12, END of period (with calculator set for: P/YR=12, END of period CFsCFs...)...)360=N, 8%=I/YR, 1000000=PV, 0=FV, Compute: PMT=7337.65360=N, 8%=I/YR, 1000000=PV, 0=FV, Compute: PMT=7337.65..

Solve for Solve for ““rr”” ::

( )∑= +

+−=360

1 165.337,7$000,000,1$0

ttr

Obviously: r = 0.667%, Obviously: r = 0.667%, i = r*m = (0.667%)*12 = i = r*m = (0.667%)*12 = 8.00% = YTM8.00% = YTM..

Here, YTM = Here, YTM = ““contract interest ratecontract interest rate””..

This will not always be the case . . .This will not always be the case . . .



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Suppose loan had Suppose loan had 1%1% ((one one ““pointpoint””) ) origination feeorigination fee((akaaka ““prepaid interestprepaid interest””, , ““discount pointsdiscount points””, , ““disbursement disbursement discountdiscount”” )...)...

Then PV Then PV ≠≠ L: L:

Borrower only gets (lender only disburses) $990,000.Borrower only gets (lender only disburses) $990,000.

Solve for Solve for ““rr”” in:in:

( )∑= +

+−=360

1 165.337,7$000,990$0

ttr

Thus: r = 0.6755%, Thus: r = 0.6755%, i = r*m = (0.6755%)*12 = i = r*m = (0.6755%)*12 = 8.11% = YTM8.11% = YTM..

(Always quote yields to nearest “basis-point” = 1/100th percent.)

360=N, 8%=I/YR, 1000000=PV, 0=FV, Compute: PMT=7337.65;360=N, 8%=I/YR, 1000000=PV, 0=FV, Compute: PMT=7337.65;Then enterThen enter 990000 = PV, 990000 = PV, Then CPT I/yr = 8.11%Then CPT I/yr = 8.11%



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Sources of Differences Sources of Differences betwbetw YTM YTM vsvs Contract Interest Rate. . .Contract Interest Rate. . .

1.1. ““PointsPoints”” (as above)(as above)2.2. Mortgage Market Valuation Changes over Time...Mortgage Market Valuation Changes over Time...

As interest rates change (or default risk in loan changes), As interest rates change (or default risk in loan changes), the the ““secondarysecondary marketmarket”” for loans will place different for loans will place different values on the loan, reflecting the need of investors to earn values on the loan, reflecting the need of investors to earn a different a different ““goinggoing--in IRRin IRR”” when they invest in the loan. when they invest in the loan. The marketThe market’’s s YTMYTM for the loan is similar to the marketfor the loan is similar to the market’’s s required required ““goinggoing--in IRRin IRR”” for investing in the loan.for investing in the loan.



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Example:Example:Suppose interest rates fall, so that the Suppose interest rates fall, so that the originatororiginator of the previous $1,000,000, of the previous $1,000,000, 8%8% loan (in the loan (in the ““primaryprimary marketmarket””) can immediately sell the loan in the ) can immediately sell the loan in the secondary market for $1,025,000. secondary market for $1,025,000. i.e., Buyers in the secondary market are willing to pay a i.e., Buyers in the secondary market are willing to pay a ““premiumpremium”” (of (of $25,000) over the loan$25,000) over the loan’’s s ““parpar valuevalue”” ((““contractual OLBcontractual OLB””).).Why would they do this? . . .Why would they do this? . . .

Mortgage market requires a YTM of 7.74% for this loan:Mortgage market requires a YTM of 7.74% for this loan:

( )∑= +

+−=360

1 165.337,7$000,025,1$0

ttr

r = 0.6452% r = 0.6452% i = 0.6452%*12 = 7.74%.i = 0.6452%*12 = 7.74%.

360=N, 1025000=PV, 7337.65=PMT, 0=FV; 360=N, 1025000=PV, 7337.65=PMT, 0=FV; Compute:Compute: I/YR=7.74%I/YR=7.74%..

This loan has an This loan has an 8% contract interest8% contract interest rate, but a rate, but a 7.74% market YTM7.74% market YTM..i.e., buyers pay 1025000 because they i.e., buyers pay 1025000 because they mustmust: : ““itit’’s the markets the market””..



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Contract interest rate Contract interest rate differsdiffers from YTM from YTM wheneverwhenever::

•• Current actual CF associated with acquisition of the Current actual CF associated with acquisition of the loan differs from current OLB (or loan differs from current OLB (or par valuepar value) of loan.) of loan.

At time of loan origination (At time of loan origination (primaryprimary market), this results market), this results from discounts taken from loan disbursement.from discounts taken from loan disbursement.

At resale of loan (At resale of loan (secondarysecondary market), YTM reflects market market), YTM reflects market value of loan regardless of par value or contractual interest value of loan regardless of par value or contractual interest rate on the loan.rate on the loan.

Contract Interest Rates Contract Interest Rates vsvs YTMsYTMs . . .. . .



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APRs & APRs & ““Effective Interest RatesEffective Interest Rates””. . .. . .

““APRAPR”” ((““Annual Percentage RateAnnual Percentage Rate””) = YTM from ) = YTM from lenderlender’’ss perspective, at time perspective, at time of loan origination.of loan origination.

((““Truth in Lending ActTruth in Lending Act””: Residential mortgages & consumer loans.): Residential mortgages & consumer loans.)

Sometimes referred to as Sometimes referred to as ““effective interest rateeffective interest rate””..

CAVEAT (from borrowerCAVEAT (from borrower’’s perspective):s perspective):•• APR is defined from lenderAPR is defined from lender’’s perspective.s perspective.•• Does not include effect of costs of some items required by Does not include effect of costs of some items required by lender but paid by borrower to 3rd parties (e.g., title lender but paid by borrower to 3rd parties (e.g., title insurance, appraisal fee).insurance, appraisal fee).•• These costs may differ across lenders. So lowest effective These costs may differ across lenders. So lowest effective cost to borrower may not be from lender with lowest official cost to borrower may not be from lender with lowest official APR.APR.



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Reported APRs for Reported APRs for ARMsARMs . . .. . .The official APR is an The official APR is an expected yieldexpected yield (ex ante) at the time of loan (ex ante) at the time of loan origination, based on the origination, based on the contractual termscontractual terms of the loan.of the loan.

For an ARM, the contract does not preFor an ARM, the contract does not pre--determine the future interest determine the future interest rate in the loan. Hence:rate in the loan. Hence:

The APR of an ARM must be based on a The APR of an ARM must be based on a forecastforecast of future market of future market interest rates (the interest rates (the ““indexindex”” governing the governing the ARMARM’’ss applicable rate).applicable rate).

Government regulations require that the Government regulations require that the ““officialofficial”” APR reported for APR reported for ARMsARMs be based on a be based on a flat forecastflat forecast of market interest rates (i.e., the APR is of market interest rates (i.e., the APR is calculated assuming the index rate remains constant at its currecalculated assuming the index rate remains constant at its current level nt level for the life of the loan).for the life of the loan).

This is a reasonable assumption when the yield curve has its This is a reasonable assumption when the yield curve has its ““normalnormal””slightly upwardslightly upward--sloping shape (i.e., when the shape is due purely to sloping shape (i.e., when the shape is due purely to interest rate risk and preferred habitat).interest rate risk and preferred habitat).

It is a poor assumption for other shapes of the yield curve (i.eIt is a poor assumption for other shapes of the yield curve (i.e., when ., when bond market bond market expectationsexpectations imply that future shortimply that future short--term rates are likely to term rates are likely to differ from current shortdiffer from current short--term rates).term rates).



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YTMsYTMs vsvs ““expected returnsexpected returns””. . .. . .

““Expected returnExpected return””= Mortgage investor= Mortgage investor’’s expected total return (goings expected total return (going--in in IRR for mortgage investor), IRR for mortgage investor), = Borrower= Borrower’’s s ““cost of capitalcost of capital””, , E[rE[r]]..

YTM YTM ≠≠ E[rE[r], for two reasons:], for two reasons:1)1) YTM based on YTM based on contractualcontractual cash flows, ignoring cash flows, ignoring probability of default. probability of default. (Ignore this for now.)(Ignore this for now.)2)2) YTM assumes loan remains to YTM assumes loan remains to maturitymaturity, even if loan , even if loan has prepayment clause...has prepayment clause...



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Suppose previous 30Suppose previous 30--yr yr 8%8%, 1, 1--point (point (8.11% YTM8.11% YTM) loan is ) loan is expected to be expected to be prepaidprepaid after 10 years...after 10 years...

( ) ( )∑= +

++

+−=120

11201

247,877$1

65.337,7$000,990$0t

t rr

Solve for r = 0.6795%, Solve for r = 0.6795%, E[rE[r]/yr]/yr = (0.6795%)*12 = = (0.6795%)*12 = 8.15%8.15%..

360=N, 8=I/YR, 1000000=PV, 0=FV; 360=N, 8=I/YR, 1000000=PV, 0=FV; Compute: PMT= Compute: PMT= --7337.65. 7337.65.

Then:Then:120=N; Compute FV= 120=N; Compute FV= --877247; 877247; thenthen 990000=PV; Compute: 990000=PV; Compute:

I/YR=8.15%.I/YR=8.15%.



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The shorter the prepayment horizon, the greater the effect of The shorter the prepayment horizon, the greater the effect of any disbursement discount on the realistic yield (expected any disbursement discount on the realistic yield (expected return) on the mortgage...return) on the mortgage...

Similar (slightly smaller) effect is caused by prepayment penalties.

Effect of Prepayment on Loan Yield (8%, 30-yr)

7%

8%

9%

10%

11%

1 6 11 16 21 26Prepayment Horizon (Yrs)

Loan

Yie

ld (I

RR

0 fee, 0 pen

1% fee, 0 pen

2% fee, 0 pen

1% fee, 1% pen



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Effect of Prepayment on Loan Yield (8%, 30-yr)

7%

8%

9%

10%

11%

1 6 11 16 21 26Prepayment Horizon (Yrs)

Loan

Yie

ld (I

RR

0 fee, 0 pen

1% fee, 0 pen

2% fee, 0 pen

1% fee, 1% pen

Prepayment horizon & Expected Return (OCC):Prepayment horizon & Expected Return (OCC):

Exhibit 17-2b: Yield (IRR) on 8%, 30-yr CP-FRM:Prepayment Horizon (Yrs)

Loan Terms: 1 2 3 5 10 20 300 fee, 0 pen 8.00% 8.00% 8.00% 8.00% 8.00% 8.00% 8.00%1% fee, 0 pen 9.05% 8.55% 8.38% 8.25% 8.15% 8.11% 8.11%2% fee, 0 pen 10.12% 9.11% 8.77% 8.50% 8.31% 8.23% 8.21%1% fee, 1% pen 10.01% 9.01% 8.67% 8.41% 8.21% 8.13% 8.11%



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The tricky part in loan yield calculation: (a) The holding period over which we wish to calculate the

yield may not equal the maturity of the loan (e.g., if the loan will be paid off early, so N may not be the original maturity of the loan): N ≠ maturity ;

(b) The actual time-zero present cash flow of the loan may

not equal the initial contract principal on the loan (e.g., if there are "points" or other closing costs that cause the cash flow disbursed by the lender and/or the cash flow received by the borrower to not equal the contract principal on the loan, P): PV = CF0 ≠ L ;

(c) The actual liquidating payment that pays off the loan at

the end of the presumed holding period may not exactly equal the outstanding loan balance at that time (e.g., if there is a "prepayment penalty" for paying off the loan early, then the borrower must pay more than the loan balance, so FV is then different from OLB): CFN ≠ PMT+OLBN ; FV to include ppmt penalty.

So we must make sure that the amounts in the N, PV, and FV registers reflect the actual cash flows…



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Example:Example:Computation of 10Computation of 10--yr yield on 8%, 30yr yield on 8%, 30--yr, CPyr, CP--FRM with FRM with 1 1

point discount & 1 point prepayment penaltypoint discount & 1 point prepayment penalty::1.1. First, enter loan initial contractual terms to compute First, enter loan initial contractual terms to compute pmtpmt: :

360 360 N, 8 N, 8 I/yr, 1 I/yr, 1 PV, 0 PV, 0 FV: FV: CPTCPT PMT = PMT = --.00734.00734..2.2. Next, change N to reflect actual expected holding period to Next, change N to reflect actual expected holding period to

compute OLB at end: 120 compute OLB at end: 120 N, N, CPTCPT FV = FV = --.87725.87725..3.3. Third step: Add prepayment penalty to OLB to reflect Third step: Add prepayment penalty to OLB to reflect

actual cash flow at that time, and enter that amount into FV actual cash flow at that time, and enter that amount into FV register: register: --.87725 X 1.01 = .87725 X 1.01 = --.88602 .88602 FVFV..

4.4. Fourth step: Remove discount points from amt in PV Fourth step: Remove discount points from amt in PV register to reflect actual CFregister to reflect actual CF00: RCL PV 1 : RCL PV 1 X .99 = X .99 = .99.99 PVPV..

5.5. Last: Compute interest (yield) of the actual loan cash flows Last: Compute interest (yield) of the actual loan cash flows for the 10for the 10--yr hold now reflected in registers: yr hold now reflected in registers: CPTCPT I/yr = I/yr = 8.21%8.21%..



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17.2.2 Why do points & fees exist?. . .17.2.2 Why do points & fees exist?. . .1.1. Compensate brokers who find & filter applications for the Compensate brokers who find & filter applications for the

lender.lender.2.2. Pay back originators for overhead & administrative costs that Pay back originators for overhead & administrative costs that

occur upoccur up--front in the front in the ““originationorigination”” process.process.

Above reasons apply to small points and fees.Above reasons apply to small points and fees.3.3. To develop a To develop a ““mortgage menumortgage menu””, trading off up, trading off up--front payment front payment vsvs

onon--going monthly payment. (Match borrowergoing monthly payment. (Match borrower’’s payment s payment preferences.) preferences.)

e.g., All of the following 30e.g., All of the following 30--yr loans provide an 8.15% 10yr loans provide an 8.15% 10--year yield:year yield:

Discount Points

Interest Rate Monthly Payment

0 8.15% $7444.86 1 8.00% $7337.65 2 7.85% $7230.58 3 7.69% $7124.08



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17.2.3 Using Yields to Value Mortgages. . .17.2.3 Using Yields to Value Mortgages. . .

The Market Yield is (similar to) the The Market Yield is (similar to) the Expected ReturnExpected Return(going(going--in) required by in) required by InvestorsInvestors in the in the Mortgage Mortgage MarketMarket……

MktMkt YTM = YTM = ““OCCOCC”” = Discount Rate (applied to = Discount Rate (applied to contractual contractual CFsCFs))

Thus, Thus, MktMkt Yields are used to Yields are used to ValueValue mortgages (in mortgages (in either the primary or secondary market).either the primary or secondary market).



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Example:Example:

$1,000,000, 8%, 30$1,000,000, 8%, 30--yryr--amort, 10amort, 10--yryr--balloon loan again.balloon loan again.How much is this loan worth if the Market Yield is How much is this loan worth if the Market Yield is

currently 7.5% (= 7.5/12 = 0.625%/mo) MEY (i.e., currently 7.5% (= 7.5/12 = 0.625%/mo) MEY (i.e., 7.62% CEY 7.62% CEY yldyld in bond in bond mktmkt)?)?……

(Just the “inverse” of the previous yield computation problem.)

( ) ( )∑=

+=120

112000625.1

247,877$00625.1

65.337,7$509,033,1$t

t

Answer: $1,033,509:Answer: $1,033,509:

N = 360, I/yr = 8, PV = 1000000, FV = 0, CPT PMT = -7337.65; THEN:

N = 120, CPT FV = -877247; THEN:

I/yr = 7.5, CPT PV = 1033509.www.bsscommunitycollege.in www.bssnewgeneration.in www.bsslifeskillscollege.in


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If you know:If you know:

1)1) Required loan amount (from borrower)Required loan amount (from borrower)2)2) Required yield (from mortgage market)Required yield (from mortgage market)

Then you can compute required Then you can compute required PMTsPMTs, hence, , hence, required contract INT & Points . . .required contract INT & Points . . .



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( ) ( )∑=

+=120

11200070833.1

247,877$0070833.1

65.337,7$888,967$t

t

Above example (8%, 30Above example (8%, 30--yr, 10yr, 10--yr prepayment), suppose yr prepayment), suppose mktmktyield is 8.5% (instead of 7.5%).yield is 8.5% (instead of 7.5%).

How many How many POINTsPOINTs must lender charge on 8% loan (to avoid must lender charge on 8% loan (to avoid NPV < 0)?NPV < 0)?

Answer: (1000000 Answer: (1000000 –– 967888)/1000000 = 3.2% = 3.2 Points.967888)/1000000 = 3.2% = 3.2 Points.

= 8.5% / yr

N = 360, I/yr = 8, PV = 1000000, FV = 0, CPT PMT = -7337.65; THEN:

N = 120, CPT FV = -877247; THEN:

I/yr = 8.5, CPT PV = 967888.



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17.3 Refinancing Decision17.3 Refinancing Decision

If loan has prepayment optionprepayment option, borrower can choose to pay off early.

• Why would she do this?...

How to evaluate this decision?...How to evaluate this decision?...

Compare two loans: existing (“old”) loan vs “new” loan that would replace it.

Traditionally, make this comparison using DCF (& NPV) methodology you are familiar with.

In this section we will:• Present this traditional approach, then • Explore something important that is left out of the traditional picture:

the prepayment option value in the old loan.



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17.3.1 The traditional refinancing calculation17.3.1 The traditional refinancing calculationNPV (refin) = PV(Benefit) – PV(Cost)

= PV(outflows saved) – PV(new outflows) – X= PV(CFOLD) – PV(CFNEW) – X = PV(CFOLD - CFNEW) – X,

Where:• CFOLD = Remaining CFs on old loan;• CFNEW = New loan CFs;• X = Transaction costs of refinancing;• Both loans evaluated over the same time horizon (likely prepmttime), for the same loan amount = (old ln OLB + PrePmt Penalty)/(1-New ln Pts) Refin is zero net CF at time 0:

Apples vs apples, Don’t confuse refinance question with capital structure

(leverage) decision.• OCC (disc rate) in PV() operation = New Ln Yld (over common time horizon).

Because discount rate= Current OCC, same for

both.*



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Shortcut ProcedureShortcut Procedure

You don’t need to compute the loan amount for the new loan:

1) Common OCC (= new loan yield) PV(CFOLD - CFNEW) = PV(CFOLD) – PV(CFNEW)

2) Capital structure neutrality (new loan amt such that Refin is CF neutral at time zero)

PV(CFNEW) = OLBOLD

3) Preceding (1) & (2) together PV(CFOLD - CFNEW) = PV(CFOLD) – OLBOLD

Therefore:Just subtract old loan balance (plus Just subtract old loan balance (plus prepmtprepmt penalty) from old penalty) from old loan PV (based on old loan remaining loan PV (based on old loan remaining CFsCFs) computed with ) computed with

new loan yield as the discount rate.*new loan yield as the discount rate.** New loan yield can be computed without knowing loan amt (set P* New loan yield can be computed without knowing loan amt (set PV=1 in calc).V=1 in calc).



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Shortcut procedure is not only methodologically convenient,Shortcut procedure is not only methodologically convenient,

It raises an important substantive economic point:It raises an important substantive economic point:

Refinancing decision is not Refinancing decision is not reallyreally a comparison a comparison between two loans:between two loans:

Rather, it is a decision simply regarding the old loan:Rather, it is a decision simply regarding the old loan:

““Does it make sense to exercise the Old LoanDoes it make sense to exercise the Old Loan’’s s Prepayment Option?Prepayment Option?”” **

* It does not matter whether the old loan would be paid off with* It does not matter whether the old loan would be paid off withcapital obtained from:capital obtained from:

•• A new loan,A new loan,•• Additional equity,Additional equity,•• Some combinationSome combination

(Capital structure decision is separate from refinancing decisio(Capital structure decision is separate from refinancing decision.)n.)



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Old Loan:Old Loan:Previous $1,000,000, 30Previous $1,000,000, 30--yr yr amortamort, , 8%, 108%, 10--yr maturityyr maturity loan.loan.Taken out 4 years ago, Taken out 4 years ago, 2 pts prepayment penalty2 pts prepayment penalty..Expected to be Expected to be prepaid prepaid after another 6 yrs (at maturity):after another 6 yrs (at maturity):

Numerical ExampleNumerical Example

( ) ( )∑= +

++

+−=120

112012/08.1

247,877$12/08.165.337,7$000,000,1$0

tt

New Loan:New Loan:Available @ 7% interest, 6Available @ 7% interest, 6--yr maturity, 30yr maturity, 30--yr yr amortamort, , 1 pt 1 pt fee upfrontfee upfront..

What is NPV of Refinancing?What is NPV of Refinancing?(Ignore transaction cost & option value.)(Ignore transaction cost & option value.)



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( ) ( )∑= +

++

=72

17212/08.1

247,877$12/08.165.337,7$190,962$

tt

2) Step Two:Compute Old Loan Liquidating Payment (= OLB + PPMT Penalty):

= $981,434 = 1.02 X $962,190, where:

1) Step One: Compute Current OCC (based on new loan terms).= 7.21%, as new 30-yr amort, 6-yr mat., 7%, 1-pt loan per $ of loan amt, gives IRR = 7.21%:

( ) ( )∑= +

++

+−=

−===

72

17212/0721.1

926916.0$12/0721.1

006653.0$99.0$0

.926916.]006653.,12*6,12/07[.]006653.,12*24,12/07[.006653.]1,12*30,12/07.0[

tt

FVPVPMT

Numerical Example (cont.)Numerical Example (cont.)

Per $ of Loan Amt.

1 Pt Fee Upfront.



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Numerical Example (cont.)Numerical Example (cont.)3) Step Three:Compute Present Value of Old Loan Liability.= $997,654, as:

( ) ( )∑= +

++

=72

17212/0721.1

247,877$12/0721.1

65.337,7$654,997$t

t

4) Step Four:Compute the NPV of Refinancing:

NPV = $997,654 NPV = $997,654 -- $981,434 = +$16,220.$981,434 = +$16,220.

The Long Route (Specifying New Loan Amt.):The Long Route (Specifying New Loan Amt.):• (1.02) 962190 = $981,434 = Old Loan Liquidating Pmt Amt (inclu penalty).• 981434 / 0.99 = $991,348 = New Loan Amt.• PMT [ .07/12, 30*12, 991348 ] = $6,595.46 / mo.• PV [ .07/12, 24*12, 6595.46 ] = FV [.07/12, 6*12, 6595.46 ] = $918,896 balloon.

( ) ( ).220,16$434,981$654,997$

12/0721.1896,918$

12/0721.146.595,6$434,981$

72

172

+=−=+

++

=∑=

NPVt

t

From Previous Step (2)From Previous Step (3)



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17.3.2 What is Left Out of The traditional Calculation17.3.2 What is Left Out of The traditional Calculation:Prepayment Option ValuePrepayment Option Value

Suppose refinancing transaction cost: X = $10,000.Suppose refinancing transaction cost: X = $10,000.Then according to traditional DCF calculation:Then according to traditional DCF calculation:

NPV = $16,220 NPV = $16,220 -- $10,000 = +$6,220$10,000 = +$6,220Should Refinance.Should Refinance.

But something important has been left out:But something important has been left out:•• Old Loan includes prepayment option.Old Loan includes prepayment option.•• This option has value to borrower.This option has value to borrower.•• Borrower gives up (loses) the option when she exercises it Borrower gives up (loses) the option when she exercises it (prepays the old loan).(prepays the old loan).•• Hence, Loss of the value of this option is an Hence, Loss of the value of this option is an opportunity costopportunity cost of of refinancing, for the borrower.refinancing, for the borrower.•• i.e., Instead of refinancing today, the borrower could wait andi.e., Instead of refinancing today, the borrower could wait andrefinance next month, or next year, . . . This might be better.refinance next month, or next year, . . . This might be better.



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Numerical Example (cont.)Numerical Example (cont.)In previous example current int. rate = 7%.In previous example current int. rate = 7%.Suppose int. rate next yr could be either 5% (50% Suppose int. rate next yr could be either 5% (50% probprob) or 9% (50% ) or 9% (50% probprob).).Can either refinance today or wait 1 year.Can either refinance today or wait 1 year.With 5% int. rate New Loan (30 yr amort, 5-yr balloon) 5.24% yld.

1 yr from now Old Loan will have 5 yrs left (60 month horizon), and OLBOLD = $950,699, X1.02 = $969,713 Liq.Pmt.

PV(CFOLD) = $1,062,160.NPV (next yr, @5%) = 1062160 – 969713 – 10000 = +$82,448.

Similarly, if int. rate next yr is 9%:NPV (next yr, @9%) = -$75,079. Thus, would not prepay: NPV = 0.Exptd Val (as of today) of Prepayment Option next year:

= (50%)$82448 + (50%)0 = $41,224.This option may be quite risky. Suppose it requires an OCC = 30%, then:

PV(today) of Prepayment Option = 41224/1.30 = $31,711.NPV (Refin today, inclu oppty cost of option) = +$6,220 - $31,711 < 0:DonDon’’t Refinance today.t Refinance today.



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17.3.2 What is Left Out of The traditional Calculation17.3.2 What is Left Out of The traditional Calculation:Prepayment Option ValuePrepayment Option Value

Prepayment option value is included in Prepayment option value is included in Market ValueMarket Value of of the Old Loan.the Old Loan.

Let Let ““D(OldD(Old))”” = = MktMkt Val. of Old Loan;Val. of Old Loan;

““C(PrepayC(Prepay))”” = = MktMkt Val of Prepayment Option:Val of Prepayment Option:

D(OldD(Old) = PV(CF) = PV(CFOLDOLD) ) –– C(PrepayC(Prepay))

Thus, if we can observe the Thus, if we can observe the MktMkt Val of Old Loan, then we Val of Old Loan, then we can compute correct NPV of Refinancing as:can compute correct NPV of Refinancing as:

NPV(PrepayNPV(Prepay) = ) = D(OldD(Old) ) –– OLBOLBOLDOLD –– XX



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Real estate loans are often illiquid: Difficult to observe Real estate loans are often illiquid: Difficult to observe their their mktmkt val.val.

Old ruleOld rule--ofof--thumb used to be for residential loans, wait thumb used to be for residential loans, wait until current int. rate is about 200 bps below old loan until current int. rate is about 200 bps below old loan contract rate.contract rate.

Now transaction costs (X) are lower, the threshold may Now transaction costs (X) are lower, the threshold may be lower, butbe lower, but……

Many borrowers also may not be accounting for the Many borrowers also may not be accounting for the option cost, &/or the effect of a possibly short holding option cost, &/or the effect of a possibly short holding horizon for the old loan due to possibility of a house horizon for the old loan due to possibility of a house move. move. Too much residential refinancing?Too much residential refinancing?



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Consider again our previous example Old Loan:Consider again our previous example Old Loan:Previous $1,000,000, 30Previous $1,000,000, 30--yr yr amortamort, , 8%, 108%, 10--yr maturityyr maturity loan.loan.Taken out 4 years ago.Taken out 4 years ago.Expected to be Expected to be prepaid prepaid after another 6 yrs (at maturity):after another 6 yrs (at maturity):

““WraparoundWraparound”” MortgageMortgage

( ) ( )∑= +

++

+−=120

112012/08.1

247,877$12/08.165.337,7$000,000,1$0

tt

Now suppose interest rates have gone Now suppose interest rates have gone upup instead of down, instead of down, such that a new 6 yr 1such that a new 6 yr 1stst mortgage would be:mortgage would be:Available @ 10% interest, 6Available @ 10% interest, 6--yr maturity, 30yr maturity, 30--yr yr amortamort..

Suppose the original borrower now wants to sell the Suppose the original borrower now wants to sell the property, but they hate to lose the value of the belowproperty, but they hate to lose the value of the below--mktmkt--interest old loan, and suppose the old loan is not interest old loan, and suppose the old loan is not

““assumableassumable”” but has no but has no ““due on saledue on sale”” clauseclause……



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Seller (original borrower) could offer buyer a Seller (original borrower) could offer buyer a ““wraparoundwraparound”” second second mortgage at, say, 9.5% (below market rate), and use this to cashmortgage at, say, 9.5% (below market rate), and use this to cash out out her value in the belowher value in the below--mktmkt--rate old loan, and help sell the property.rate old loan, and help sell the property.Suppose value of the building is now $1,500,000, and buyer wouldSuppose value of the building is now $1,500,000, and buyer wouldwant to finance purchase with an $1,100,000 mortgage.want to finance purchase with an $1,100,000 mortgage.Suppose wrap has 30Suppose wrap has 30--yr yr amortamort, 6, 6--yr balloon.yr balloon.

$7337.65 Old Loan (1st Mortg) pmt

$9249.40 Wrap Loan (2nd Mortg) pmt

72

$877,247 Old Balloon

$1,047,764 Wrap Balloon

$1911.75 = incremental pmt $170,517 = Incr Balloon

Old Loan Bal = PV(8%/12, 48, 7337.65) = $962,190.

“New Money” = $1,100,000 - $962,190 = $137,810.

Wrap yld = Rate(72, 1911.75, -137810, 170517) = 18.81% !www.bsscommunitycollege.in www.bssnewgeneration.in www.bsslifeskillscollege.in


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The 18.8% wrap yield is a “super-normal” yield (above the OCC of the new money investment), reflecting the positive NPV of the old loan’s below-mkt interest rate, realized by the old loan borrower via the wrap transaction.



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pN

pO

pmt

NO NN

“New Money” = LN – LO =

General wrap loan mechanics:General wrap loan mechanics:LO = OLB on old loan; LN = Contractual initial principal on wrap loan; pO = Pmt on old loan; pN = Pmt on wrap loan; NO = Periods left on old loan; NN = Periods in wrap loan; rN = IRR of wrap loan to wrap lender…

PV(AA @ rN ) +

AA

BB

PV(BB @ rN )

Old Loan



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“New Money” = LN – LO = PV(AA @ rN ) + PV(BB @ rN )

( ) ( ) ( )( ) ⎟⎟

⎠

⎞⎜⎜⎝

⎛

+⎥⎦

⎤⎢⎣

⎡ +−+⎥

⎦

⎤⎢⎣

⎡ +−−=−

−

O

ONO

NNN

NNN

NN

NN

ONON rrrp

rrppLL

11111111

Solve this equation algebraically for LN or pN , given the other variables, or solve it numerically (in calculator or spreadsheet) for rN given the other variables.

Recall that: ( ) ( ) ( )( )

⎟⎟⎠

⎞⎜⎜⎝

⎛ +−=

+++

++

+ rra

ra

ra

ra N

N111

111 2 L



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Example:Example:Old loan was originally $1,000,000 for 20 yrs (amortizing) @ 6%, taken out 15 yrs ago, with current OLB = LO = $370,578; pmt = pO = $7164.31/mo.New (wrap) loan would be for $1,000,000 with 20-yr amort and 10-yr balloon, @ 8%.What is the yield (IRR) on the new money? . . .

240 = N, 8=I, 1000000 = PV, 0=FV; pmt = $8364.40 = pN .

pN – pO = 8364.40 – 7164.31 = $1200.09/mo; NO = 240-180 = 60;

120=N; FV = $689,406 = new loan balloon month 120 = NN.

689406 + 8364.40 = $697,770 = last month’s CF (month 120).

New Money = $1,000,000 - $370,578 = $629,422 = LN – LO .

Now go to CF keys of calculator…

-629422=CF0, 1200.09=CF1, 60=N1, 8364.4=CF2, 59=N2, 697770=CF3;

IRR = 8.33% = yN .



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““BondBond--EquivalentEquivalent”” & & ““MortgageMortgage--EquivalentEquivalent”” RatesRates……

Traditionally, bonds pay interest semi-annually (twice per year).Bond interest rates (and yields) are quoted in nominal annual terms (ENAR) assuming semi-annual compounding (m = 2).This is often called “bond-equivalent yield”(BEY), or “coupon-equivalent yield”(CEY). Thus:

1 - )BEY/ + (1 = EAR 22

Recall from Chapter 8 . . .



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““BondBond--EquivalentEquivalent”” & & ““MortgageMortgage--EquivalentEquivalent”” RatesRates

Traditionally, mortgages pay interest monthly.Mortgage interest rates (and yields) are quoted in nominal annual terms (ENAR) assuming monthly compounding (m = 12).This is often called “mortgage-equivalent yield” (MEY) Thus:

1 - ) MEY/+ (1 = EAR 1212www.bsscommunitycollege.in www.bssnewgeneration.in www.bsslifeskillscollege.in


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Example:Example:

Yields in the bond market are currently 8% (CEY). What interest rate must you charge on a mortgage (MEY) if you want to sell it at par value in the bond market?



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Answer:Answer:7.8698%.

078698.00816.11212

0816.004.12121121

22

===

==

1] - )[( 1] - )EAR + [(1 MEY

1 - )(1 - )BEY/ + (1 = EAR//

HP-10B TI-BAII PLUS

CLEAR ALL I Conv

2 P/YR NOM = 8 ENTER ↓ ↓

8 I/YR C/Y = 2 ENTER ↑

EFF% gives 8.16 CPT EFF = 8.16 ↓

12 P/YR C/Y = 12 ENTER ↑↑

NOM% gives 7.8698 CPT NOM = 7.8698



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Example:Example:

You have just issued a mortgage with a 10% contract interest rate (MEY). How high can yields be in the bond market (BEY) such that you can still sell this mortgage at par value in the bond market?



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Answer:Answer:10.21%.

1021.01047.122

1047.000833.112212/1

1212

===

==

1] - )[( 1] - )EAR + [(1 BEY

1 - )(1 - ) MEY/+ (1 = EAR/

HP-10B TI-BAII PLUS

CLEAR ALL I Conv

12 P/YR NOM = 10 ENTER ↓ ↓

10 I/YR C/Y = 12 ENTER ↑

EFF% gives 10.47 CPT EFF = 10.47 ↓

2 P/YR C/Y = 2 ENTER ↑↑

NOM% gives 10.21 CPT NOM = 10.21



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Economic Analysis of Investment in Real Economic Analysis of Investment in Real Estate Development Projects,Estate Development Projects,

Part 1Part 1



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Exhibit 2-2: The “Real Estate System”: Interaction of the Space Market, Asset Market, & Development Industry

SPACE MARKET

SUPPLY(Landlords)

DEMAND(Tenants)

RENTS&

OCCUPANCY

LOCAL&

NATIONALECONOMY

FORECASTFUTURE

ASSET MARKET

SUPPLY(Owners

Selling)


CASHFLOW

MKTREQ’D

CAPRATE

PROPERTYMARKETVALUE

DEVELOPMENTINDUSTRY

ISDEVELPT

PROFITABLE?

CONSTRCOSTINCLULAND

IFYES

ADDSNEW

CAPITAL MKTS

= Causal flows.




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Development is a multiDevelopment is a multi--disciplinary, iterative process . . .disciplinary, iterative process . . .

The (famous) The (famous) GraaskampianGraaskampian SpiralSpiral..

Development is important:Development is important:•• From a finance & investment perspective, but alsoFrom a finance & investment perspective, but also•• From an urban development (physical, social, environmental) From an urban development (physical, social, environmental) perspectiveperspective……

FinancialAnalysis

Market andCompetitiveAnalysis

Political andLegal Analysis

Physical andDesign Analysis

Image by MIT OCW.



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GraaskampGraaskamp also coined the concept that most development also coined the concept that most development projects can be characterized as either:projects can be characterized as either:

•• A use looking for a site, orA use looking for a site, or

•• A site looking for a use.A site looking for a use.

Site Looking for a Use:Site Looking for a Use:

•• Developer tries to determine & build the Developer tries to determine & build the ““HBUHBU””, or, or

•• Public entity seeks developer to build a use determined Public entity seeks developer to build a use determined through a political process (presumably also through a political process (presumably also ““HBUHBU””).).

Use Looking for a Site:Use Looking for a Site:

•• Developer has a particular specialization, orDeveloper has a particular specialization, or

•• Developer is working for a specific Developer is working for a specific useruser..



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LAND OPTIONING & ASSEMBLY, PERMITTING, &

DEVLPT DESIGN

CONSTRUCTION

LANDPURCHASE“Time 0”

SHELL COMPLETION

“Time T1”

LEASE-UP & TENANT FINISHES

STABILIZED

OPERATION

$

CUMULATIVE

INVESTME NT

$DEVLPMT

COMPLETION“Time T2”

Time

RISK

AS

INVERSE

SUCCESS

PROB

VERY HIGH RISKe.g.: 40%

OCC

HIGH RISKe.g.: 20%

OCC

MODERATE RISKe.g.: 10% OCC

LOW RISKe.g.: 8% OCC

Exhibit 29-1a: Development Project Phases: Typical Cumulative Capital Investment Profile and Investment Risk Regimes

= CUMULATIVE INVESTMENT

= RISK LEVELwww.bsscommunitycollege.in www.bssnewgeneration.in www.bsslifeskillscollege.in


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LAND OPTIONING & ASSEMBLY, PERMITTING, & DEVLPT DESIGN

CONSTRUCTION

LANDPURCHASE“Time 0”

SHELL COMPLETION

“Time T1”

LEASE-UP & TENANT FINISHES

STABILIZED

OPERATION

$

CUMULATIVE

INVESTME NT

$

DEVLPMT COMPLETION

“Time T2”

ENTREPRENEURIALDEVLPR SEED EQUITY

SOURCES OF CAPITAL:

EXTERNAL EQUITY &/OR MEZZ DEBT INVESTORS:OPPTY FUNDS, INSTNS, FOREIGN INVSTRS, WEALTHY INDIVIDUALS, REITS

DEVLPT CAPITALBetw 0 & T…FROM COMMERCIAL BANKS:TRADITIONAL CONSTRUCTION LOAN DEBT, FROM Time 0 TO Time T1;AND/ORMINI-PERM LOAN DEBTFROM Time 0 TO Time T2.

PERMANENT FINANCEBeyond Time T…FROM LICs, PFs, PRIV EQUITY :L.T. EQUITYORCOMMERCIAL MORTGAGE (EITHER CMBS CONDUIT OR WHOLE LOAN)

Time

ORDER

OF

INVESTMENT

ORDER

OF

PRIORITY

IN

PAYBACK

Exhibit 29-1b: Development Project Typical Sources of Investment Capital

A

B

C

D E

F

G H I

OZ



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From Tod McGrath’s analysis of Massachusetts 40B projects…



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Risk Profile

Opera ting Expens e Ris k

P artne rs hip Ris kValuatio n Ris k

Eve nt Ris k

P ricing Ris k

Ca pital Ma rket Ris k

Credit Ris k

Le as ing/S ale s Ris k

Co ns truc tio n R is k

Entitleme nt Ris k

0%

70%

82%

30% 33%39%

45%52%

100%

Operating Expense Risk Partnership Risk Valuation Risk Event RiskPricing Risk Capital Market Risk Credit Risk Leasing/Sales RiskConstruction Risk Entitlement Risk

Appre cia tio n (P ro fit)Earned (%)

Dev

elop

men

t Risk

Ong

oing

Risk

NCREIF Accounting Committee White Paper on Timing of Recognition of Development “Entrepreneurial Profit”



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Cumulative Entrepreneurial Profit

0%

30% 33%39%

45%52%

70%

100%

82%

-20%

0%

20%

40%

60%

80%

100%

0 - Acquire Land1 - Finalize all entitlements and permits

2 - Commence construction

3 4 5 6 - Complete construction

7 8 - Complete Leasing/Sellout

Profit

Loss



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1. Entitlement Risk

•Risk of obtaining appropriate land entitlements, construction permits, and possibly zoning variances.

2. Construction Risk

•Materials pricing – risk that the cost of materials may change significantly from the original construction

•Scheduling – risk that planned construction completion could be prolonged due to weather delays, labor disputes, material delivery delays, etc.

3. Leasing/Sales Risk

•Risk that forecasted absorption (leasing or unit sales) volume will not be realized.

•Risk that early termination clauses would be invoked or that the property becomes encumbered by a long-lease with below-market rent escalation provisions (frequency and/or amount of increase).

•Risk of a market-driven restructure of leasing or sales commission rates.

4. Operating Expense Risk

•Risk of a significant change in one or more fixed or variable expense categories such as insurance, real estate taxes, etc.

5. Credit Risk

•Risk that pre-lease tenants and/or tenants’ industry segment is negatively impacted during development.

6. Partnership Risk (if applicable)

•Risk that accompanies any ownership less than 100% due to a myriad of factors regarding control, revenue distributions, etc.

Their list of “primary risk factors” . . .



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7. Capital Market Risk

•Interest Rates – risk of a significant change in interest rates during the development period. This could affect cost of construction or, in the case of a condominium project, the buyer’s ability to obtain suitable purchase price financing.

•Alternative investment risk – risk that investor allocations or rates of return for alternative investments will change resulting in shifts in capitalization and discount rates.

8. Pricing Risk•Supply Risk – risk that unanticipated competitive supply will enter the market before lease-up or sellout is achieved resulting in short-, mid-, or long-term concessions, absorption, pricing, etc.

•Real Estate Cycle Issues – risk that rental rates may be negatively affected by changes in market dynamics.

9. Event Risk•Risk of a material physical, economic, or other event occurring that significantly impacts asset operations value. Weather, discovery of previously unknown environmental contamination, exodus of major employment providers, and terrorism comprise a sampling of such events.

10. Valuation Risk•Risk that a lack of applicable, current market data exists to accurately value the subject property.

•Risk that a lack of competency exists with the appraiser engaged to specifically address issues of property geography, valuation analytics, market research, etc.

Continued . . .



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29.2 Basic Information: Enumerating Project Costs & Benefits29.2 Basic Information: Enumerating Project Costs & Benefits

Two types of project budgets are important to be developed:Two types of project budgets are important to be developed:

•• Construction & Absorption Budget:Construction & Absorption Budget:•• Covers construction (& leaseCovers construction (& lease--up, for up, for ““specspec”” projects);projects);•• Relates to the Relates to the ““COSTCOST”” side of the NPV Equation.side of the NPV Equation.

•• Operating Budget:Operating Budget:•• Covers Covers ““stabilizedstabilized”” period of building operation after leaseperiod of building operation after lease--up is complete;up is complete;•• Typically developed for a single typical projected Typically developed for a single typical projected ““stabilized stabilized yearyear””;;•• Relates to the Relates to the ““BENEFITBENEFIT”” side of the NPV Equation.side of the NPV Equation.

NPV = Benefits NPV = Benefits –– Costs = Value of Bldg Costs = Value of Bldg –– Cost of Cost of DevlptDevlpt..



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The Operating Budget The Operating Budget (Recall the items from Chapter 11)(Recall the items from Chapter 11)::•• Forecast Potential Gross Income (PGI, based on rent analysis)Forecast Potential Gross Income (PGI, based on rent analysis)

•• Less Vacancy AllowanceLess Vacancy Allowance

•• = Effective Gross Income (EGI)= Effective Gross Income (EGI)

•• Less forecast operating expenses (& capital reserve)Less forecast operating expenses (& capital reserve)

•• = Net Operating Income (NOI)= Net Operating Income (NOI)

The most important aspect is normally the rent analysis, which iThe most important aspect is normally the rent analysis, which is based s based (more or less formally) on a (more or less formally) on a market analysismarket analysis of the space market which the of the space market which the building will serve. building will serve. (See Chapter 6, or Wheaton(See Chapter 6, or Wheaton’’s 11.433 course.)s 11.433 course.)

The bottom line:The bottom line:NOI forecast, combined with NOI forecast, combined with cap ratecap rate analysis (of the asset market):analysis (of the asset market):

NOI / cap rate = Projected Completed Building Value = NOI / cap rate = Projected Completed Building Value = ““BenefitBenefit”” of the of the development project.development project.



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The Construction & Absorption Budget:The Construction & Absorption Budget:

Construction: Construction: ““Hard CostsHard Costs””•• Land costLand cost•• Site preparation costs (e.g., excavation, utilities installatioSite preparation costs (e.g., excavation, utilities installation)n)•• Shell costs of existing structure in rehab projectsShell costs of existing structure in rehab projects•• PermitsPermits•• Contractor feesContractor fees•• Construction management and overhead costsConstruction management and overhead costs•• MaterialsMaterials•• LaborLabor•• Equipment rentalEquipment rental•• Tenant finishTenant finish•• Developer feesDeveloper fees



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Construction: Construction: ““Soft CostsSoft Costs””•• Loan feesLoan fees•• Construction loan interestConstruction loan interest•• Legal feesLegal fees•• Soil testingSoil testing•• Environmental studiesEnvironmental studies•• Land planner feesLand planner fees•• Architectural feesArchitectural fees•• Engineering feesEngineering fees•• Marketing costs including advertisementsMarketing costs including advertisements•• Leasing or sales commissionsLeasing or sales commissions

The Construction & Absorption Budget The Construction & Absorption Budget (cont.)(cont.)::

Absorption Budget Absorption Budget (if separate)(if separate)::•• Marketing costs & advertisingMarketing costs & advertising•• Leasing expenses (commissions)Leasing expenses (commissions)•• Tenant improvement expenditures Tenant improvement expenditures ((““buildbuild--outsouts””))•• Working capital during leaseWorking capital during lease--up (until breakup (until break--even)even)



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29.3 Construction Budget Mechanics29.3 Construction Budget Mechanics

Construction Construction takes timetakes time (typically several months to several years).(typically several months to several years).

During this period, financial capital is being used to pay for tDuring this period, financial capital is being used to pay for the construction.he construction.

““Time is moneyTime is money””: The opportunity cost of this capital is part of the real cost : The opportunity cost of this capital is part of the real cost of of the construction.the construction.

This is true whether or not a construction loan is used to finanThis is true whether or not a construction loan is used to finance the ce the construction process. But:construction process. But:

Construction loans are Construction loans are almost alwaysalmost always used (even by equity investors who have used (even by equity investors who have plenty of cash).plenty of cash).

Why? . . .Why? . . .



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The The ““classicalclassical”” construction finance structure:construction finance structure:Phase:Phase:

Financing:Financing:

ConstructionConstruction LeaseLease--UpUp Stabilized OperationStabilized Operation……

C.O.C.O.

Construction LoanConstruction Loan Bridge LoanBridge Loan Permanent MortgagePermanent Mortgage

Source:Source:CommercialCommercial

BankBank•• Comm. BankComm. Bank•• InsurInsur Co.Co.

Via Via MortgMortg BrkrBrkror or MortgMortg Banker:Banker:•• Life Life InsurInsur. Co.. Co.•• Pension FundPension Fund•• Conduit Conduit CMBSCMBS

Construction lender wonConstruction lender won’’t approve construction t approve construction loan until permanent lender has conditionally loan until permanent lender has conditionally approved a approved a ““taketake--outout”” loan.loan.



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The construction loan collapses a series of costs (cash outflowsThe construction loan collapses a series of costs (cash outflows) ) incurred during the construction process into a incurred during the construction process into a single valuesingle value as of as of a single (future) a single (future) point in timepoint in time (the projected completion date of (the projected completion date of the construction phase).the construction phase).

Actual construction expenditures (Actual construction expenditures (““drawsdraws”” on the construction on the construction loan) are added to the accumulating loan) are added to the accumulating balancebalance due on the loan, due on the loan, and interest is charged and compounded (adding to the balance) and interest is charged and compounded (adding to the balance) on all funds drawn out from the loan commitment, from the on all funds drawn out from the loan commitment, from the time each draw is made.time each draw is made.

Thus, interest Thus, interest compounds forwardcompounds forward, and the borrower owes no , and the borrower owes no payments until the loan is due at the end of construction, when payments until the loan is due at the end of construction, when all principle and interest is due.all principle and interest is due.

Bottom line: Borrower (developer) faces no cash outflows for Bottom line: Borrower (developer) faces no cash outflows for construction until the end of the process, when the entire cost construction until the end of the process, when the entire cost is is paid (including the paid (including the ““cost of capitalcost of capital””).).



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Example:Example:Commitment for $2,780,100 of Commitment for $2,780,100 of ““future advancesfuture advances”” in a in a construction loan to cover $2,750,000 of actual construction construction loan to cover $2,750,000 of actual construction costs over a three month period. 8% interest (costs over a three month period. 8% interest (nom.annnom.ann.), .), compounded monthly, beginning of month draws:compounded monthly, beginning of month draws:

Month New Draw Current Interest New Loan Balance

1 $500,000 $3,333.33 $503,333.33

2 $750,000 $8,355.55 $1,261,688.88

3 $1,500,000 $18,411.26 $2,780,100.14

4 and so on

Construction schedule must estimate the amount and timing of theConstruction schedule must estimate the amount and timing of the draws.draws.

The accumulated interest (8333+8356+18411 = $30,100 in this caseThe accumulated interest (8333+8356+18411 = $30,100 in this case) is a) is avery real part of the very real part of the total costtotal cost of constructionof construction. AKA . AKA ““Financing CostFinancing Cost””..Typically a Typically a ““commitment feecommitment fee”” is also required, up front (in cash).is also required, up front (in cash).



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29.4 Simple Financial Feasibility Analysis in Current Practice29.4 Simple Financial Feasibility Analysis in Current Practice

The traditional and most widely employed method for the analysisThe traditional and most widely employed method for the analysis of the of the financial feasibility of development projects will be referred tfinancial feasibility of development projects will be referred to here as: o here as: ““Simple Financial Feasibility AnalysisSimple Financial Feasibility Analysis”” (SFFA)(SFFA)..

SFFA is based on the commercial mortgage market (for SFFA is based on the commercial mortgage market (for permanentpermanent loans).loans).

It assumes the developer will take out the largest permanent loaIt assumes the developer will take out the largest permanent loan possible n possible upon completion of the building.upon completion of the building.

It assumes that the development It assumes that the development costscosts will equal the market will equal the market valuevalue of the of the property on completion.property on completion.

Obviously, SFFA leaves something to be desired from a normative Obviously, SFFA leaves something to be desired from a normative perspective, but:perspective, but:

•• It is It is simplesimple and easy to understand.and easy to understand.•• It requires no specialized knowledge of the capital markets otIt requires no specialized knowledge of the capital markets other than her than familiarity with the commercial mortgage market (does not even rfamiliarity with the commercial mortgage market (does not even require equire familiarity with the relevant property asset market).familiarity with the relevant property asset market).

SFFA comes in two modes: SFFA comes in two modes: ““Front DoorFront Door””, & , & ““Back DoorBack Door”” . . .. . .



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SFFA SFFA ““Front DoorFront Door”” Procedure: Procedure: Start with costs & end with rent required for feasibilityStart with costs & end with rent required for feasibility……

Site Acquisition Costs + Construction CostsSite Acquisition Costs + Construction Costs= Total Expected Development Cost= Total Expected Development CostX Loan to Value RatioX Loan to Value Ratio= Permanent Mortgage= Permanent MortgageX Annualized Mortgage ConstantX Annualized Mortgage Constant= Cash Required for Debt Service= Cash Required for Debt ServiceX Lender Required Debt Service Coverage RatioX Lender Required Debt Service Coverage Ratio= Required Net Operating Income or NOI= Required Net Operating Income or NOI+ Estimated Operating Expenses (Not passed through to tenants)+ Estimated Operating Expenses (Not passed through to tenants)= Required Effective Gross Income= Required Effective Gross Income÷÷ Expected Occupancy RateExpected Occupancy Rate= Required Gross Revenue= Required Gross Revenue÷÷ LeasableLeasable Square FeetSquare Feet= Rent Required Per Square Foot= Rent Required Per Square Foot

Question: Is this average required rent per square foot achievabQuestion: Is this average required rent per square foot achievable?le?

Typical approach for Typical approach for ““Site looking for a UseSite looking for a Use””..www.bsscommunitycollege.in www.bssnewgeneration.in www.bsslifeskillscollege.in


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Example:Example:•• Class B office building rehab project: 30,000 SF (of which 27,2Class B office building rehab project: 30,000 SF (of which 27,200 NRSF).00 NRSF).•• Acquisition cost = $660,000; Acquisition cost = $660,000; •• Rehab construction budget: $400,000 hard costs + $180,000 soft Rehab construction budget: $400,000 hard costs + $180,000 soft costs.costs.•• Estimated operating costs (to landlord) = $113,000/yr.Estimated operating costs (to landlord) = $113,000/yr.•• Projected stabilized occupancy = 95%.Projected stabilized occupancy = 95%.•• Permanent loan available on completion @ 11.5% (20Permanent loan available on completion @ 11.5% (20--yr yr amortamort) with 120% DSCR.) with 120% DSCR.•• Estimated feasible rents on completion = $10/SF.Estimated feasible rents on completion = $10/SF.

Site and shell costs:Site and shell costs: $ 660,000$ 660,000+ Rehab costs:+ Rehab costs: 580,000580,000= Total costs:= Total costs: $1,240,000$1,240,000X Lender required LTVX Lender required LTV x 80%x 80%= Permanent mortgage amount: $ 992,000= Permanent mortgage amount: $ 992,000X Annualized mortgage constant: x 0.127972X Annualized mortgage constant: x 0.127972= Cash required for debt svc:= Cash required for debt svc: $ 126,948$ 126,948X Lender required DCR:X Lender required DCR: x 1.20x 1.20= Required NOI:= Required NOI: $ 152,338$ 152,338+ + EstdEstd. . OperOper. Exp. (Landlord):. Exp. (Landlord): 113,000113,000= Required EGI:= Required EGI: $ 265,338$ 265,338÷÷ Projected occupancy (1Projected occupancy (1--vac):vac): ÷÷ 0.950.95= Required PGI:= Required PGI: $ 279,303$ 279,303÷÷ Rentable area:Rentable area: ÷÷ 27200 SF27200 SF---------------------------- ------------------= Required rent/SF:= Required rent/SF: $10.27 /SF $10.27 /SF

What major What major issue is left issue is left out here?out here?

Lender will Lender will base base mortgmortg on on MktMkt Val, not Val, not constrconstr cost.cost.

Use Use mktmkt cap cap rate info to rate info to est. bldg val.est. bldg val.



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SFFA SFFA ““Back DoorBack Door”” Procedure: Procedure: Start with rents & building, and end with supportable developmenStart with rents & building, and end with supportable development costst costs……

Total Total LeaseableLeaseable Square Feet (based on the building efficiency ratio Square Feet (based on the building efficiency ratio times the gross area)times the gross area)X Expected Average Rent Per Square FootX Expected Average Rent Per Square Foot= Projected Potential Gross Income (PGI)= Projected Potential Gross Income (PGI)-- Vacancy AllowanceVacancy Allowance= Expected Effective Gross Income= Expected Effective Gross Income-- Projected Operating ExpensesProjected Operating Expenses= Expected Net Operating Income= Expected Net Operating Income÷÷ Debt Service Coverage RatioDebt Service Coverage Ratio÷÷ Annualized Mortgage ConstantAnnualized Mortgage Constant÷÷ Maximum Loan to Value RatioMaximum Loan to Value Ratio= Maximum Supportable Total Project Costs= Maximum Supportable Total Project Costs(Question: Can it be built for this including all costs?)(Question: Can it be built for this including all costs?)-- Expected Construction Costs (Other than Site)Expected Construction Costs (Other than Site)= Maximum Supportable Site Acquisition Cost= Maximum Supportable Site Acquisition Cost

Question: Can the site be acquired for this or less? Question: Can the site be acquired for this or less?

Typical approach for Typical approach for ““Use looking for a SiteUse looking for a Site””..www.bsscommunitycollege.in www.bssnewgeneration.in www.bsslifeskillscollege.in


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Example:Example:•• Office building 35,000 SF (GLA), 29,750 SF (NRA) Office building 35,000 SF (GLA), 29,750 SF (NRA) (85% (85% ““Efficiency RatioEfficiency Ratio””))..•• $12/SF (/yr) realistic rent (based on market analysis, pre$12/SF (/yr) realistic rent (based on market analysis, pre--existing tenant wants space).existing tenant wants space).•• Assume 8% vacancy (typical in market, due to extra space not prAssume 8% vacancy (typical in market, due to extra space not pree--leased).leased).•• Preliminary design construction cost budget (hard + soft) = $2,Preliminary design construction cost budget (hard + soft) = $2,140,000.140,000.•• Projected operating expenses (not passed through) = $63,000.Projected operating expenses (not passed through) = $63,000.•• Permanent mortgage on completion available at 9% (20Permanent mortgage on completion available at 9% (20--yr yr amortamort), 120% DCR.), 120% DCR.•• Site has been found for $500,000: Site has been found for $500,000: Is it feasible?Is it feasible?

Potential Gross Revenue = 29,750 x $12 =Potential Gross Revenue = 29,750 x $12 = $ 357,000$ 357,000Less Vacancy at 8% = Less Vacancy at 8% = -- 28,56028,560= Effective Gross Income= Effective Gross Income $ 328,440$ 328,440Less Operating Expenses Less Operating Expenses -- 63,00063,000= Net Operating Income= Net Operating Income $ 265,000$ 265,000÷÷ 1.20 = Required Debt Svc:1.20 = Required Debt Svc: $ 221,200$ 221,200÷÷ 12 = Monthly debt svc: 12 = Monthly debt svc: $ 18,433$ 18,433

Supportable mortgage amount =Supportable mortgage amount = $ 2,048,735$ 2,048,735÷÷ 0.75 LTV = Min. 0.75 LTV = Min. ReqdReqd. Value:. Value: $ 2,731,647$ 2,731,647Less Construction CostLess Construction Cost -- 2,140,0002,140,000------------------------ ----------------------

Supportable site acquisition Supportable site acquisition costcost:: $ 591,647.$ 591,647.

So, the project seems feasible.So, the project seems feasible.

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛+

−=240

1209.1

1112/09.

18433

But again, something seems left outBut again, something seems left out…… Project may be feasible, Project may be feasible, butbut……www.bsscommunitycollege.in www.bssnewgeneration.in www.bsslifeskillscollege.in


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Problems with the SFFA:Problems with the SFFA:•• Just because a project is financially Just because a project is financially feasiblefeasible, does not necessarily , does not necessarily mean that it is mean that it is desirabledesirable..•• Just because a project is Just because a project is not feasiblenot feasible using debt financing, does using debt financing, does not necessarily mean that it is not necessarily mean that it is undesirableundesirable: :

•• A project may appear unfeasible with debt financing, yet it migA project may appear unfeasible with debt financing, yet it might be a ht be a desirable project from a total return to investment perspective desirable project from a total return to investment perspective (and (and might obtain equity financing).might obtain equity financing).

DonDon’’t confuse an SFFA feasibility analysis with a normatively t confuse an SFFA feasibility analysis with a normatively correct assessment of the correct assessment of the desirabilitydesirability of a development project of a development project from a financial economic investment perspective.from a financial economic investment perspective.

SFFA does not compute the SFFA does not compute the value of the completed propertyvalue of the completed property. . Hence, does not compute the NPV of the development investment deHence, does not compute the NPV of the development investment decision:cision:

NPV = Value NPV = Value –– Cost . Cost . SFFA merely computes whether it is possible to take out a permanSFFA merely computes whether it is possible to take out a permanent loan to finance ent loan to finance (most of) the development costs.(most of) the development costs.



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The The correctcorrect way to evaluate the financial economic way to evaluate the financial economic desirabilitydesirability of of a development project investment:a development project investment:

“THE NPV INVESTMENT DECISION RULE”:

1) MAXIMIZE THE NPV ACROSS ALL MUTUALLY-EXCLUSIVE ALTERNATIVES; AND

2) NEVER CHOOSE AN ALTERNATIVE THAT HAS: NPV < 0.

(Recall Chapter 10.)

For development investments:For development investments:NPV = Benefit NPV = Benefit –– Cost = Value of Bldg Cost = Value of Bldg –– Cost of Cost of DevlptDevlpt..



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To see the problem with the SFFA, consider again the example we just looked at (left). The project seemed feasible with a $500,000 land cost. But suppose (as is reasonable)…• Expected cap rate at completion = 10%• OCC for investment in such property when stabilized (unlvd) E[rV] = 11%• OCC for construction cost E[rK] = 6%• Time to build = 1 year.

Then the correctly determined NPV of this project is as follows:

( ) ( )

132000$500000$2019000$2387000$

500000$06.1

2140000$11.1

2650000$500000$06.01

2140000$11.01

10.0265000$][][][

11

−=−−=

−−=−+

−+

=

−−= LandPVConstrPVBldgPVNPV

which is a negative NPV. (Even tho supportable site acquisition cost appears to be +$91647 above land price.)Thus, the NPV Rule says: Don’t invest.And the NPV Rule is based on Wealth Maximization.www.bsscommunitycollege.in www.bssnewgeneration.in www.bsslifeskillscollege.in


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Economic Analysis of Investment in Real Economic Analysis of Investment in Real Estate Development Projects,Estate Development Projects,

Part 2Part 2



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Three considerations are important and unique about applying theThree considerations are important and unique about applying the NPV rule NPV rule to evaluating investment in development projects as compared to to evaluating investment in development projects as compared to investments in stabilized operating properties:investments in stabilized operating properties:

1.1. ““TimeTime--toto--BuildBuild””:: Investment cash outflow occurs Investment cash outflow occurs over timeover time, not all at , not all at once up front, due to the once up front, due to the construction phaseconstruction phase..

2.2. Construction loans:Construction loans: Debt financing for the construction phase is Debt financing for the construction phase is almost almost universaluniversal (even when the project will ultimately be financed entirely (even when the project will ultimately be financed entirely by equity).by equity).

3.3. Phased risk regimes:Phased risk regimes: Investment risk is very different (greater) Investment risk is very different (greater) between the construction phase (the between the construction phase (the development investmentdevelopment investment per se) per se) and the stabilized operational phase. (Sometimes an intermediateand the stabilized operational phase. (Sometimes an intermediatephase, phase, ““leaselease--upup””, is also distinguishable.), is also distinguishable.)

We need to account for these differences in the methodology of hWe need to account for these differences in the methodology of how we ow we applyapply the NPV Rule to development investments. . .the NPV Rule to development investments. . .



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NPV = Benefits NPV = Benefits –– Costs Costs

The benefits and costs must be measured in an The benefits and costs must be measured in an ““apples apples vsvs applesapples””manner. That is, in dollars:manner. That is, in dollars:

•• As of theAs of the samesame point in point in timetime..•• That have been adjusted to That have been adjusted to account for riskaccount for risk..

As with all DCF analyses, time and risk can be accounted for by As with all DCF analyses, time and risk can be accounted for by using using riskrisk--adjusted discountingadjusted discounting. . Key is to identify: Key is to identify: opportunity cost of capitalopportunity cost of capital

•• Reflects amount of Reflects amount of riskrisk in the cash flowsin the cash flows•• Can be applied to either Can be applied to either discountdiscount CFsCFs back in time, orback in time, or•• To To growgrow (compound) (compound) CFsCFs forward in time forward in time •• e.g., to the projected time of completion of the constructione.g., to the projected time of completion of the constructionphase.phase.



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Hereandnow Place:• Twin buildings, $75,000/mo net rent perpetuity• OCC = 9%/yr ( 0.75%/mo, 1.007512 – 1 = 9.38% EAR)•in total, V0 is:

000,000,10$0075.

000,75$0075.1

000,75$0075.1

000,75$2 ==++ L

NPV0 = V0 – P0 = $10,000,000 – $10,000,000 = 0

Futurespace Centre:• Across the street from Hereandnow.• Will be same asset as Hereandnow, complete in 12 mos• Constr cost $1,500,000 X 4 payable @ mos 3, 6, 9, 12.• First building complete in 6 mos.• This is definitely HBU of site; irreversible commitment to develop now is appropriate

Typical investment deal for this stablized property:



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Development investment valuation question :

What is the price that can be paid today for the What is the price that can be paid today for the FutureSpaceFutureSpaceland site such that the development investment will be zero land site such that the development investment will be zero NPV?NPV? . . .. . .

This is the value of the land, the price the FutureSpace land site would presumably sell for in a competitive market. Hence, equivalently:

What is the NPV of the development project investment What is the NPV of the development project investment apart from the land cost? . . .apart from the land cost? . . .

Answer:

NPV0 = V0 – P0 = V0 – (K0 + Land)

So, what is V0 ?, and what is K0 ? For Futurespace Project . . .



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000,000,5$0075.

500,37$0075.1

500,37$0075.1

500,37$2 ==++ L

First consider V0 …In 6 mos Furturespace One will be complete, expected to be worth:

And in 12 mos Futurespace Two is expected to be worth:

000,000,5$0075.

500,37$0075.1

500,37$0075.1

500,37$2 ==++ L

Thus, gross PV of project benefit is:

000,352,9$0075.1

000,000,5$0075.1

000,000,5$1260 =+=V

000,352,9$0075.1

000,000,10$0075.1

500,37$12

12

70 =+=∑

=ttV

Or, equivalently:

Why is Futurespace worth less than Hereandnow ? . . .

Why do we cut off the analysis at month 12 ? . . . www.bsscommunitycollege.in www.bssnewgeneration.in www.bsslifeskillscollege.in


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Now consider K0 …Construction cost is 4 quarterly pmts of $1,500,000 each.These CFs have very little “risk” as capital mkt defines “risk”:• Low beta, low correlation w financial mkts.Hence: OCC for constr CFs near rrff , say 3%3% per annum (0.25%/mo, 3.04% EAR).*So, PV of construction costs is:

000,889,5$0025.1

000,500,1$0025.1

000,500,1$0025.1

000,500,1$0025.1

000,500,1$129630 =+++=K

* Note that by using a lower OCC for construction CFs, we discount them to a higher PV, thus causing construction costs to figure more prominently in the development investment decision.

In this sense we are treating construction cost as a greater “risk”factor to be considered in the decision.

This is not the capital market definition of “risk”, but it is consistent with common parlance.www.bsscommunitycollege.in www.bssnewgeneration.in www.bsslifeskillscollege.in


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Thus, excluding Land cost, we have Futurespace project valuation:

V0 – K0 = $9,352,000 – $5,889,000 = $3,463,000.

If the price of the Land is x, then:NPV0 = $3,463,000 – x .

For any Land price <= $3,463,000, the Futurespace project makes economic sense.

Because of the way we have defined economic value (based in market opportunity cost), if the project passes the above criterion, it should be possible to put together financial arrangements to make it happen (otherwise, $$$ are being “left on the table” – recall: NPV rule based on wealth-maximization).

If the project does not pass the above criterion, it will either be difficult to put together financing, or at least one of the parties is likely to regret it later on if they did contribute…



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Further investment analysis . . .

29.1.2. Operational Leverage and Estimation of the OCC for Development Investments

Recall that we are dealing with a high-risk/high-return phase (“style”) of investment (the yellow or yellow & blue phases):



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./%59.161)0129.1(,/%29.1)/1(

000,500,3$)/1(

000,500,1$)/1(

000,500,3$)/1(

000,500,1$000,463,3$

12

12963

yrmoIRRmoIRRmoIRRmoIRRmoIRR

=−⇒=⇒

++

+−

++

++−

=

How risky is this development project investment ? . . .We can quantify the answer to this question.

The 16.59% going-in IRR for the development investment phase itself reflects the capital market’s required ex ante risk premium:

Risk

E[r]

rf = 3%

16.59% = 3% + RP

Given that $3,463,000 is the market value of the development project:

Futurespace: Mo. 3 Mo. 6 Mo. 9 Mo.12 K -$1,500,000 -$1,500,000 -$1,500,000 -$1,500,000V 0 +$5,000,000 0 +$5,000,000

Net CF -$1,500,000 +$3,500,000 -$1,500,000 +$3,500,000



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Risk

E[r]

rf = 3%

16.59% = 3% + RP

The Futurespace development project has…

16.59% - 3.04% 13.55%-------------------- = ---------- = 2.14 times9.38% - 3.04% 6.34%

the investment risk of an unlevered investment in stabilized property like what we are building in the Futurespace project.



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Risk

E[r]

rf = 3%

16.59%

9.38%

Hereandnow Futurespace

E[RP]

If this relationship does not hold, then there are “super-normal”(disequilibrium) profits (expected returns) to be made somewhere, and correspondingly “sub-normal” profits elsewhere, across the markets for: Land, Stabilized Property, and Bonds (“riskless” CFs).



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The added risk in Futurespace compared to Hereandnow:16.59% - 3.04% 13.55%-------------------- = ---------- = 2.14 times9.38% - 3.04% 6.34%

reflects ““operational leverageoperational leverage”” in the development project.

Recall: NPV = V – P

Operational leverage arises whenever P (= K + Land) does not occur entirely at time zero and is not perfectly positively correlated with the subsequent realization of V.

Bigger K relative to V, and/or later K in time relative to the realization of V (at time T), Greater operational leverage.

Investments in stabilized properties have no operational leverage because the investment cost (P) occurs entirely at time zero.



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Example of operational leverage:Example of operational leverage:

Suppose asset values turn out to be 10% less10% less than previously anticipated . . .

./%04.11)99913.0(,/%087.0

)/1(000,000,9$

)/1(000,75$000,000,10$

12

12

12

1

yrmoIRR

moIRRmoIRRtt

−=−⇒−=⇒

++

+=∑

=

Hereandnow:

Ex post return is 9.38% - (-1.04%) = 10.42 points below ex ante.

Futurespace:

Ex post return is 16.59% - (-13.42%) = 30.01 points below ex ante:30.01 / 10.42 = 2.9 times the investment return risk.

./%42.131)9881.0(,/%19.1

)/1(000,000,3$

)/1(000,500,1$

)/1(000,000,3$

)/1(000,500,1$000,463,3$

12

12963

yrmoIRR

moIRRmoIRRmoIRRmoIRR

−=−⇒−=⇒

++

+−

++

++−

=



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Same kind of impact on risk and return as in Ch.13 (“leverage”).

In Ch.13 the effect was due to financial leverage (use of debt financing of the investment).

Here no debt financing is being employed (hence, no financial leverage).



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How did we compute the OCC of the Futurespace development project (the 16.59%) ? . . .

We backed it out, that is:

We first computed the NPV of the project exclusive of Land:V0 – K0

Then we assumed market value for Land:NPV0 = V0 – P0 = V0 – (K0 + Land) = 0

Land = V0 – K0

And then we derived the IRR implied by this ($3,463,000) value for the Land (16.59%):

./%59.161)0129.1(,/%29.1

)/1(000,500,3$

)/1(000,500,1$

)/1(000,500,3$

)/1(000,500,1$000,463,3$

12

12963

yrmoIRR

moIRRmoIRRmoIRRmoIRR

=−⇒=⇒

++

+−

++

++−

=



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We did not need to know the OCC of the development project investment in order to compute the NPV of that investment,

or (therefore) to determine whether the investment made economic sense or not.

We only needed to know the OCC of the project benefit(the E[rV] = 9.38%) and of the project cost (the E[rK] = 3.04%), together with the projected CFs of each of those:

NPV[dvlpt] = PV[V] – PV[K] – Land .



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Nevertheless, we still found it useful to compute the OCC of thedevelopment project itself (the 16.59%).

e.g., we used it to quantify the relative investment risk in thedevelopment investment vs a stabilized property investment (2.14 times).

But here we face a problem of consistency in concept or practice, regarding how we quantify the development project OCC . . .

The specific numerical value of the development phase OCC depends on the particular cash flow and value realization timingassumptions employed in the IRR computation.



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Suppose,

instead of assuming that each of Futurespace’s two buildings’values would be realized upon the completion of each building (in months 6 & 12), as we did in computing the 16.59% IRR,

we assume that we hold the entire project until its complete realization in month 12:

./%58.131)0107.1(,/%07.1

)/1(500,537,8$

)/1(500,37$

)/1(500,462,1$

)/1(500,37$

)/1(000,500,1$

)/1(000,500,1$000,463,3$

12

12

11

109

8

763

yrmoIRR

moIRRmoIRRmoIRRmoIRRmoIRRmoIRR tt

tt

=−⇒=⇒

++

++

+−

++

++−

++−

= ∑∑==

Now it looks like the IRR (and hence the OCC) of this samedevelopment project is 13.58%, instead of 16.59%.

Which is the real (true) Futurespace OCC?...



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Answer:They can both be true!(So long as they both represent realistic, feasible plans for disposition of the project.)

But this is not a very satisfying or practical answer for purposes where we need some consistency in quantifying development project investment OCC, for example,

For comparisons across different types of projects (e.g., for strategic planning purposes).

Also, this approach ignores the ubiquity of use of construction loans to finance the construction costs of development projects (even by deep-pocket institutions, such as pension funds).

The use of a construction loan pushes all of the construction cost cash outflows (from the developer/borrower’s perspective) to the end of the construction phase (“time T”). . .



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The “Canonical Form” of the Development Project OCC:

The idea is to use the ubiquity of the construction loan (in itsclassical form, with interest accrued until the end), to develop a simplified “stylized” representation of development project cash flows as occurring at two and only two points in time:

Time “zero”, and Time “T”• Time 0 = The moment when the irreversible decision to commit to development (construction) is made (opportunity cost of the land is incurred);• Time T = The time when the construction phase is completed (and/or when lease-up is projected to be completed), resulting in a stabilized asset.And then compute the standardized (“canonical”) IRR of the development project investment based on this 2-point cash flow assumption.



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( ) ( ) ( )TD

TT

V

TT

C

TT

rEK

rEV

rEKV

][1][1][1 +−

+=

+−

The canonical formula for the OCC of development investments can be expressed by the following condition of equilibrium across the markets for developable land, built property, and contractually fixed cash flows (debt assets):

Where:VT = Gross value of the completed building(s) as of time T.KT = Total construction costs compounded to time T.E[rV] = OCC of the completed building(s).E[rD] = E[rK] = OCC of the construction costs (usually ≈ rf ).E[rC] = OCC of the development phase investment (“Canonical Form”).T = The time required for construction.



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( ) ( ) ( )TD

TT

V

TT

C

TT

rEK

rEV

rEKV

][1][1][1 +−

+=

+−

LHS represents the investment in developable land.

RHS represents a way to duplicate this development investment:• by investing in a combination of:

• a long position in built property of the type being developed and • a short position (borrowing) in an asset that pays contractually fixed cash flows (debt) in the amount of the construction costs of the project.

The “Canonical” Formula:



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( ) ( ) ( )TD

TT

V

TT

C

TT

rEK

rEV

rEKV

][1][1][1 +−

+=

+−

As noted before, if this formula does not hold, then there will be “super-normal” (disequilibrium) profits (expected returns) to be made somewhere, and correspondingly “sub-normal” profits elsewhere, across the markets for: Land, Stabilized Property, and Bonds (“riskless” CFs).

The “Canonical” Formula:



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In most cases, all of the variables in the canonical formula can be observed or estimated with relatively high confidence except forthe OCC of the development phase investment, E[rC]. Solving for E[rC] we obtain:

( )( ) ( )( ) ( )

( )

1][1][1

][1][1][

1

−⎥⎥⎦

⎤

⎢⎢⎣

⎡

+−+

++−=

T

TT

VTT

D

TD

TVTT

C KrEVrErErEKV

rE

If you prefer, a simpler more intuitive (and equivalent) way to derive E[rC] is to first compute V0 – K0 using the previous method, and then derive the canonical development phase OCC as:

T

TTC KV

KVrE1

00

][1 ⎟⎟⎠

⎞⎜⎜⎝

⎛−−

=+



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NPV = Benefits NPV = Benefits –– Costs Costs

The benefits and costs must be measured in an The benefits and costs must be measured in an ““apples apples vsvs applesapples””manner. That is, in dollars:manner. That is, in dollars:

•• As of theAs of the samesame point in point in timetime..•• That have been adjusted to That have been adjusted to account for riskaccount for risk..

As with all DCF analyses, time and risk can be accounted for by As with all DCF analyses, time and risk can be accounted for by using using riskrisk--adjusted discountingadjusted discounting. . Key is to identify: Key is to identify: opportunity cost of capitalopportunity cost of capital

•• Reflects amount of Reflects amount of riskrisk in the cash flowsin the cash flows•• Can be applied to either Can be applied to either discountdiscount CFsCFs back in time, orback in time, or•• To To growgrow (compound) (compound) CFsCFs forward in time forward in time •• e.g., to the projected time of completion of the constructione.g., to the projected time of completion of the constructionphase.phase.

Another perspective on the Canonical Formula…



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[ ] [ ] [ ]TTTT KPVVPVKVPV −=−

For the development project:

NPV exclusive of land cost =NPV exclusive of land cost =

Where:• VT = Gross value of the completed building(s) as of time T.• KT = Total construction costs (excluding land) compounded to time T.• PV[VT – KT] = Present Value of the construction profit.• PV[VT] = Present Value of the property to be built.• PV[KT] = Present Value of the construction costs.• T = The time required for construction.



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[ ] [ ] [ ]TTTT KPVVPVKVPV −=−



Property Mkt Debt MktDevelopable Land Mkt

This is a cross-market equilibrium condition.



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( ) ( ) ( )TD

TT

V

TT

C

TT

rEK

rEV

rEKV

][1][1][1 +−

+=

+−

Here we simply expand the formula to show the relevant rates of return, the OCC rates in the three markets . . .

Where:• VT = Gross value of the completed building(s) as of time T.• KT = Total construction costs (excluding land) compounded to time T.• E[rV] = OCC of the completed building(s), from the property mkt.• E[rD] = E[rK] = OCC of the construction costs (usually ≈ rf ), from debt mkt.• E[rC] = OCC of the development project (“Canonical Form”).• T = The time required for construction.



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( ) ( ) ( )TD

TT

V

TT

C

TT

rEK

rEV

rEKV

][1][1][1 +−

+=

+−

Here we simply expand the formula to show the relevant rates of return, the OCC rates in the three markets . . .

Property Mkt Debt MktDevelopable Land Mkt

This is still the same cross-market equilibrium condition.



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( )

( )

000,229,10$

000,000,10$0075.1500,37$

000,000,5$0075.1000,000,5$

12

7

12

6

=

+=

+=

∑=

−

t

t

TV

Numerical Example of the Canonical FormulaNumerical Example of the Canonical Formula

Derivation of the canonical OCC for the Futurespace Project:

First compute the forward VT value of the project benefit as of Time T:



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Numerical Example of the Canonical FormulaNumerical Example of the Canonical FormulaNext compute the forward KT value of the project construction cost as of Time T:

( ) ( ) ( ) 000,068,6$000,500,1$0025.1000,500,1$0025.1000,500,1$0025.1000,500,1$ 369 =+++=TK

To obtain the projected net development profit as of month 12:VT – KT = $10,229,000 – $6,068,000 = $4,161,000.

Then substituting into the Canonical Formula we obtain the canonical OCC of the Futurespace Project:

( )

( )( ) ( )( ) ( )

( )

./%16.201)0154.1(

./%54.11000,068,6$0075.1000,229,10$0025.1

0025.10075.1000,161,4$][

0025.1000,068,6$

)0075.1(000,229,10$

][1000,068,6$000,229,10$

12

121

1212

1212

121212

yr

morE

rE

C

C

=−⇒

=−⎥⎦

⎤⎢⎣

⎡

−=

⇒

−=+

−

Canonical OCC = 20.16% / year.www.bsscommunitycollege.in www.bssnewgeneration.in www.bsslifeskillscollege.in


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Numerical Example of the Canonical FormulaNumerical Example of the Canonical FormulaAlternatively (and equivalently):

0154.12016.1000,463,3$000,161,4$

000,889,5$000,352,9$000,068,6$000,229,10$

][1

121121

121

1

00

==⎟⎠

⎞⎜⎝

⎛=

⎟⎠

⎞⎜⎝

⎛−−

=

⎟⎟⎠

⎞⎜⎜⎝

⎛−−

=+T

TTC KV

KVrE

Canonical OCC = 20.16% / year.www.bsscommunitycollege.in www.bssnewgeneration.in www.bsslifeskillscollege.in


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This canonical 20.16% exceeds the previously derived 16.59% and 13.58% OCC numbers because the canonical assumption involves more leverage, due to the assumption, in effect, of theuse of a construction loan (all CFs at only Time 0 and Time T).

Numerical Example of the Canonical FormulaNumerical Example of the Canonical Formula(Futurespace Project)

Returning to our risk comparison between the development project and the stabilized property, from the canonical perspective, Futurespace Centre has…

20.16% - 3.04% 17.12%-------------------- = ---------- = 2.70 times9.38% - 3.04% 6.34%

the risk of Hearandnow Place.



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Relation of the Canonical Formula to the WACC:Relation of the Canonical Formula to the WACC:

As the Canonical Formula reduces the development project to a single-period investment (between Time 0 and Time T ), the Canonical OCC can be equivalently derived using the “WACC”Formula that we introduced in Chapter 13:

E[rC] = E[rD] + LR(E[rV] – E[rD])

Defining LR as the leverage ratio: V/(V-K), based on the Time Zero valuations of the asset to be built and the land value:

70.2

000,889,5$000,352,9$000,352,9$

00

0 =−

=−

=KV

VLR

we have the development (land) OCC given as:

E[rC] = 3.04% + 2.70(9.38% – 3.04%) = 20.16%.Thus further illustrating how a development project investment may be thought of as like a levered investment in a stabilized property like the one being built.



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In whatever manner the canonical OCC is determined, it will of course yield the same NPV of the development project (land value) as we derived originally:

000,463,3$000,889,5$000,352,9$

0304.1000,068,6$

0938.1000,229,10$

2016.1000,161,4$

=−=−=

However, prior knowledge of this NPV is not necessary to ascertain the canonical OCC of the development project, as E[rC] is determined solely by the variables on the right-hand side of the Canonical Formula equation:

( )( ) ( )( ) ( )

( )

1][1][1

][1][1][

1

−⎥⎥⎦

⎤

⎢⎢⎣

⎡

+−+

++−=

T

TT

VTT

D

TD

TVTT

C KrEVrErErEKV

rE

It should also be noted (for future reference) that the Canonical Formula is completely consistent with the real options valuationof the development project investment, once the option is at thepoint where immediate exercise (development) is optimal (our original assumption here).



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Summarizing the advantages of the recommended procedure:Summarizing the advantages of the recommended procedure:Consistent with underlying theory. (i.e., consistent with NPV Rule, based on

Wealth Maximization Principle. Based on market opportunity costs, equilibrium across markets.)

Simplicity. Avoids need to make assumptions about permanent loan or form ofpermanent financing (equity vs debt).

Explicit identification of the relevant OCC. Identifies explicit expected return (OCC) to each phase (each risk regime) of the investment: Development, Lease-up (if appropriate), Stabilized operation.

Explicit identification of land value. Procedure results in explicit identification of current opportunity value of the land.

“Front-door” or “Back-door” flexibility possible. Procedure amenable to “backing into” any one unknown variable. E.g., if you know the land value and the likely rents, you can back into the required construction cost. If you know (or posit) all of the costs and values, then you can back into the expected return on the developer's equity contribution for the development phase. Or you can back into the implied land value (supportable price).



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Do developers really use the Do developers really use the ““NPV RuleNPV Rule””? . . .? . . .• Most don’t use NPV explicitly.• But remember: NPV Wealth Maximization.• By definition, successful developers maximize their wealth.• Thus, implicitly (if not explicitly), successful developers must (somehow) be employing the NPV Rule:

• e.g., in deciding which projects to pursue,• An intuitive sense of correctly rank-ordering mutually-exclusive projects or designs by NPV, and picking those with the highest NPV (they may think of it as “best profit potential”), must be employed (by the most successful developers).

• Suggestion in Ch.29 is that by making this process more explicit, it may be executed better, or by more developers (i.e., making more developers “successful”),• The NPV approach also should improve the ability of the development industry to “communicate” project evaluation in the “language of Wall Street”(e.g., “NPV”, “OCC”, phased risk regimes, risk/return “styles”).



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Note that in this approach, there is no need to Note that in this approach, there is no need to prepre--assumeassume what type of what type of permanent financing will be used for the completed project. permanent financing will be used for the completed project.

There is no assumption at all about what will be done with the cThere is no assumption at all about what will be done with the completed ompleted project at project at time Ttime T. It may be:. It may be:

•• Financed with a permanent mortgage,Financed with a permanent mortgage,•• Financed or sold (wholly or partly) tapping external equity, orFinanced or sold (wholly or partly) tapping external equity, or•• Held without recourse to external capital.Held without recourse to external capital.

Project evaluation is independent of project financing, as it shProject evaluation is independent of project financing, as it should be.*ould be.*

* Unless subsidized (non* Unless subsidized (non--marketmarket--rate) financing is available contingent on rate) financing is available contingent on project acceptance: Recall Chapter 14, the project acceptance: Recall Chapter 14, the ““APVAPV”” (Adjusted Present Value) (Adjusted Present Value) approach to incorporating financing in the investment evaluationapproach to incorporating financing in the investment evaluation..

Another important reason for this approach:Another important reason for this approach:•• RiskRisk characteristics of characteristics of development phasedevelopment phase differentdifferent from risk from risk characteristics of characteristics of stabilized phasestabilized phase. . •• Thus, Thus, different different OCCsOCCs, therefore:, therefore:•• Two phases must be analyzed in two Two phases must be analyzed in two separate stepsseparate steps..



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*29.2 Advanced Topic: The Relationship of Development Valuation to the Real Option

Model of Land Value

The NPV & canonical OCC development project investment valuation and analysis procedure previously described is

Consistent with the real option model . . .

To see this, consider a binomial model of the preceding Hereandnow / Futurespace example . . .



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To see this, consider a binomial model of the preceding Hereandnow / Futurespace example . . .

Suppose that risk in the property market is such that the ex anteexpected value of the project at Time T, what we have labeled and quantified as:

VT = $10,229,000

is actually based on a binomial outcome possibility of a 50/50 chance of either $11,229,000 or $9,229,000 value:

PV[VPV[VTT]=]=$9.352M$9.352M

VVTTupup==

$11.229M$11.229M

VVTTdowndown==

$9.229M$9.229M

pp = .50= .50

11--pp = .50= .50

With in any case the construction cost having a KT value of $6,068,000 (as before), and recalling that we have previously determined that the PV of this 1-yr forward claim is $9,352,000.



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Then applying the certainty-equivalence form of the DCF present value model that we first introduced in Chapter 10 Appendix C and which formed the basis of the binomial option value model we described in Chapter 28, we have the following present value computation for the FutureSpaceproject as of time zero:

( )

f

downupfVdownup

rVV

rrECCCE

CPV+

−

−−−

=1

%%][

$$][][ 11

01110

1

( ) ( ) ( )

( ) 463.3$0304.1

568.3$0304.1

2964.000.2$161.4$0304.1

%38.21%34.6000.2$161.4$

0304.1352.9229.9229.11

%04.3%38.9)068.6229.9()068.6229.11()068.6229.9)(5.0()068.6229.11)(5.0(][ 1

==−

=⎟⎠⎞

⎜⎝⎛−

=

−−

−−−−−+−=CPV

Which is identical to the PV of the project (land value) that we found before.



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Note that in percentage terms the development project investment outcome spread (which may be viewed as a measure of risk) is:

( )

%75.57000,463,3$000,000,2$

000,463,3$000,161,3$000,161,5$

000,463,3$)000,068,6$000,229,9($000,068,6$000,229,11$

==−

=

−−−

Whereas that in (the T-period forward purchase of) the stabilized property is:

%38.21000,352,9$000,000,2$

000,352,9$000,229,9$000,229,11$

==−

The ratio of these outcome spreads (risk): 57.75 / 21.38 = 2.7057.75 / 21.38 = 2.70,

is exactly the same as the ratio of the ex ante risk premia between the development project and its underlying asset (using the Canonical OCC):

(20.16%(20.16%--3.04%) / (9.38%3.04%) / (9.38%--3.04%) = 17.12% / 6.34% = 2.703.04%) = 17.12% / 6.34% = 2.70.



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Risk

rf = 3.04%

E[r]

20.16%

9.38%

Hereandnow21.38% range

Futurespace57.75% range

E[RP]


The “price of risk” (the ex ante investment return risk premium per unit of risk) must be the same across the relevant asset markets:



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29.3.1 How Developers Think About All This…

Developers don’t usually explicitly apply the NPV Rule.

But remember . . .

Proof that Wealth Maximization implies the NPV Decision Rule:• Suppose not.• Then I could maximize my wealth and still contradict NPV Rule.• I could choose a project with NPV < 0, or with NPV less than that of another mutually-exclusive feasible alternative.• But if I did that I would be “leaving money (i.e. “wealth”) on the table”, taking less wealth when I could have more.• This would not be wealth-maximization.• Hence: Contradiction.QED (“Proof by Contradiction”).

Thus, if our definition of a “successful” developer is one who maximizes wealth, then successful developers must be applying the NPV Rule (implicitly if not explicitly).



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What sort of quantitative performance measures What sort of quantitative performance measures dodo developers developers look at ? . . .look at ? . . .

• Sometimes, just the SFFA described earlier in Ch 28 (but that is only a feasibility analysis, not an evaluation). Other times:

• Profit Margin RatioProfit Margin Ratio

• Enhanced Cap Rate on CostEnhanced Cap Rate on Cost

• Blended LongBlended Long--run IRRrun IRR

But developers But developers mustmust apply these approaches in a manner that apply these approaches in a manner that gives the same result as the NPV Rule, or else they are not gives the same result as the NPV Rule, or else they are not maximizing wealth. maximizing wealth. And their evaluations And their evaluations mustmust be consistent with market equilibrium, be consistent with market equilibrium, or they or they ““wonwon’’t be able to play the gamet be able to play the game””..



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Profit Margin RatioProfit Margin Ratio

Definition: Expected Gross Value---------------------------

Total Costs(undiscounted)

Evaluation is then based on some conventional but ad hoc “Rule of Thumb”, such as 20%20% (for a relatively quick project, when

land is included in the cost).e.g., for our Futurespace example project:

000,333,2$000,000,6$20.1

000,000,10$arg1

20.1000,000,6$

000,000,10$arg1

=−=−+

==

⇒

=+

=+

=+

KinM

VCValueLand

CCKV

inM

T

T



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Profit Margin RatioProfit Margin Ratioe.g., for our Futurespace example project:

000,333,2$000,000,6$20.1

000,000,10$arg1

20.1000,000,6$

000,000,10$arg1

=−=−+

==

⇒

=+

=+

=+

KinM

VCValueLand

CCKV

inM

T

T

But we have seen that this answer is wrong, if the OCC of the built property is 9% and the riskfree rate is 3%.

The margin that would give the correct answer is 5.7%:%7.51

000,463,3$000,000,6$000,000,10$

=−+

(This will provide the canonical expected return of 20.16% as we have seen.)

(A land price of $2,333,000 will provide the developer with a (canonical) expected return of 78% ! )



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Profit Margin RatioProfit Margin Ratioe.g., for our Futurespace example project:

000,333,2$000,000,6$20.1

000,000,10$arg1

20.1000,000,6$

000,000,10$arg1

=−=−+

==

⇒

=+

=+

=+

KinM

VCValueLand

CCKV

inM

T

T

But perhaps the developer is applying the 20% margin with the historical cost of the land.

And perhaps the land was acquired some 1.77 years before, for the $2,333,000 price, and has earned a speculative (real option based) return of 25%/year since then:

$2,333,000*(1.25)1.77 = $3,463,000



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Enhanced Cap Rate on CostEnhanced Cap Rate on Cost

Definition: Expected Initial Stabilized NOI/yr---------------------------------------------Total Cost inclu Land (undiscounted)

Evaluation is then based on a required cap rate that is somewhatgreater than what currently prevails in the market for stabilized

properties of the type to be built.e.g., for Futurespace example:

Market cap rate for stabilized is 9% (see Hereandnow),so developer might require 10% cap rate for the Futurespace development

project:

NOI / 10% = $900,000 / 0.1 = $9,000,000.

So, if total costs <= $9,000,000, project looks good:

Land value = $9,000,000 – $6,000,000 = $3,000,000.



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Blended LongBlended Long--run IRRrun IRR

Definition:Append a projected multi-year (usually 10 years) operating phase cash flow projection to the development phase cash flow projection, including land cost (e.g., a 10+T year projection), and apply a hurdle IRR requirement that is greater than that for stabilized investments, by some ad hoc amount (e.g., maybe 100bps or so, for unlevered holding).e.g., in our Futurespace example, if we extended the CF projection out another 9 years (108 months), and applied a 10% discount rate (instead of the 9% OCC for stabilized property) across the entire 10-year projection, we would get a PV of $3,049,000, suggesting that this could be paid for the land.

However, from a capital markets perspective, this muddies the waters by mixing two very different investment styles together.

And from a development decision perspective it concatenates two different decisions that need not be fused.



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29.3.2 Including Lease-up & Land Assembly:

Unblending the blended IRR

LR Blended Rate for Futurespace:Year: 1 2 3 4 5 6 7 8 9 10

($3,463,000) ($5,775,000) $900,000 $900,000 $900,000 $900,000 $900,000 $900,000 $900,000 $900,000 $10,900,0009.73% = IRR

Survey: Ask developers what long-run (blended) IRR they will accept (or typically face) for projects at different stages.

Example, suppose developers say that for a project like Futurespacethey would be looking for a long-run IRR of 9.00% for an investment in the completed stabilized property, but would require 9.73% to come in at the construction phase even if the building were pre-leased.

Implication is that the required going-in return expectation for the 1-year development phase alone is 20.16% (canonical).

Because 9% stabilized IRR gives $10,000,000 building value, and 9.73% IRR at construction outset gives $3,463,000 value of the construction project, which we saw implies 20.16% canonical devlptphase IRR.



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Results of Tod McGrath survey of Boston area developers (2004):Exhibit 29-2: An Example of Risk and Return Regimes for Phases of the Development Process. (Taken from a study of affordable housing development in Massachusetts.)



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29.4 & Appendix 29:29.4 & Appendix 29:

The Phasing Option . . .The Phasing Option . . .

The ability (and need) to break the development project into twoThe ability (and need) to break the development project into twoor more sequential or more sequential phasesphases rather than committing to its complete rather than committing to its complete construction all at once complicates the option model of construction all at once complicates the option model of development and land value (but is an important aspect of large development and land value (but is an important aspect of large projects).projects).

The phased option can be modeled as a The phased option can be modeled as a ““compound optioncompound option”” ::

An Option on an OptionAn Option on an OptionBuilding the first phase gives you the option to build the seconBuilding the first phase gives you the option to build the second d phase, and so onphase, and so on……



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The phasing option can be modeled using the binomial procedure The phasing option can be modeled using the binomial procedure as before, applying the same formulas as before (with as before, applying the same formulas as before (with timetime--toto--buildbuildas appropriate), repeatedly, starting with the last phase (as a as appropriate), repeatedly, starting with the last phase (as a simple option), then the nextsimple option), then the next--toto--last phase is modeled as an option last phase is modeled as an option on the last phase, and so onon the last phase, and so on……

That is, the nextThat is, the next--toto--last phase is an option whose last phase is an option whose ““underlying underlying assetasset”” is another option, namely, the last phase.is another option, namely, the last phase.

LetLet’’s walk through a simple numerical example . . .s walk through a simple numerical example . . .

The Phasing Option . . .The Phasing Option . . .



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Roth Harbor . . .Roth Harbor . . .

The following numerical example will demonstrate all of the optiThe following numerical example will demonstrate all of the option on modeling techniques presented in this lecture . . .modeling techniques presented in this lecture . . .

Roth HarborRoth Harbor is a strategically and scenically located former is a strategically and scenically located former brownfieldbrownfieldsite on the shore near the center of site on the shore near the center of WheatonvilleWheatonville, ME., ME.

WheatonvilleWheatonville is a former shipbuilding city now booming with highis a former shipbuilding city now booming with high--tech startups and an influx of young professionals and emptytech startups and an influx of young professionals and empty--nesters, nesters, creating a serious housing shortage.creating a serious housing shortage.

The 50 acres of former industrial and warehouse property in RothThe 50 acres of former industrial and warehouse property in RothHarbor are currently zoned to allow 500 marketHarbor are currently zoned to allow 500 market--rate apartments to be rate apartments to be developed.developed.

The property is owned by The property is owned by CiochettiCiochetti Enterprises LLCEnterprises LLC (CEC), which has (CEC), which has plans to build the 500 units in a single project, to be called plans to build the 500 units in a single project, to be called RentlegRentlegGardensGardens..

The Planning Commission of The Planning Commission of WheatonvilleWheatonville ““has a better ideahas a better idea…”…”



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RentlegRentleg GardensGardens::

Current apartment rents in Current apartment rents in WheatonvilleWheatonville suggest that the suggest that the RentlegRentlegGardens apartments could charge gross rents of $1100/mo, with Gardens apartments could charge gross rents of $1100/mo, with operating expenses of $6533/year per occupied unit, and average operating expenses of $6533/year per occupied unit, and average vacancy of 4%. Cap rates (vacancy of 4%. Cap rates (yyVV ) on such properties are currently 8%.) on such properties are currently 8%.

If the 500 If the 500 RentlegRentleg Gardens units existed today, the property would be Gardens units existed today, the property would be worth:worth:

[ (1100*12 [ (1100*12 –– 6533)*0.96 / .08 ] * 500 = $40,000,0006533)*0.96 / .08 ] * 500 = $40,000,000

based on a projected current NOI of $3,200,000/yr and an averagebased on a projected current NOI of $3,200,000/yr and an average unit unit value of $80,000.value of $80,000.

Construction cost as of today would be $32,000,000, with a projeConstruction cost as of today would be $32,000,000, with a projected cted deterministic (deterministic (risklessriskless) growth rate of 2%/yr. Construction would take ) growth rate of 2%/yr. Construction would take 1 year (implying a bill due next year of: (1.02)$32 million = $31 year (implying a bill due next year of: (1.02)$32 million = $32.64 M).2.64 M).

(Environmental cleanup of the site has already been done by CEC,(Environmental cleanup of the site has already been done by CEC,and the site is now ready for development.)and the site is now ready for development.)




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The Planning CommissionThe Planning Commission’’s s ““Better IdeaBetter Idea”…”…

““Roth Harbor PlaceRoth Harbor Place””::

The PC would approve a The PC would approve a Special Zoning ExemptionSpecial Zoning Exemption that would allow that would allow much greater densitymuch greater density, in a , in a two phasetwo phase development to be called development to be called ““Roth Roth Harbor PlaceHarbor Place”” (RHP). In return, the landowner would commit to:(RHP). In return, the landowner would commit to:

1.1. Provide mixedProvide mixed--income housing (approximately 25% of units belowincome housing (approximately 25% of units below--mktmkt rent).rent).

2.2. Start construction on Phase I ( Start construction on Phase I ( ““Frenchman CoveFrenchman Cove”” ) no later than 3 ) no later than 3 years from now.years from now.

3.3. Start construction on Phase II ( Start construction on Phase II ( ““Fisher LandingFisher Landing”” ) no later than 5 ) no later than 5 years from now.years from now.

Phase II cannot be started until Phase I is complete, and if PhaPhase II cannot be started until Phase I is complete, and if Phase I is se I is not started within 3 years the special exemption expires and thenot started within 3 years the special exemption expires and theland reverts to its previous asland reverts to its previous as--ofof--right based value based on a right based value based on a project like project like RentlegRentleg Gardens.Gardens.




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Roth Harbor . . .Roth Harbor . . .Here is a Here is a decision treedecision tree representation of the RHP Project:representation of the RHP Project:

Abandon RHP Allow Phase I

option to expire, Build

Rentleg or Sell Land for As-of-Right Val

Build Phase I of RHP

Build Phase II of RHP

Allow Phase II option to

expire, Hold or Sell with Phase

I only

Is Phase I a success?

Yes

No

Initial Decision

w/in3 yrs

w/in5 yrs

w/in5 yrs



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The economics of the Roth Harbor Place proposal are as follows:The economics of the Roth Harbor Place proposal are as follows:

•• Phase I (Frenchman Cove):Phase I (Frenchman Cove):•• 900 units, At today900 units, At today’’s rents NOI = $4,800,000/yrs rents NOI = $4,800,000/yr•• At todayAt today’’s cap rate of s cap rate of yyVV == 8%, 8%, •• Current value Current value VV00 = $60,000,000= $60,000,000•• Construction cost as of today would be Construction cost as of today would be KK00 == $48,000,000 and $48,000,000 and

timetime--toto--build is 2 years.build is 2 years.

•• Phase II (Fisher Landing):Phase II (Fisher Landing):•• 1600 units, At today1600 units, At today’’s rents NOI = $8,000,000/yrs rents NOI = $8,000,000/yr•• At todayAt today’’s cap rate of s cap rate of yyVV == 8%, 8%, •• Current value Current value VV00 = $100,000,000= $100,000,000•• Construction cost as of today would be Construction cost as of today would be KK0 0 == $80,000,000 and $80,000,000 and

timetime--toto--build is 2 years.build is 2 years.

•• In both cases (as also with In both cases (as also with RentlegRentleg Gardens):Gardens):•• Market OCC for stabilized apartments (plus small leaseMarket OCC for stabilized apartments (plus small lease--up up

risk premium) = 9%/yr, a 5% risk premium over risk premium) = 9%/yr, a 5% risk premium over rrff = 4%.= 4%.•• Growth in construction costs Growth in construction costs ggKK = = inflainfla/yr = 2%/yr (/yr = 2%/yr (risklessriskless).).•• Volatility of built property = 15%/yr.Volatility of built property = 15%/yr.




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Roth Harbor . . .Roth Harbor . . .Important questions:Important questions:

•• What is the current value of the Roth Harbor site based on its What is the current value of the Roth Harbor site based on its current ascurrent as--ofof--right development option as typified by the right development option as typified by the RentlegRentlegGardens project? . . . This question is important because:Gardens project? . . . This question is important because:

•• This value suggests how much the city might have to pay the This value suggests how much the city might have to pay the current landowner to take over the site if they doncurrent landowner to take over the site if they don’’t want to work t want to work together to create the RHP Project or if the city feels the projtogether to create the RHP Project or if the city feels the project ect should be put out to an open bid.should be put out to an open bid.

•• This is the opportunity cost for the RHP Project, necessary to This is the opportunity cost for the RHP Project, necessary to compute the NPV of the project.compute the NPV of the project.

•• Future values of this asFuture values of this as--ofof--right asset represent the right asset represent the ““abandonment valueabandonment value”” of the RHP Project (if the developer of the RHP Project (if the developer decides not to pursue the project).decides not to pursue the project).

•• If the asIf the as--ofof--right project currently equals or exceeds its right project currently equals or exceeds its SamuelsonSamuelson--McKean McKean ““hurdle valuehurdle value”” ((V*V*), this suggests ), this suggests urgencyurgency in in getting the alternative RHP Project to supercede getting the alternative RHP Project to supercede RentlegRentlegGardens, as the landowner should optimally immediately proceed Gardens, as the landowner should optimally immediately proceed with the aswith the as--ofof--right development in the absence of the special right development in the absence of the special zoning exemption.zoning exemption.



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Roth Harbor . . .Roth Harbor . . .Important questions Important questions (cont.)(cont.)::

•• What is the value of the proposed special zoning exemption for tWhat is the value of the proposed special zoning exemption for the he 22--phase RHP Project? . . . This question is important because:phase RHP Project? . . . This question is important because:

•• It suggests how much someone (either the current landowner, or It suggests how much someone (either the current landowner, or another entity via an open bid process if the city takes over thanother entity via an open bid process if the city takes over the e site) could profitably bid (to make their NPV =site) could profitably bid (to make their NPV = 0) for the RHP 0) for the RHP Project (e.g., how much the city could sell the site for with thProject (e.g., how much the city could sell the site for with the e special zoning exemption if the city takes the land).special zoning exemption if the city takes the land).

•• It allows computation of the additional value created by the It allows computation of the additional value created by the special zoning for the RHP Project, necessary to compute the special zoning for the RHP Project, necessary to compute the NPV of the project.NPV of the project.

•• Do the economics of the RHP project make it realistic for Do the economics of the RHP project make it realistic for immediate start of Phase I construction? That is, will an immediimmediate start of Phase I construction? That is, will an immediate ate construction start be sufficiently profitable (optimal) so that construction start be sufficiently profitable (optimal) so that a a private sector developer would not delay starting the project? .private sector developer would not delay starting the project? . . . . . This question is important because:This question is important because:

•• The city for political reasons wants the site developed soon.The city for political reasons wants the site developed soon.www.bsscommunitycollege.in www.bssnewgeneration.in www.bsslifeskillscollege.in


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Roth Harbor . . .Roth Harbor . . .Step 1: Compute the asStep 1: Compute the as--ofof--right land value.right land value.

•• Clearly a job for the SamuelsonClearly a job for the Samuelson--McKean Formula;McKean Formula;•• Based on the Based on the RentlegRentleg Gardens Project as the underlying asset;Gardens Project as the underlying asset;•• With 1With 1--yr timeyr time--toto--build . . .build . . .

yyVV = 8%, = 8%, yyKK = = (1+r(1+rff )/(1+g)/(1+gKK))--1 1 = 1.96%, = 1.96%, σσ = 15%, = 15%, KK00 = $32, V= $32, V00 = $40,= $40,

ηη == {{yyVV –– yyKK + + σσ22/2 + [(/2 + [(yyKK –– yyVV –– σσ22/2)/2)22 + 2y+ 2yKKσσ22]]1/21/2} / } / σσ22

= {.08= {.08--.0196+.15.0196+.1522/2+[(.0196/2+[(.0196--.08.08-- .15.1522/2)/2)22+2(.0196).15+2(.0196).1522]]1/21/2}/.15}/.1522

= 6.63= 6.63..

V*V* == KK00(1+g(1+gKK)/(1+r)/(1+rf f )[)[ηη/(/(ηη--1)] = $31.38[6.63/(6.631)] = $31.38[6.63/(6.63--1)] 1)]

= $31.38(1.178) = $36.96.= $31.38(1.178) = $36.96.



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( )( ) ( ) ( )

( ) ( )

otherwiseyKyV

VyVifV

yVyK-V

= LAND

KV

VV

K

⎪⎪⎪

⎩

⎪⎪⎪

⎨

⎧

+−+

≤+⎟⎠⎞

⎜⎝⎛ +

+

,11

*1,*

11*η

Step 1 (cont.): Computing the asStep 1 (cont.): Computing the as--ofof--right land value . . .right land value . . .

In this case:In this case:( ) *96.36$04.37$08.140$1 VyV V =>==+

( ) ( ) million

yKyV = LAND KV

65.5$38.31$04.37$0196.13208.14011

=−=−=+−+

Therefore:Therefore:

The asThe as--ofof--right land value (based on right land value (based on RentlegRentleg Gardens) is $5.65 million.Gardens) is $5.65 million.

Furthermore, Furthermore, RentlegRentleg Gardens exceeds its hurdle and so is ripe for Gardens exceeds its hurdle and so is ripe for immediate development. immediate development. UrgencyUrgency in dealing with CEC.in dealing with CEC.



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Roth Harbor . . .Roth Harbor . . .Step 2: Develop the asStep 2: Develop the as--ofof--right land value binomial tree, to provide the right land value binomial tree, to provide the

““abandonment valueabandonment value”” contingencies in the RHP Project analysiscontingencies in the RHP Project analysis

This is done by applying the preceding SamuelsonThis is done by applying the preceding Samuelson--McKean Formula McKean Formula to to VVi,ji,j and and KKjj in each in each i, ji, j of a binomial tree.of a binomial tree.

The next slide shows binomial trees for seven years of (annual) The next slide shows binomial trees for seven years of (annual) projections of projections of VV , , KK , and , and LANDLAND based on based on RentlegRentleg Gardens Gardens (T/n(T/n = 1 year)= 1 year)..

Note: Use of such a small Note: Use of such a small nn (long period) will tend to bias (long period) will tend to bias the option valuation downward. In real world analysis a the option valuation downward. In real world analysis a shorter period length (such as monthly rather than annual) shorter period length (such as monthly rather than annual) would be preferable. Annual periods are used here for would be preferable. Annual periods are used here for clarity of presentation.clarity of presentation.



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Roth Harbor . . .Roth Harbor . . .Year ("j "): 0 1 2 3 4 5 6 7

Rentleg Gardens Expected Values: $40.37 $40.74 $41.12 $41.50 $41.89 $42.27 $42.67"down" moves ("i"):Rentleg Gardens Value Tr ee (as if new, ex dividend):

0 40.00 42.59 45.35 48.29 51.42 54.76 58.30 62.081 32.21 34.29 36.52 38.88 41.40 44.09 46.942 25.93 27.61 29.40 31.31 33.34 35.503 20.88 22.23 23.67 25.21 26.844 16.81 17.90 19.06 20.305 13.53 14.41 15.356 10.90 11.607 8.77Year ("j "): 0 1 2 3 4 5 6 7

"down" moves ("i"):Rentleg Construction Cost Tree :0 32.00 32.64 33.29 33.96 34.64 35.33 36.04 36.761 32.64 33.29 33.96 34.64 35.33 36.04 36.762 33.29 33.96 34.64 35.33 36.04 36.763 33.96 34.64 35.33 36.04 36.764 34.64 35.33 36.04 36.765 35.33 36.04 36.766 36.04 36.767 36.76

Year ("j "): 0 1 2 3 4 5 6"down" moves ("i"):Rentleg Land Value Tr ee (Samuelson-McKean, reflecting 1 yr time-to-build):

0 5.65 7.43 9.34 11.41 13.64 16.05 18.641 1.20 1.63 2.21 3.00 4.07 5.522 0.26 0.35 0.47 0.64 0.863 0.05 0.07 0.10 0.144 0.01 0.02 0.025 0.00 0.006 0.00



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Step 3: Compute the value of the option to build Phase II (Step 3: Compute the value of the option to build Phase II (Fisher Fisher LandingLanding), by:), by:

•• First build the Fisher Landing underlying asset value tree forwaFirst build the Fisher Landing underlying asset value tree forward rd in time, through Year 7 (the latest it can be obtained, if the oin time, through Year 7 (the latest it can be obtained, if the option ption is exercised at its expiration time in Year 5, given the 2is exercised at its expiration time in Year 5, given the 2--year timeyear time--toto--build requirement), starting from time 0 where build requirement), starting from time 0 where VV00 = $100M.= $100M.

•• Build the corresponding Fisher Landing construction cost tree Build the corresponding Fisher Landing construction cost tree forward in time, through Year 7, starting from forward in time, through Year 7, starting from KK00 = $80 million.= $80 million.

•• Then build the call option value tree through Year 5 (option Then build the call option value tree through Year 5 (option expiration), working backwards from Year 5 to time 0. Option expiration), working backwards from Year 5 to time 0. Option exercise gets completed Fisher Landing 2 yrs after exercise.exercise gets completed Fisher Landing 2 yrs after exercise.

Note: The Fisher Landing option cannot be obtained prior to Year 2, the earliest possible completion date of Phase I. Thus, we won’t end up using the Year 0 and Year 1 values of this option, but we might as well calculate them anyway.

The next slide shows these three trees.The next slide shows these three trees.



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Roth Harbor . . .Roth Harbor . . .Year ("j "): 0 1 2 3 4 5 6 7

Fisher Landing Expected Values: $100.93 $101.86 $102.80 $103.76 $104.72 $105.69 $106.66"down" moves ("i"):Fisher Landing Underlying Asset Value Tr ee (as if new, ex dividend):

0 100.00 106.48 113.38 120.73 128.56 136.89 145.76 155.211 80.52 85.73 91.29 97.21 103.51 110.22 117.362 64.83 69.03 73.50 78.27 83.34 88.743 52.20 55.58 59.18 63.02 67.104 42.03 44.75 47.65 50.745 33.84 36.03 38.376 27.24 29.017 21.94Year ("j "): 0 1 2 3 4 5 6 7

"down" moves ("i"):Fisher Landing Construction Cost Tree:0 80.00 81.60 83.23 84.90 86.59 88.33 90.09 91.891 81.60 83.23 84.90 86.59 88.33 90.09 91.892 83.23 84.90 86.59 88.33 90.09 91.893 84.90 86.59 88.33 90.09 91.894 86.59 88.33 90.09 91.895 88.33 90.09 91.896 90.09 91.897 91.89

Value of Option on Phase II (Fisher Landing), reflecting 2-yr time-to-build:Year ("j "): 0 1 2 3 4 5

"down" moves ("i"): Opt Expires0 8.78 12.80 17.15 21.85 26.92 32.401 0.44 0.75 1.29 2.21 3.782 0.00 0.00 0.00 0.003 0.00 0.00 0.004 0.00 0.005 0.00



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( ) ( ) ( ) ( ) ( )( ) ( ) ( ) ( )

( ) ( ) ( ) ( ) 60.81$80$02.111152.80$08.1100$15.1/11)/1(1

48.106$08.1100$15.11/11

001

0.00.01,1

0.01,0

==+=++=

==+=+=

==++=+=

KgyKrKyVuydVV

yVnTyuVV

KKf

VV

VtV σ

For example . . .For example . . .

( ) ( )( ) ( ) 786.0

15.1115.115.1109.1

/11/1/111

=−−

=+−+

+−+=

nTnTnTrp V

σσσ

VV00==$100$100

VV0,10,1==$106.48$106.48

VV1,11,1==$80.52$80.52

pp = .786= .786

11--pp = .214= .214



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( ) ( )

( ) ( ) ( ) ( )

⎪⎪

⎭

⎪⎪

⎬

⎫

⎪⎪

⎩

⎪⎪

⎨

⎧

+

⎥⎦

⎤⎢⎣

⎡

+−+

−−−−+

+−

+=

++++++

f

fVjijijiji

K

ji

V

jiji r

nTnTrr

CCCppC

yK

yV

MaxC1

/11/1)1(

,11

1,11,1,11,

2,

2,

,σσ

And the option value is given by:And the option value is given by:

For example:For example:

( ) ( )

( ) ( ) ( ) ( )

{ } 78.8$65.7$,78.8$

04.115.1115.1

%4%944.080.1244.0)214(.80.12)786(.,

0196.180

08.1100

220,0

==

⎪⎪⎭

⎪⎪⎬

⎫

⎪⎪⎩

⎪⎪⎨

⎧⎥⎦

⎤⎢⎣

⎡−−

−−+−=

Max

MaxC



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Roth Harbor . . .Roth Harbor . . .Step 4: Compute the value of the compound option to build Phase Step 4: Compute the value of the compound option to build Phase I, I,

which obtains both which obtains both Frenchman CoveFrenchman Cove and also the option to build and also the option to build Fisher LandingFisher Landing, by:, by:

•• First step the Phase II option value we just calculated back twoFirst step the Phase II option value we just calculated back two periods in periods in time, to obtain its present value in each period as a part of thtime, to obtain its present value in each period as a part of the underlying e underlying asset for the Phase I compound option, reflecting the Phase I tiasset for the Phase I compound option, reflecting the Phase I timeme--toto--build. build. (i.e., if you exercise the Phase I option, you will get the Phas(i.e., if you exercise the Phase I option, you will get the Phase II option only e II option only after a 2after a 2--yr lag. We want to know the PV of the Phase II option as of the yr lag. We want to know the PV of the Phase II option as of the time when the Phase I option may be exercised.)time when the Phase I option may be exercised.)

•• Then develop the other part of the Phase I optionThen develop the other part of the Phase I option’’s underlying asset value s underlying asset value by building the Frenchman Cove value tree forward in time, throuby building the Frenchman Cove value tree forward in time, through Year gh Year 5 (the last year it could be obtained, as the Phase I option exp5 (the last year it could be obtained, as the Phase I option expires in Year 3 ires in Year 3 and the project takes 2 years to build), starting from and the project takes 2 years to build), starting from VV00 = $60 million.= $60 million.

•• Build the corresponding Frenchman Cove construction cost tree foBuild the corresponding Frenchman Cove construction cost tree forward rward in time, through Year 5, starting from in time, through Year 5, starting from KK00 = $48 million.= $48 million.

•• Finally build the Phase I compound call option value tree workinFinally build the Phase I compound call option value tree working g backwards in time from Year 3 (option expiration) to time 0. Optbackwards in time from Year 3 (option expiration) to time 0. Option ion exercise gets completed Frenchman Cove + Phase II option, both 2exercise gets completed Frenchman Cove + Phase II option, both 2 yrs yrs after exercise.after exercise. Abandonment for asAbandonment for as--ofof--right land value is always an right land value is always an alternative to either holding or exercising the Phase I option.alternative to either holding or exercising the Phase I option.



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Roth Harbor . . .Roth Harbor . . .PV of 1 period delayed receipt of Phase 2 option value:

Year ("j "): 0 1 2 3 4"down" moves ("i"):

0 7.65 10.30 13.25 16.57 20.361 0.44 0.75 1.29 2.212 0.00 0.00 0.003 0.00 0.004 0.00

PV of 2 period delayed receipt of Phase 2 option valuYear ("j "): 0 1 2 3

"down" moves ("i"):0 6.19 8.03 10.17 12.731 1.20 1.63 2.212 0.26 0.353 0.05

Here we are simply applying the certaintyHere we are simply applying the certainty--equivalence valuation equivalence valuation formula 1 period at a time to the Phase II option value (previouformula 1 period at a time to the Phase II option value (previously sly calculated).calculated).

For example . . .For example . . .



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( ) ( ) ( ) ( )30.10$

04.115.1115.1

%4%975.015.1775.0)214(.15.17)786(.][ 21,0 =

⎥⎦

⎤⎢⎣

⎡−−

−−+=CPV


PV in the PV in the 0,10,1 node of Year 1 of the Phase II option in Year 2 is:node of Year 1 of the Phase II option in Year 2 is:

PV in the PV in the 0,00,0 node of Year 0 (the present) of the Phase II option in Year node of Year 0 (the present) of the Phase II option in Year 2 is:2 is:

( ) ( ) ( ) ( )19.6$

04.115.1115.1

%4%944.030.1044.0)214(.30.10)786(.]][[][ 210,020 =

⎥⎦

⎤⎢⎣

⎡−−

−−+== CPVPVCPV

This This PVPVtt of the Phase II option as of time of the Phase II option as of time t t is part of what one obtains in is part of what one obtains in time time tt by exercising the Phase I option in time by exercising the Phase I option in time tt..

The other part of what one obtains is the The other part of what one obtains is the PVPVtt as of time as of time tt of the of the Frenchman Cove development project (which would be completed 2 Frenchman Cove development project (which would be completed 2 years later):years later):

( ) ( ) ( ) ( )2222

22

22 1111][][

K

t

V

t

f

t

V

ttttt y

Ky

Vr

Kr

VEKVPV+

−+

=+

−+

=− ++++



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Here are the Frenchman Cove underlying asset value and constructHere are the Frenchman Cove underlying asset value and construction ion cost trees, obtained in the usual manner:cost trees, obtained in the usual manner:

Year ("j "): 0 1 2 3 4 5Frenchman Cove Expected Values: $60.56 $61.12 $61.68 $62.25 $62.83

"down" moves ("i"):Frenchman Cove Underlying Asset Value Tr ee (as if new, ex-dividend):0 60.00 63.89 68.03 72.44 77.13 82.131 48.31 51.44 54.77 58.32 62.102 38.90 41.42 44.10 46.963 31.32 33.35 35.514 25.22 26.855 20.30

Year ("j "): 0 1 2 3 4 5"down" moves ("i"):Frenchman Cove Construction Cost Tree:

0 48.00 48.96 49.94 50.94 51.96 53.001 48.96 49.94 50.94 51.96 53.002 49.94 50.94 51.96 53.003 50.94 51.96 53.004 51.96 53.005 53.00



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The value of the Phase I option is then calculated working backwThe value of the Phase I option is then calculated working backwards in ards in time from its expiration in Year 3. time from its expiration in Year 3.

The value in Year 3 is the maximum of either: (i) the asThe value in Year 3 is the maximum of either: (i) the as--ofof--right land right land value (land value based on the value (land value based on the RentlegRentleg Gardens Project, which is the Gardens Project, which is the ““abandonment valueabandonment value”” of the RHP Project); or (ii) the value of of the RHP Project); or (ii) the value of immediate exercise of the Phase I option (which obtains the compimmediate exercise of the Phase I option (which obtains the completed leted Frenchman Cove Project plus the Phase II option, both 2 years laFrenchman Cove Project plus the Phase II option, both 2 years later):ter):

CC33 == Max Max {{ AsAs--ofof--right Land Valueright Land Value3 3 , PV, PV33[[VV55 –– KK55 ] + ] + PVPV33[[Ph.II OptPh.II Opt55 ]}]}


The value in any earlier year is the current value of the maximuThe value in any earlier year is the current value of the maximum of m of either of the above two alternatives (i) and (ii) plus the thirdeither of the above two alternatives (i) and (ii) plus the third alternative alternative of holding the of holding the ““livelive”” option unexercised for at least one more year: option unexercised for at least one more year:

CCtt = Max= Max {{ AsAs--ofof--right Land right Land ValueValuett , PV, PVtt[[VVt+2t+2 –– KKt+2t+2 ] + ] + PVPVtt[[Ph.IIPh.II OptOptt+2t+2 ] , ] , PVPVtt[[CCt+1t+1]}]}



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Roth Harbor . . .Roth Harbor . . .Here is the Phase I option value tree:Here is the Phase I option value tree:

Value of Option on Phase I (Frenchman Cove), reflecting 2-yr time-to-build:Year ("j "): 0 1 2 3

"down" moves ("i"): Opt Expires0 11.46 15.71 20.45 25.841 1.20 1.63 2.212 0.26 0.353 0.05

The Phase I option is worth $11.46 million:The Phase I option is worth $11.46 million:

( ) ( )

( ) ( ) ( ) ( )

{ } 46.11$63.9$,46.11$,65.5$

04.115.1115.1

%4%920.171.1520.1)214(.71.15)786(.,19.6

0196.148

08.160,65.5 220,0

==

⎪⎪⎭

⎪⎪⎬

⎫

⎪⎪⎩

⎪⎪⎨

⎧⎥⎦

⎤⎢⎣

⎡−−

−−++−=

Max

MaxC

This $11.46 million is in fact the value of the Roth Harbor landThis $11.46 million is in fact the value of the Roth Harbor land with the with the special zoning exemption, the value of the RHP Project option.special zoning exemption, the value of the RHP Project option.

All of these calculations are available in a downloadable Excel file.www.bsscommunitycollege.in www.bssnewgeneration.in www.bsslifeskillscollege.in


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Note that since the $11.46 million valuation of the Phase I optiNote that since the $11.46 million valuation of the Phase I option is in fact on is in fact the value of immediate exercise of the option, our model of optithe value of immediate exercise of the option, our model of option on value is telling us that it is in fact optimal for the landownervalue is telling us that it is in fact optimal for the landowner to to immediately begin construction on Phase I of the RHP Project.immediately begin construction on Phase I of the RHP Project.

Our real options analysis has therefore now allowed us to answerOur real options analysis has therefore now allowed us to answerrigorouslyrigorously all three of the important questions that we set out to all three of the important questions that we set out to answer:answer:

1.1. The current value of the site based on its preThe current value of the site based on its pre--existing asexisting as--ofof--right right development option (development option (RentlegRentleg Gardens) is Gardens) is $5.65 million$5.65 million. .

2.2. The value of the site with the proposed special zoning exemptionThe value of the site with the proposed special zoning exemption for for the 2the 2--phase RHP Project is phase RHP Project is $11.46 million$11.46 million. The . The incremental valueincremental valueadded over the preadded over the pre--existing land value by the special zoning for the existing land value by the special zoning for the RHP Project is: $11.46 RHP Project is: $11.46 –– $5.65 = $5.65 = $5.81 million$5.81 million. .

3.3. The RHP Project (like the The RHP Project (like the RentlegRentleg Gardens Project) is Gardens Project) is ““riperipe”” for for IMMEDIATE DEVELOPMENTIMMEDIATE DEVELOPMENT..



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The preceding analysis included in a rigorous manner both the The preceding analysis included in a rigorous manner both the opportunity cost of capital (OCC) and the value of flexibility aopportunity cost of capital (OCC) and the value of flexibility and nd phasing in the possible development projects.phasing in the possible development projects.

The analysis allows us to say:The analysis allows us to say:

1.1. A fair price for a A fair price for a ““takingtaking”” of the Roth Harbor site based on its preof the Roth Harbor site based on its pre--existing existing rights would be $5.65 million.rights would be $5.65 million.

2.2. A fair bid for the site with the proposed special zoning exemptiA fair bid for the site with the proposed special zoning exemption for the on for the twotwo--phase RHP Project would be $11.46 million.phase RHP Project would be $11.46 million.

3.3. Our best guess of the NPV of the special zoning exemption is $5.Our best guess of the NPV of the special zoning exemption is $5.81 million.81 million.

4.4. A recipient of the site with the special zoning exemption would A recipient of the site with the special zoning exemption would likely seek to likely seek to immediately begin construction on Phase I.immediately begin construction on Phase I.

5.5. There is some urgency in closing an agreement with the current lThere is some urgency in closing an agreement with the current landowner, andowner, as the asas the as--ofof--right project is also ripe for immediate development (the currenright project is also ripe for immediate development (the current t owner is suffering an opportunity cost by not proceeding with thowner is suffering an opportunity cost by not proceeding with that at development).development).



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Roth Harbor . . .Roth Harbor . . .Here is the Phase I option optimal exercise tree*:Here is the Phase I option optimal exercise tree*:

Year ("j "): 0 1 2 3"down" moves ("i"):1st Phase Optimal Exercise :

0 exer exer exer exer1 hold hold sell2 hold sell3 sell

Corresponding to the following Frenchman Cove value contingencieCorresponding to the following Frenchman Cove value contingencies:s:Year ("j "): 0 1 2 3

Frenchman Cove Expected Values: $60.56 $61.12 $61.68"down" moves ("i"):Frenchman Cove Underlying Asset Value Tr ee (as if

0 60.00 63.89 68.03 72.441 48.31 51.44 54.772 38.90 41.423 31.32

Which have the following probabilities of occurrence as of time Which have the following probabilities of occurrence as of time 0:0:Year ("j "): 0 1 2 3

"down" moves ("i"):Contingency Probabilities:0 100.0% 78.6% 61.8% 48.6%1 21.4% 33.6% 39.7%2 4.6% 10.8%3 1.0%



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( )][

][11,

1][

][1][

1][

1

1,

,

111,

, +

++++ +=+⇒+

=++

=+

=j

jjfji

ji

jj

Cf

jj

f

jji CCEQ

CErOCC

OCCCE

RPErCE

rCCEQ

Cji

Roth Harbor . . .Roth Harbor . . .Here is the Phase I option opportunity cost of capital tree:Here is the Phase I option opportunity cost of capital tree:

Year ("j "): 0 1 2 3"down" moves ("i"):Roth Harbor OCC:

0 30.85% 30.71% 30.44% 24.84%1 27.37% 27.37% 27.37%2 27.37% 27.37%3 27.37%

Based on the following formula introduced earlier:Based on the following formula introduced earlier:

( )

( ) ( ) ( ) ( )

3085.102.10$60.12$04.1

15.1115.1%4%920.171.1520.1)214(.71.15)786(.

20.1)214(.71.15)786(.04.1

][][1110

100,0

==

⎥⎦

⎤⎢⎣

⎡−−

−−+

+=

=+=+CCEQ

CErOCC f

For example, for the initial OCC:For example, for the initial OCC:



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Thus, the RHP Project currently has over Thus, the RHP Project currently has over 5 times5 times the amount of the amount of investment risk (as evaluated by the capital market) as does an investment risk (as evaluated by the capital market) as does an unleveredunlevered investment in a completed apartment property, as indicated investment in a completed apartment property, as indicated by:by:

37.5%00.5%85.26

%4%9%4%85.30

][][

==−−

=V

C

RPERPE



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How would the RHP Project be evaluated according to typical currHow would the RHP Project be evaluated according to typical current ent practice in the real estate investment business? . . .practice in the real estate investment business? . . .

Typically, a conventional DCF analysis would be applied:Typically, a conventional DCF analysis would be applied:

•• Ignoring the flexibility (but not ignoring the Ignoring the flexibility (but not ignoring the expectedexpected phasing) in phasing) in the project;the project;

•• Using a nonUsing a non--rigorous rigorous ad hocad hoc OCC as the discount rate.OCC as the discount rate.

Thus:Thus:

•• A particular phasing scenario is assumed (e.g., A particular phasing scenario is assumed (e.g., each phase will each phase will begin as soon as possiblebegin as soon as possible););

•• A particular discount rate is assumed (e.g., A particular discount rate is assumed (e.g., ““20%20%””, because it, because it’’s a s a nice round number and consistent with the nice round number and consistent with the ““conventional wisdomconventional wisdom””for required returns on development projects.for required returns on development projects.))

LetLet’’s see how this might be done for our RHP Project example . . .s see how this might be done for our RHP Project example . . .



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If both Phase I and Phase II are built as soon as possible, the If both Phase I and Phase II are built as soon as possible, the net cash net cash flow from the liquidation of each phase would be obtained in Yeaflow from the liquidation of each phase would be obtained in Years 2 rs 2 and 4 respectively.and 4 respectively.

Using the projected values of Using the projected values of EE[[VV22]] and and KK22 , and of , and of EE[[VV4 4 ] and ] and KK44 , in , in years 2 and 4 for Frenchman Cove and Fisher Landing respectivelyyears 2 and 4 for Frenchman Cove and Fisher Landing respectively, we , we get the following net cash flow projection for the RHP Project aget the following net cash flow projection for the RHP Project as a s a whole:whole:

Year: 1 2 3 4

Net Cash:0 $61.12 –

$49.94= $11.18

0 $103.76 –$86.59

= $17.16

04.16$20.1

16.17$20.1

18.11$42 =+=PV

Discounting these cash flows @ 20% gives a gross PV for the RHP Discounting these cash flows @ 20% gives a gross PV for the RHP Project of:Project of:

Thus, the conventional procedure would suggest a bid price of Thus, the conventional procedure would suggest a bid price of $16.04$16.04million for the RHP site with the special zoning exemption. As million for the RHP site with the special zoning exemption. As compared to compared to $11.46$11.46 million using the real options approach.million using the real options approach.



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In this example the conventional approach has substantially overIn this example the conventional approach has substantially over--estimated the more rigorously estimated value, due primarily to*estimated the more rigorously estimated value, due primarily to*::

•• Using a discount rate that is too small (20% Using a discount rate that is too small (20% vsvs OCC = 30.85%).OCC = 30.85%).

•• Assuming the most optimistic project schedule (both phases Assuming the most optimistic project schedule (both phases implemented, and each as soon as possible).implemented, and each as soon as possible).

While in the above example the conventional approach overWhile in the above example the conventional approach over--values the values the development project, in general, the conventional approach may edevelopment project, in general, the conventional approach may either ither overover-- or underor under--estimate the project value, relative to the real options estimate the project value, relative to the real options valuation . . .valuation . . .

Our point is Our point is notnot that the conventional approach is that the conventional approach is systematically biasedsystematically biased..



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While a systematic bias (in one direction) in the conventional aWhile a systematic bias (in one direction) in the conventional approach pproach maymay exist, . . .exist, . . .

Well functioning investment markets for land, built properties, Well functioning investment markets for land, built properties, and real and real estate debt instruments, should cause the conventional practice estate debt instruments, should cause the conventional practice to tend to tend to get valuation about right on average. to get valuation about right on average.

Otherwise opportunities for Otherwise opportunities for ““supersuper--normalnormal”” profit (excess investment profit (excess investment returns) would be widespread. returns) would be widespread.

The fact that our real options model is based fundamentally on tThe fact that our real options model is based fundamentally on the he elimination of superelimination of super--normal (normal (““arbitragearbitrage””) profit, suggests that the ) profit, suggests that the options approach and the conventional approach should tend to agoptions approach and the conventional approach should tend to agree ree on averageon average (across projects and over time).(across projects and over time).

Summarizing Real Options Summarizing Real Options vsvs Conventional DCF . . .Conventional DCF . . .



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The key difference between real options The key difference between real options vsvs conventional valuation, conventional valuation, however, is that:however, is that:

•• The options approach is more The options approach is more rigorousrigorous, providing a valuation that is less , providing a valuation that is less errorerror--prone, more likely to be prone, more likely to be ““more correctmore correct”” in more individual instances in more individual instances (even if not on average across all projects). And through this r(even if not on average across all projects). And through this rigor, . . .igor, . . .

•• The options approach provides a deeper understanding of: (i) thThe options approach provides a deeper understanding of: (i) the sources e sources of the project value; and (ii) the true nature of the project inof the project value; and (ii) the true nature of the project investment risk vestment risk and return;and return;

•• The conventional approach is based on The conventional approach is based on ad hocad hoc assumptions regarding assumptions regarding project execution and OCC, ignoring important realities of the pproject execution and OCC, ignoring important realities of the project such roject such as its flexibility.as its flexibility.

•• Even if the conventional approach gives a correct answer in a gEven if the conventional approach gives a correct answer in a given case iven case (i.e., the same valuation as the options approach), there is no (i.e., the same valuation as the options approach), there is no way in itself to way in itself to know know whetherwhether the valuation is correct, or the valuation is correct, or whywhy it is correct if it is correct it is correct if it is correct (except by basing it on the more rigorous options approach).(except by basing it on the more rigorous options approach).




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The previous conventional DCF valuation approach used The previous conventional DCF valuation approach used net cash flowsnet cash flowsand an and an ad hocad hoc discount rate.discount rate.An alternative approach to applying conventional DCF valuation uAn alternative approach to applying conventional DCF valuation uses ses gross cash flowsgross cash flows and rigorous OCC discount rates:and rigorous OCC discount rates:

Year: 1 2 3 4

Gross Cash:0 E0[V2] = $61.12

K2 = $49.94 0 E0[V4] = $103.76

K4 = $86.59

75.4$52.0$27.5$04.1

59.86$09.1

76.103$04.1

94.49$09.1

12.61$4422 =−=⎟⎠⎞

⎜⎝⎛ −+⎟

⎠⎞

⎜⎝⎛ −=PV

Although the OCCs and cash flow projections used in this procedure are well justified, this procedure implicitly assumes an irreversible commitment at time 0 to complete the entire project as scheduled. It thus ignores the flexibility that actually exists, and thereby systematically under-estimates the project present value (in this case: $4.75 million versus $11.46 million.

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ⎟⎟⎠

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⎞⎜⎜⎝

⎛

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II

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Back to the Back to the ““Big PictureBig Picture””: Types of Development Options: Types of Development Options

We have now presented an inWe have now presented an in--depth and practical depth and practical methodology for addressing two of the common types of methodology for addressing two of the common types of options found in development projects:options found in development projects:

•• ““Wait OptionWait Option””: The option to : The option to delaydelay start of the project start of the project construction;construction;

•• ““Phasing OptionPhasing Option””: The breaking of the project into : The breaking of the project into sequential sequential phasesphases rather than building it all at once;rather than building it all at once;

The third type:The third type:

•• ““Switch OptionSwitch Option””: The option to choose among : The option to choose among alternative alternative typestypes of buildings to construct on the given land parcel.of buildings to construct on the given land parcel.

Requires much more advanced technical capability. Suffice it Requires much more advanced technical capability. Suffice it to say at this point that: to say at this point that: optionalityoptionality (rights without (rights without corresponding obligations) corresponding obligations) never reduces valuenever reduces value..



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Step back and look at the bigger picture of the Roth Harbor PlacStep back and look at the bigger picture of the Roth Harbor Place e Project. Recall our Project. Recall our decision treedecision tree representation of the RHP Projectrepresentation of the RHP Project……

Abandon RHP Allow Phase I

option to expire, Build

Rentleg or Sell Land for As-of-Right Val

Build Phase I of RHP

Build Phase II of RHP

Allow Phase II option to

expire, Hold or Sell with Phase

I only

Is Phase I a success?

Yes

No

Initial Decision

w/in3 yrs

w/in5 yrs

w/in5 yrs

The The ““Big PictureBig Picture””: Project Design : Project Design ““ArchitectureArchitecture””

Project design Project design ““architecturearchitecture”” refers to how this overall structure of refers to how this overall structure of the project is designed . . .the project is designed . . .



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The The ““Big PictureBig Picture””: Project Design : Project Design ““ArchitectureArchitecture””

Project design Project design ““architecturearchitecture”” refers to how the overall structure of the refers to how the overall structure of the project is designed. For the RHP Project:project is designed. For the RHP Project:

•• Why were there 2 phases, not 3, or 1, or 4? . . .Why were there 2 phases, not 3, or 1, or 4? . . .•• Why did the options have to expire after 3 and 5 years? . . .Why did the options have to expire after 3 and 5 years? . . .•• Why 900 units in Phase I and 1600 in Phase II? . . .Why 900 units in Phase I and 1600 in Phase II? . . .•• Why a total of 2500 units, not 3000 or 2000? . . .Why a total of 2500 units, not 3000 or 2000? . . .

These overarching design questions can have a huge impact on proThese overarching design questions can have a huge impact on project value.ject value.As yet we have no comprehensive, systematic and rigorous method As yet we have no comprehensive, systematic and rigorous method of of

optimizing project design architecture.*optimizing project design architecture.*The real options valuation theory presented in this lecture doesThe real options valuation theory presented in this lecture does not solve this not solve this

problem.problem.But it does provide a framework and metric by which mutually excBut it does provide a framework and metric by which mutually exclusive lusive

alternative project architectures can be evaluated and rankalternative project architectures can be evaluated and rank--ordered, by ordered, by which the best architecture can be selected from among alternatiwhich the best architecture can be selected from among alternativesves……

The architecture with the highest net value based on its real opThe architecture with the highest net value based on its real options valuation is tions valuation is the best architecture.the best architecture.



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“Capital Structure”= How investment (asset ownership) is financed . . .

= Use of debt vs equity (how much of each) as sources of financial capital.

Traditionally this question has focused on publicly-traded corporations, but…

• Much real estate investment is made more directly, not through publicly-traded companies.

• Much real estate investment is financed at the project level (individual assets are financed directly).

• Real estate assets trade directly, and are relatively simple, transparent cash generators.



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15.1 Debt When There is an Equity Capital Constraint

In theory, publicly-traded corporations never face an equity capital constraint (if the stock market is efficient). Whenever they face a positive-NPV investment opportunity, they can simply issue new stock to obtain equity financing.

This is not the case for private companies or individuals.

Nor for tax-exempt institutions such as pension funds.

In real estate investment, debt finance can be useful simply as a NECESSARY source of capital if you face an equity constraint, and:

1. You face a positive (or at least non-negative) NPV opportunity (at least from IV perspective), or

2. You seek more diversification across properties than your equity alone can allow, given the size of properties and the amount of your equity.



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A particular point for small-scale individual entrepreneurs:

Use debt financing to leverage your “human capital” (as well as your financial capital:

• Your skill and talent and knowledge enable you to successfully manage income property.

• This enables you to earn “wages” or “profits” effectively as a “property manager” or “asset manager”.

• The more properties you own, the more you can guarantee yourself a job managing, hence, the more earnings you can make on your managerial human capital.

• Use of debt allows you to own more properties, to extend your human capital earnings.

(How else could you possibly cash in on such human capital without taking on the financial investment role as well?...)



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How would the leveraging of human capital show up in the quantitative DCF and NPV mechanics we described in previous chapters? . . .

• Define multiple “profit centers” for the firm, some of which derive from operations as distinct from passive investment.

• “Operating expenses” that are pure cash outflows from the investment perspective, may contain an element of profit from the operational perspective.

Thus, a deal contains more than one source of value:

• NPV from the pure investment perspective (return on financial capital).

• NPV from operational profit centers (return on human capital).

• Together the two (or more) NPVs above equal the total NPV of the deal from the firm’s (or individual’s) particular IV (“investment value”) perspective (see Ch.12).

15.1.3: Beware: constraints on equity capital availability may not be as great or as binding as you first might think. There are lots of ways to “joint venture” in real estate deals.



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3. Leverage as a "disciplinary tool" to "incentivize" good mgt: - Real estate physical assets are "easy to manage, not much risk

or excitement or growth potential in bricks & mortar" (e.g., compared to high-tech industries, world trade, etc).

- With not much downside and not much upside, managers may tend to get "lazy", letting value-enhancing possibilities pass them by unnoticed.

- With sufficient leverage, real estate becomes a high-risk, high-growth investment, making it sufficiently "exciting" to attract good mgrs, giving mgrs sufficient incentive to max value.

- This argument not based on a capital constraint or capital mkt failure for small investors, and so this argument for debt financing applies not only to small individual investors but to large insts & REITs.

15.2.1

Debt as an Incentive and Disciplinary Tool for Management



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15.2.2

Debt and Liquidity

1. Leverage reduces the equity investor's "liquidity": - "Liquidity" = Ability to quickly obtain "full value" as cash. - Underlying (physical) R.E. assets are illiquid. - By not borrowing to the hilt, you can obtain cash by mortgaging

the prop. (i.e., if you don't borrow now, you can borrow later), thereby reducing the illiquidity problem of real estate investment.

- Liq. valuable because it gives the investor flexibility, provides options: Pounce on pos.-NPV opportunities; Avoid being foreced into neg.-NPV deals.

- Liq. Allows you to use the R.E. cycle to your advantage instead of being a victim of it. (More important in R.E. than stocks due to lack of info.effic. in R.E. mkts.



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2. The "Cost of Financial Distress" (COFD): - (See Brealey-Myers Ch.18.) - Bankruptcy or foreclosure has large "deadweight costs". - Also “agency costs”: High L / V ratio Conflict of interest betw

equity owner vs debtholder. Can cause prop.owner to act suboptimally (e.g.: avoid CI, pad expenses, high-stakes “repositioning” of rent roll, exercise mortgagor’s “put”): "moral hazard".

- Mere probability of these costs (deadweight, agency) reduces value of prop. if L / V too high (even though L / V still < 1).

- Thus, optimal L / V always < 1. However,… - The "easy management", low risk nature of R.E., & transparency

(relatively easy for outsider to detect poor mgt, in part via ability to observe prop.val. in asset mkt) COFD does not “kick in” for R.E. until higher L / V ratio than for other types of investments (e.g., typical stock)

15.2.3

Cost of Financial Distress



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Exhibit 15-1: Cost of Financial Distress

V-COFD PropertyProperty

Industrial firm

LTV

Effect of Expected Costs of Financial Distress (COFD) on theValue of the Firm and on Property Value

Image by MIT OCW.



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2. Inflation: - "The more you borrow, the more money you make just from

inflation!" - Do borrowers know more about inflation than lenders? . . . - Inflation is only the borrower’s friend ex post.

- Ex ante (which is when it matters for leverage decision) the

inflation argument is a fallacy. No positive NPV to borrower in loan transaction due to inflation.

However, fixed-rate debt leverage makes equity position more of an

"inflation hedge".

15.2.4

Debt and Inflation



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Exhibit 15-2: Example of effect of inflation on ex-post levered equity appreciation returns with 1-year loan...

Scenario: Ex Post- Ex Ante Ex Post+ Inflation: 0% 2% 4% Values*... Property: Yr.0 $100 $100 $100 Yr.1 $99 $101 $103 Debt Balance Payable: Yr.0 $60 $60 $60 Yr.1 $60 $60 $60 Levered Equity: Yr.0 $40 $40 $40 Yr.1 $39 $41 $43 Appreciation %... Nominal Returns: Property: -1.0% 1.0% 3.0% Levered Equity: -2.5% 2.5% 7.4% Nominal Deviation from ex ante: Property: -2.0% 0.0% 2.0% Levered Equity: -5.0% 0.0% 5.0% Real Returns: Property: -1.0% -1.0% -1.0% Levered Equity: -2.5% 0.5% 3.3% Real Deviation from ex ante: Property: 0.0% 0.0% 0.0% Levered Equity: -2.9% 0.0% 2.8% *Real depreciation rate = 1%/yr.



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15.3

Project Level Capital Structure in Real Estate

Much real estate finance occurs at the micro-level of individual investments in properties, projects, or “deals ."

Hence, much “capital structure” in real estate occurs at this micro-level.

Why?...

• Much real estate investment is still done directly by individuals or small entrepreneurial firms.

• Also real estate assets are relatively simple, tangible and “transparent”: Makes them ideal candidates for secured debt and other types of project-level financing

• (External investors need to feel confident that they know what is going on in the investment even if they don’t have direct management control or highly specialized expertise.)

• Also, the law governing real property rights facilitates this type of finance.



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Just because finance is at the project (asset) level does not alter the basic principles and considerations we have already discussed.

Classical micro-level real estate finance consists of equity and debt(mortgag):

• Chs 13 & 14, & Sects 15.1 & 15.2 apply.

In recent years, capital markets have become more sophisticated.

More types of investment vehicles tailored to a more diverse range of investors. Result is growth in more complex capital structures at the micro-level.

Consider some of the new, additional types of financing and capital structures being used for real estate investments in the U.S. today . . .

General points:



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So-called “mez debt” is an investment vehicle structured as a loan, typically including a “lien” on the underlying property, but subordinated to other specified senior investment vehicles.

Mez debt investors typically don’t receive return of or on their investment until after senior debt holders are fully compensated for what is owed them.

Mez debt capital is typically “drawn” or placed into the investment before the senior debt capital.

Mez debt thus provides a buffer of capital exposure helping to protect the senior debt investors.

Mez debt typically carries interest rates considerably above those of first mortgages.

Mezzanine Debt



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Similar to mez debt (provides a contractually-stated dividend or yield payment in the form of a “guaranteed” return).

But normally subordinated to any secured debt on the property (including mez debt).

Differs from mez debt in lack of collateral, no formal lien on the underlying real estate.

Preferred equity precedes common equity in priority of claims.

Preferred equity obtains its returns usually purely in the form of a preferred dividend (no appreciation of principle or capital paid in).

Sometimes the preferred return not paid out currently accumulates with (or without) compounding.

In capital structures where there is both mez debt and preferred equity, usually the preferred equity goes in before, and comes out after, the mez debt capital, and the preferred equity return is higher than the mez debt return.

Preferred Equity



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This is normally the property ownership entity that has the operational management responsibility and primary governing control of the project.

Common equity has no guaranteed or contractual return and receives only the residual cash flow after the other senior investment vehicles have been paid their preferred returns.

(However, common equity is sometimes entitled to return of its paid-in capital with zero return prior to preferred equity being paid its preferred return.)

Common (or Residual) Equity



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Differentiate investors according to what they bring into the deal and what they want to get out of it.

Entrepreneurial investor may essentially bring operational management ability and the deal itself (e.g., in a development, the land with entitlements and permits, as well as the project design).

Money partner brings most of the required equity cash but lacks the ability or desire to manage the operation of the project or property.

Define different “classes” of partners or stockholders in the ownership equity entity, e.g.:

Entrepreneurial partner has operational control.

Money partner has control over major capital decisions (financing and asset buy/sell decisions).

Entrepreneurial partner may or may not subordinate some of its equity claim to that of the money partner (though the entrepreneurial partner may also take a fee for service).

Differentiated Equity Partners (Classes)



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Common arrangement splits the equity entity’s overall cash flow among the partners on a “pro rata pari passu” basis (proportionately relative to their capital contributions)…

Until the equity entity achieves a certain “hurdle” return (specified either on a cumulative current or a look-back IRR basis, or both);

Beyond that hurdle return the cash flow split is differentiated to provide entrepreneurial partner with a proportion greater than its capital contribution (either on a current or back-end basis).

This is called a “promote," and surpassing the return hurdle is referred to as “earning the promote."

Provides partner charged with operational management more incentive to make the project a success. (Such success benefits all investors in the project.)

(The promote structure may also provide some degree of “reward” for putting the deal together in the first place.)

Differentiated Equity Partners (Classes), cont.:

“Splits” . . .



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15.3.2: Numerical Example of Multi-tiered Project Capital Structure

Consider the $1,000,000 apartment property investment example of Ch.14.

Only now let’s assume it is a development project:

• Time-to-build: 1 year (projected value on completion = $1,000,000).

• Up-front land cost: $200,000.

• Construction cost: $750,000 payable on completion (including interest), financed by 1st-lien construction loan.

• Hence: $950,000 total devlpt cost ($50,000 projected “entrepreneurial profit”).

• Take out construction loan on completion with $750,000 permanent mortgage (1st -lien).

• Equity ownership entity is a “joint venture” with 2 partners: “entrepreneurial” (residual) and “money” (preferred), as follows:

Permanent Mortgage Interest Rate 5.50%Preferred Equity Partner Contribution 90%Preferred Return 6.00%Preferred Partner Residual Share 50%

Amort $2000/yr.



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Property Purchase Price (Year 0): $1,000,000 Unlevered: Levered:Depreciable Cost Basis: $800,000 Before-tax IRR: 6.04% 7.40%Ordinary Income Tax Rate: 35.00% After-tax IRR: 4.76% 6.44%Capital Gains Tax Rate: 15.00% Ratio AT/BT: 0.787 0.870Depreciation Recapture___________ 25.00% _____________________________________________ _____________________________________________________________________________________







=EATCF $20,369 $20,831 ($28,704) $21,766 $22,239 $22,716 $23,198 ($26,317) $24,173 $24,667 =EATCF $301,202 $325,868


______________________________ ________________________________________________________ _____________________________________________________________________________________CASH FLOW COMPONENTS FORMAT





+ DTS $10,182 $10,182 $10,182 $10,182 $10,182 $10,182 $10,182 $10,182 $10,182 $10,182 - AccDTS ($72,727) ($62,545)+ ITS $14,438 $14,399 $14,361 $14,322 $14,284 $14,245 $14,207 $14,168 $14,130 $14,091 $14,091

=EATCF $20,369 $20,831 ($28,704) $21,766 $22,239 $22,716 $23,198 ($26,317) $24,173 $24,667 EATCF $301,202 $325,868

Recall the apartment investment example of Chapter 14 . . .




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Money partner contributes 90% of the equity cash requirement (that is, $180,000 of the $200,000 land price at Year 0).

Entrepreneurial partner contribute the rest of the cash, has operational management control.

Money partner receives annual preferred return of 6% (any unpaid current return accumulates forward with annual compounding).

Any positive net operating cash flow from the property (after the debt service has been paid) will go:

1st) To provide money partner with preferred 6% return, then

2nd) Split 50/50 between the two partners (even though the money partner contributes 90% of the equity capital).

Reversion cash flow from net resale proceeds (after debt repayment) will go first to provide the money partner with her preferred 6% return.

Any remaining cash available upon termination will go:

1st) To pay back the entrepreneurial partner for his capital contribution (with zero return) and next

2nd) Split 50/50 between the two partners.

The deal structure . . .



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Calendar Years Ending: Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Year 8 Year 9 Year 10 Year 11Project Cash Requirements as Proposed: Site Acquisition 200,000 Hard & Soft Development Costs 750,000 Total Devlpt Phase Cash Requirements (200,000) (750,000) Devlpt Phase Total Equity Funding 200,000Devlpt Phase Debt Funding (Constr Loan) 750,000Construction Loan Repayment (750,000)Proposed Permanent Loan Amount (Take Out) 750,000Operating PBTCF 60,000 60,600 11,206 61,818 62,436 63,061 63,691 14,328 64,971 65,621Reversion PBTCF 0 0 0 0 0 0 0 0 0 1,104,622PBTCF 60,000 60,600 11,206 61,818 62,436 63,061 63,691 14,328 64,971 1,170,243Permanent Loan Debt Service (43,250) (43,140) (43,030) (42,920) (42,810) (42,700) (42,590) (42,480) (42,370) (42,260)Permanent Loan Repayment (730,000)Permanent Loan Debt CFs 750,000 (43,250) (43,140) (43,030) (42,920) (42,810) (42,700) (42,590) (42,480) (42,370) (772,260)Operating EBTCF 16,750 17,460 (31,824) 18,898 19,626 20,361 21,101 (28,152) 22,601 23,361Reversion EBTCF 0 0 0 0 0 0 0 0 0 374,622EBTCF 16,750 17,460 (31,824) 18,898 19,626 20,361 21,101 (28,152) 22,601 397,983

Preferred Equity Capital Account:Preferred Return Allocation: Beginning Equity Investment Balance 0 180,000 190,800 190,800 190,800 230,890 230,890 230,890 230,890 230,890 270,080 270,080 Annual Preferred Investment 180,000 0 0 0 28,642 0 0 0 0 25,337 0 0 Preferred Return Earned 0 10,800 11,448 11,448 11,448 13,853 13,853 13,853 13,853 13,853 16,205 16,205 Preferred Return Paid 0 0 (11,448) (11,448) 0 (13,853) (13,853) (13,853) (13,853) 0 (16,205) (16,205) Accrued But Unpaid Preferred Return 0 10,800 0 0 11,448 0 0 0 0 13,853 0 0 Ending Equity Investment Balance 180,000 190,800 190,800 190,800 230,890 230,890 230,890 230,890 230,890 270,080 270,080 270,080Reversion Preferred Allocations: Allocation to Satisfy Preferred Return Requirement (270,080) Allocation to Return Subordinated Investment Requirement (25,998)

Annual CF approximations for purpose of checking fairness of splitsYear 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Year 8 Year 9 Year 10 Year 11

Project Level Cash Flows*: IRR Construction Phase 25.00% (200,000) 250,000Operational Phase 6.04% (1,000,000) 60,000 60,600 11,206 61,818 62,436 63,061 63,691 14,328 64,971 1,170,243Both Phases 6.54% (200,000) (750,000) 60,000 60,600 11,206 61,818 62,436 63,061 63,691 14,328 64,971 1,170,243

Debt Investor Cash Flows: 5.50% (750,000) 43,250 43,140 43,030 42,920 42,810 42,700 42,590 42,480 42,370 772,260

Entity Level Cash Flows (EBTCF)**:Construction Phase 25.00% (200,000) 250,000Operational Phase 7.40% (250,000) 16,750 17,460 (31,824) 18,898 19,626 20,361 21,101 (28,152) 22,601 397,983Both Phases 9.09% (200,000) 0 16,750 17,460 (31,824) 18,898 19,626 20,361 21,101 (28,152) 22,601 397,983

Preferred Partner Level Cash Flows: 5,302 2,651 14,099Construction Phase (If sell on completion) 16.89% (180,000) 210,400Both Phases 8.07% (180,000) 0 14,099 14,454 (28,642) 16,376 16,740 17,107 17,477 (25,337) 19,403 329,135

Subordinated Partner Level Cash Flows:Construction Phase (If sell on completion) 98.00% (20,000) 39,600Both Phases 16.14% (20,000) 0 2,651 3,006 (3,182) 2,522 2,886 3,254 3,624 (2,815) 3,198 68,848

* Sometimes referred to as "Asset Level".** To the LLC joint venture partnership as a whole.




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Calendar Years Ending: Year 0 Year 1 Year 2Project Cash Requirements as Proposed: Site Acquisition 200,000 Hard & Soft Development Costs 750,000 Total Devlpt Phase Cash Requirements (200,000) (750,000) Devlpt Phase Total Equity Funding 200,000Devlpt Phase Debt Funding (Constr Loan) 750,000Construction Loan Repayment (750,000)Proposed Permanent Loan Amount (Take Out) 750,000Operating PBTCF 60,000Reversion PBTCF 0PBTCF 60,000Permanent Loan Debt Service (43,250)Permanent Loan RepaymentPermanent Loan Debt CFs 750,000 (43,250)Operating EBTCF 16,750Reversion EBTCF 0EBTCF 16,750

Preferred Equity Capital Account:Preferred Return Allocation: Beginning Equity Investment Balance 0 180,000 190,800 Annual Preferred Investment 180,000 0 0 Preferred Return Earned 0 10,800 11,448 Preferred Return Paid 0 0 (11,448) Accrued But Unpaid Preferred Return 0 10,800 0 Ending Equity Investment Balance 180,000 190,800 190,800

Preferred equity capital account: First two years…

Return “on”

But not yet return “of”

(current only)www.bsscommunitycollege.in www.bssnewgeneration.in www.bsslifeskillscollege.in


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Terminal

year

(yr.11)

Cash

Flows

and

Splits

Reflects cumulated unpaid current preferred returns, plus additional capital paid in to finance capital improvement expenditures

Year 11Operating PBTCF 65,621Reversion PBTCF 1,104,622PBTCF 1,170,243Permanent Loan Debt Service (42,260)Permanent Loan Repayment (730,000)Permanent Loan Debt CFs (772,260)Operating EBTCF 23,361Reversion EBTCF 374,622EBTCF 397,983

Preferred Equity Capital Account:Preferred Return Allocation: Beginning Equity Investment Balance 270,080 Annual Preferred Investment 0 Preferred Return Earned 16,205 Preferred Return Paid (16,205) Accrued But Unpaid Preferred Return 0 Ending Equity Investment Balance 270,080Reversion Preferred Allocations: Allocation to Satisfy Preferred Return Requirement (270,080) Allocation to Return Subordinated Investment Requirement (25,998)

Annual CF approximations for purpose of checking fairness of splitsYear 11

Project Level Cash Flows*:Construction PhaseOperational Phase 1,170,243Both Phases 1,170,243

Debt Investor Cash Flows: 772,260

Entity Level Cash Flows (EBTCF)**:Construction PhaseOperational Phase 397,983Both Phases 397,983

Preferred Partner Level Cash Flows:Construction Phase (If sell on completion)Both Phases 329,135

Subordinated Partner Level Cash Flows:Construction Phase (If sell on completion)Both Phases 68,848

Entrepreneurial investment (0 return)

Asset levelNet sale proceeds of property

OLB on permanent mortgage

Remainder

Includes from yr.11 operations: 16205 = 6% of 270080 + 0.5*(23361-16205)=3578.From reversion:270080 + 0.5*(374622-270080-25998).

Entity level reversion.

Entity level oper.CF yr.11.



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Resulting expected returns (ex ante):

Are these “ fair ” ? . . .

Going- in IRR to:

Underlying Project

Undifferentiated Equity Entity

Preferred Equity Partner

Residual Equity Partner

For Development Phase(1 year)

For Both Phases(11 years)

25.00%

25.00%

16.89%

98.00%

6.54%

9.09%

8.07%

16.14%

Image by MIT OCW.



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One way to approach this is to conduct sensitivity analysis . . .e.g., Construct “Optimistic” and “Pessimistic” outcome scenarios, as follows:

• Initial rents such that Year 2 NOI is either $63,000 or $57,000 instead of the proforma (expected) assumption of $60,000. (This results in Year 1 completed building values either $1,050,000 or $950,000, instead of the $1,000,000 base case assumption.)

• Annual NOI growth rate beyond Year 2 either up to 2% or down to 0% instead of the base-case assumption of 1%.

• Year-11 terminal yield (going-out resale cap rate) either down to 4.5% or up to 7.5% from the base case assumption of 6.0%.

Then see if ex ante (going-in expected) return risk premia are proportional to risk as defined by the spread in the IRR outcomes…



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Sensitivity Analysis: Ex Post Return Outcome Range & Risk/Return Analysis:Preferred Equity Partner Contribution 90%Preferred Return 6.00%Preferred Partner Residual Share 50%Riskfree Rate = 3.00%Annual CF approximations for purpose of checking fairness of splits

IRRs: Range: E[RP]: RP/Range: Downside Range RP/DnsdRangeProject Level Cash Flows*: Expctd: Optimstc PessimstcConstruction Phase 25.00% 50.00% 0.00% 50.00% 22.00% 0.44 25.00% 0.88Both Phases 6.54% 10.59% 3.14% 7.45% 3.54% 0.47 3.40% 1.04

Entity Level Cash Flows (EBTCF)**:Construction Phase 25.00% 50.00% 0.00% 50.00% 22.00% 0.44 25.00% 0.88Both Phases 9.09% 18.81% -10.58% 29.40% 6.09% 0.21 19.67% 0.31

Preferred Partner Level Cash Flows:Construction Phase (If sell on completion) 16.89% 30.78% 6.00% 24.78% 13.89% 0.56 10.89% 1.28Both Phases 8.07% 14.77% -9.05% 23.82% 5.07% 0.21 17.11% 0.30

Subordinated Partner Level Cash Flows:Construction Phase (If sell on completion) 98.00% 223.00% -54.00% 277.00% 95.00% 0.34 152.00% 0.62Both Phases 16.14% 35.96% -100.00% 135.96% 13.14% 0.10 116.14% 0.11

Risk & Return Analysis: Partner Breakout…

Subordinated (entrepreneurial) partner in this deal is getting less expected return risk-premium per unit of risk than the Senior (money) partner…



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This suggests perhaps a modification of the deal structure is in order…

(e.g., this deal structure did not include a pro rata pari passu component.)

Going-in IRR

98.00%

16.89%

25%

rf

277%

Preferred Partner: Residual Partner: Relative Risk(Proxied by IRROutcome Range)

Diagonal line representsequilibrium or normativereturn expectations.

Residual Partner is below line.

Chart not drawn to scale.

Framework for Evaluating Fairness of Capital Structure Terms

Image by MIT OCW.



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Chapter 27Chapter 27

The Real Options Model of Land Value and The Real Options Model of Land Value and Development Project ValuationDevelopment Project Valuation

Major references include*:

•J.Cox & M.Rubinstein, “Options Markets”, Prentice-Hall, 1985

•L.Trigeorgis, “Real Options”, MIT Press, 1996

•T.Arnold & T.Crack, “Option Pricing in the Real World: A Generalized Binomial Model with Applications to Real Options”, Dept of Finance, University of Richmond, Working Paper, April 15, 2003 (available on the Financial Economics Network (FEN) on the Social Science Research Network at www.ssrn.com).



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Chapter 27 in perspective . . .Chapter 27 in perspective . . .

In the typical development project (or parcel of developable In the typical development project (or parcel of developable land), there are three major types of options that may present land), there are three major types of options that may present themselves:*themselves:*

•• ““Wait OptionWait Option””: The option to : The option to delaydelay start of the project start of the project construction (Ch.27);construction (Ch.27);

•• ““Phasing OptionPhasing Option””: The breaking of the project into : The breaking of the project into sequential sequential phasesphases rather than building it all at once rather than building it all at once (Ch.29);(Ch.29);

•• ““Switch OptionSwitch Option””: The option to choose among : The option to choose among alternative alternative typestypes of buildings to construct on the given land parcel.of buildings to construct on the given land parcel.

All three of these types of options can affect optimal All three of these types of options can affect optimal investment decisioninvestment decision--making, add significantly to the value of making, add significantly to the value of the project (and of the land), affect the risk and return the project (and of the land), affect the risk and return characteristics of the investment, and they are difficult to characteristics of the investment, and they are difficult to accurately account for in traditional DCF investment analysis.accurately account for in traditional DCF investment analysis.



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Exhibit 2-2: The “Real Estate System”: Interaction of the Space Market, Asset Market, & Development Industry

SPACE MARKET

SUPPLY(Landlords)

DEMAND(Tenants)

RENTS&

OCCUPANCY

LOCAL&

NATIONALECONOMY

FORECASTFUTURE

ASSET MARKET

SUPPLY(Owners

Selling)


CASHFLOW

MKTREQ’D

CAPRATE

PROPERTYMARKETVALUE

DEVELOPMENTINDUSTRY

ISDEVELPT

PROFITABLE?

CONSTRCOST

INCLULANDLAND

IFYES

ADDSNEW

CAPITAL MKTS

= Causal flows.




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Land value plays a pivotal role in determining whether, when, Land value plays a pivotal role in determining whether, when, and what type of development will (and should) occur.and what type of development will (and should) occur.

•• From a finance/investments perspective:From a finance/investments perspective:-- Development activity links the asset & space markets;Development activity links the asset & space markets;-- Determines L.R. supply of space, Determines L.R. supply of space, L.R. rents.L.R. rents.-- Greatly affects profitability, returns in the asset market.Greatly affects profitability, returns in the asset market.

•• From an urban planning perspective:From an urban planning perspective:-- Development activity determines urban form;Development activity determines urban form;-- Affects physical, economic, social character of cityAffects physical, economic, social character of city..

LandLandValueValue

OptimalOptimalDevlptDevlpt

Relationship is twoRelationship is two--way:way:

Recall relation of land value to land use boundaries noted in ChRecall relation of land value to land use boundaries noted in Ch.5.5……



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Different conceptions of Different conceptions of ““land valueland value”” (Recall Property Life Cycle theory from Ch.5) . . .. . .Property Value, Location Value, & Land ValueProperty Value, Location Value, & Land Value

Evolution of the Value (& components) of a Fixed Site (parcel)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

C C C C

Time ("C" Indicates Reconstruction times)

Valu

e Le

vels

($)

HBU Value As IfVacant = PotentialUsage Value, or"Location Value"("U")

Property Value("P") = Mkt Val(MV) = StructureValue + LandValue.

Land Value byLegal/AppraisalDefn. ("land compsMV").

Land Value byEcon.Defn. =Redevlpt OptionValue. ("LAND")

In Ch.27we In Ch.27we focus on the focus on the Econ.DefnEcon.Defn.: .: ““LANDLAND””

Exh.5-10, Sect.5.4



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Different conceptions of Different conceptions of ““land valueland value”” . . .. . .Property Value, Location Value, & Land ValueProperty Value, Location Value, & Land Value


0.0

0.5

1.0

1.5

2.0

2.5

3.0

C C C C

Time ("C" Indicates Reconstruction times)

Valu

e Le

vels

($)

HBU Value As IfVacant = PotentialUsage Value, or"Location Value"("U")

Property Value("P") = Mkt Val(MV) = StructureValue + LandValue.

Land Value byLegal/AppraisalDefn. ("land compsMV").

Land Value byEcon.Defn. =Redevlpt OptionValue. ("LAND")

Note that there Note that there are points in are points in time when time when three of the three of the four definitions four definitions all give the all give the same value, same value, namely, namely, property value property value = land value = land value defined by defined by either either defndefn at at the times of the times of optimal optimal redevelopment redevelopment (construction) (construction) on the site.on the site.



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The economic definition of land value (The economic definition of land value (““LANDLAND””) is based on ) is based on nothing more or less than the fundamental capability that land nothing more or less than the fundamental capability that land ownership gives to the landowner (unencumbered):ownership gives to the landowner (unencumbered):

The right without obligation to develop (or redevelop) The right without obligation to develop (or redevelop) the property.the property.



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0.0

0.5

1.0

1.5

2.0

2.5

3.0

C C C CTime ("C" Indicates Reconstruction times)

Valu

e Le

vels

($)

This definition of land value is most relevant . . .This definition of land value is most relevant . . .

Just prior to the times when development or Just prior to the times when development or redevelopment occurs on the site.redevelopment occurs on the site.



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To understand the economic conception of land value, a To understand the economic conception of land value, a famous theoretical development from financial economics famous theoretical development from financial economics is most useful: is most useful: ““Option Valuation TheoryOption Valuation Theory”” (OVT)(OVT) ::

In particular, a branch of that theory known a In particular, a branch of that theory known a ““Real Real OptionsOptions””..



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Some history:Some history:Call option model of land arose from two strands of theory:Call option model of land arose from two strands of theory:•• Financial economicsFinancial economics study of corporate capital budgeting,study of corporate capital budgeting,•• Urban economicsUrban economics study of urban spatial form.study of urban spatial form.Capital BudgetingCapital Budgeting::•• How corporations should make capital investment decisions How corporations should make capital investment decisions (constructing physical plant, long(constructing physical plant, long--lived productive assets).lived productive assets).•• Includes question of optimal timing of investment.Includes question of optimal timing of investment.•• e.g., McDonald, Siegel, Myers, (others), 1970se.g., McDonald, Siegel, Myers, (others), 1970s--80s.80s.

Urban EconomicsUrban Economics::•• What determines density and rate of urban development.What determines density and rate of urban development.•• Titman, Williams, Titman, Williams, CapozzaCapozza, (others), 1980s., (others), 1980s.

It turned out the 1965 SamuelsonIt turned out the 1965 Samuelson--McKean Model of a perpetual McKean Model of a perpetual American warrant was the essence of what they were all using.American warrant was the essence of what they were all using.



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27.1 27.1 Real OptionsReal Options: The Call Option Model of Land Value : The Call Option Model of Land Value

Options whose underlying assets (either what is obtained or Options whose underlying assets (either what is obtained or what is given up on the exercise of the option) are real assets what is given up on the exercise of the option) are real assets (i.e., physical capital).(i.e., physical capital).

Real Options:Real Options:

The call option model of land value (introduced in Chapter 5) isThe call option model of land value (introduced in Chapter 5) is a a real option model:real option model:

Land ownership gives the owner the Land ownership gives the owner the right without obligationright without obligation to develop (or to develop (or redevelop) the property upon payment of the construction cost. Bredevelop) the property upon payment of the construction cost. Built uilt property is underlying asset, construction cost is exercise pricproperty is underlying asset, construction cost is exercise price (including e (including the opportunity cost of the loss of any prethe opportunity cost of the loss of any pre--existing structure that must be existing structure that must be torn down).torn down).

In essence, all real estate development projects are real optionIn essence, all real estate development projects are real options, s, though in some simple cases the though in some simple cases the optionalityoptionality may be fairly trivial may be fairly trivial and can be safely ignored.and can be safely ignored.



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Today Next YearProbability 100% 30% 70%

Value of Developed Property $100.00 $78.62 $113.21

Development Cost (exclu land) $88.24 $90.00 $90.00NPV of exercise $11.76 -$11.38 $23.21(Action) (Don’t build) (Build)

Future Values 0 $23.21Expected Values $11.76 $16.25= Sum[ Probability X Outcome ] (1.0)11.76 (0.3)0 + (0.7)23.21PV(today) of Alternatives @20% $11.76 16.25 / 1.2 = $13.54

Note: In this example the Note: In this example the expected growthexpected growth in the HBU value of the built property is in the HBU value of the built property is 2.83%2.83%: : as as (.3)78.62 + (.7)113.21 = $102.83(.3)78.62 + (.7)113.21 = $102.83..What is the value of this land today?What is the value of this land today? Answer: = Answer: = MAX[11.76, 13.54] = $13.54MAX[11.76, 13.54] = $13.54Should owner build now or wait?Should owner build now or wait? Answer: = Answer: = Wait. Wait. (100.00 (100.00 –– 88.24 88.24 –– 13.54< 0.)13.54< 0.)

The $13.54 The $13.54 –– $11.76 = $1.78 option premium is due to $11.76 = $1.78 option premium is due to uncertainty or volatilityuncertainty or volatility..

27.2 A Simple Numerical Example of OVT Applied to Land 27.2 A Simple Numerical Example of OVT Applied to Land Valuation and the Development Timing DecisionValuation and the Development Timing Decision



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Note the importance of Note the importance of flexibilityflexibility inherent in the option (inherent in the option (““right right without without obligationobligation””), which allows the negative downside outcome to be avoided. ), which allows the negative downside outcome to be avoided. This gives the option a positive value and results in the This gives the option a positive value and results in the ““irreversibility irreversibility premiumpremium”” in the land value (noted in Geltnerin the land value (noted in Geltner--Miller Ch.5).Miller Ch.5).

Consider the effect of Consider the effect of uncertaintyuncertainty (or volatility) in the (or volatility) in the evolution of the built evolution of the built property valueproperty value (for whatever building would be built on the site), and the (for whatever building would be built on the site), and the fact that development at any given time is fact that development at any given time is mutually exclusivemutually exclusive with with development at any other time on the same site development at any other time on the same site ((““irreversibilityirreversibility””)). e.g.:. e.g.:



Development Cost (exclu land) $88.24 $90.00 $90.00NPV of exercise $11.76 -$11.38 $23.21(Action) (Don’t build) (Build)Future Values 0 $23.21Expected Values $11.76 $16.25= Sum[ Probability X Outcome ] (1.0)11.76 (0.3)0 + (0.7)23.21PV(today) of Alternatives @20% $11.76 16.25 / 1.2 = $13.54



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Representation of the preceding problem as a Representation of the preceding problem as a ““decision treedecision tree””::

Build: Get113.21-90.00= $23.21

70%

30%

Don’t build:Get 0.

•• Identify decisions and alternatives (nodes & branches).Identify decisions and alternatives (nodes & branches).•• Assign probabilities (sum across all branches @ ea. node = 100%Assign probabilities (sum across all branches @ ea. node = 100%).).•• Locate nodes in time.Locate nodes in time.•• Assume Assume ““rationalrational”” (highest value) decision will be made at each node.(highest value) decision will be made at each node.•• Discount node expected values (means) across time reflecting riDiscount node expected values (means) across time reflecting risk.sk.

Choice Next Yr.:Choice Next Yr.:

Node Value = Node Value = (7.)23.21+ (.3)0 = (7.)23.21+ (.3)0 = $16.25.$16.25.

1 Yr1 YrWait Today:Wait Today:

PV = 16.25/1.2 PV = 16.25/1.2 = 13.54.= 13.54.

Build Today:Build Today:

Get 100.00Get 100.00--88.24 = 88.24 = $11.76.$11.76.

ChoiceChoice

TodayToday

Decision Tree Analysis is closely related to Decision Tree Analysis is closely related to Option Valuation Methodology, but requires a Option Valuation Methodology, but requires a different type of simplification (finite number of different type of simplification (finite number of discrete alternatives).discrete alternatives).www.bsscommunitycollege.in www.bssnewgeneration.in www.bsslifeskillscollege.in


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A problem with traditional decision tree analysisA problem with traditional decision tree analysis……

1 Yr1 Yr

ChoiceChoice

TodayToday

But is this really the correct discount rate But is this really the correct discount rate (and hence, the correct decision and (and hence, the correct decision and valuation of the project)?...valuation of the project)?...

Build: Get113.21-90.00= $23.21

70%

30%




Wait Today:Wait Today:

PV = 16.25/1.2 PV = 16.25/1.2 = 13.54.= 13.54.


Get 100.00Get 100.00--88.24 = 88.24 = $11.76.$11.76.

We were only able to completely evaluate this decision because We were only able to completely evaluate this decision because we somehow knew what we thought to be the appropriate riskwe somehow knew what we thought to be the appropriate risk--adjusted discount rate to apply to it (here assumed to be 20%).adjusted discount rate to apply to it (here assumed to be 20%).



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Where Where diddid the 20% discount rate (OCC) come from anyway?...the 20% discount rate (OCC) come from anyway?...

1 Yr1 Yr

ChoiceChoice

TodayToday

To be honestTo be honest……

It was a nice round number that seemed It was a nice round number that seemed ““in the ballparkin the ballpark”” for for required returns on development investment projects.required returns on development investment projects.

Can we be a bit more Can we be a bit more ““scientificscientific”” or or rigorous? . . .rigorous? . . .

Build: Get113.21-90.00= $23.21

70%

30%





Get 100.00Get 100.00--88.24 = 88.24 = $11.76.$11.76.


PV = 16.25/1.2 PV = 16.25/1.2 = 13.54.= 13.54.



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Suppose there were Suppose there were ““complete marketscomplete markets”” in land, and buildings, and in land, and buildings, and bonds, such that we could buy or sell (short if necessary) infinbonds, such that we could buy or sell (short if necessary) infinitely itely divisible quantities of each, including land and buildings like divisible quantities of each, including land and buildings like our subject our subject development projectdevelopment project……Thus, we could buy today:Thus, we could buy today:•• 0.67 units of a building just like the one our subject developm0.67 units of a building just like the one our subject development would ent would produce next year that will either be worth $113.21 or $78.62 thproduce next year that will either be worth $113.21 or $78.62 then.en.And we could partially finance this purchase by issuing:And we could partially finance this purchase by issuing:•• $51.21 worth of $51.21 worth of risklessriskless bonds (with a 3% interest rate).bonds (with a 3% interest rate).

Then this Then this ““replicating portfolioreplicating portfolio”” (long in the bldg, short in the bond) (long in the bldg, short in the bond) next year will be worth:next year will be worth:

•• In the In the ““upup”” scenario: (0.67)$113.21 scenario: (0.67)$113.21 -- $$51.21(1.03) = $75.95 51.21(1.03) = $75.95 –– $52.74 = $52.74 = $23.21, or:$23.21, or:

•• In the In the ““downdown”” scenario: (0.67)$78.62 scenario: (0.67)$78.62 -- $ 51.21(1.03) = $52.74 $ 51.21(1.03) = $52.74 –– $52.74$52.74 = 0.= 0.

Exactly Equal to the Development Project in Exactly Equal to the Development Project in All Future ScenariosAll Future Scenarios!!

27.3.1 27.3.1 An Arbitrage AnalysisAn Arbitrage Analysis……



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Recall:Recall:

These are the future scenarios, describing all These are the future scenarios, describing all possible future outcomes.possible future outcomes.

In the upside outcome, the project In the upside outcome, the project will be worth $23.21, same as the will be worth $23.21, same as the replicating portfolio.replicating portfolio.

In the downside outcome, the In the downside outcome, the project will be worth 0, same as project will be worth 0, same as the replicating portfolio.the replicating portfolio.

1 Yr1 Yr

ChoiceChoice

TodayToday

27.3.1

Build: Get113.21-90.00= $23.21

70%

30%





Get 100.00Get 100.00--88.24 = 88.24 = $11.76.$11.76.


PV = 16.25/1.2 PV = 16.25/1.2 = 13.54.= 13.54.



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Thus, this Thus, this ““replicating portfolioreplicating portfolio”” mustmust be worth the same as the land be worth the same as the land (the development option) today.(the development option) today.

Suppose not:Suppose not:•• If the land can be bought for less than the replicating portfolIf the land can be bought for less than the replicating portfolio, then I io, then I can sell the replicating portfolio short, buy the land, pocket tcan sell the replicating portfolio short, buy the land, pocket the he difference as profit today, and have zero net value impact next difference as profit today, and have zero net value impact next year (as year (as the land and replicating portfolio will in all cases be worth ththe land and replicating portfolio will in all cases be worth the same e same next year, so my long position offsets my short position exactlynext year, so my long position offsets my short position exactly).).•• If the land costs more than the replicating portfolio, then I cIf the land costs more than the replicating portfolio, then I can sell an sell the land short, buy the replicating portfolio, pocket the differthe land short, buy the replicating portfolio, pocket the difference as ence as profit today, and once again have zero net impact next year.profit today, and once again have zero net impact next year.

This is what is known as an This is what is known as an ““arbitragearbitrage”” –– risklessriskless profit!profit!

In equilibrium (within and across markets), arbitrage opportunitIn equilibrium (within and across markets), arbitrage opportunities ies cannot exist, for they would be bid away by competing market cannot exist, for they would be bid away by competing market

participants seeking to earn superparticipants seeking to earn super--normal profits.normal profits.

27.3.1



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In real estate, markets are not so perfect and complete to enablIn real estate, markets are not so perfect and complete to enable e actual construction of technical arbitrage. But nevertheless actual construction of technical arbitrage. But nevertheless competition tends to eliminate supercompetition tends to eliminate super--normal profit, so we can use normal profit, so we can use this kind of analysis to model prices and values.this kind of analysis to model prices and values.

Fundamentally, this approach will always equalize the expected Fundamentally, this approach will always equalize the expected return risk premium per unit of risk, across the asset markets.return risk premium per unit of risk, across the asset markets.

So, how much So, how much isis the land worth in our example . . .the land worth in our example . . .

The replicating portfolio is:The replicating portfolio is:

(0.67)V(0) (0.67)V(0) -- $51.21$51.21

And thus must have this value.And thus must have this value.

The only question is, what is the value of V(0), the value of thThe only question is, what is the value of V(0), the value of the e underlying asset (the project to be developed) underlying asset (the project to be developed) todaytoday (time(time--0)?...0)?...

27.3.1



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We know that a similar asset already completed today is worth $1We know that a similar asset already completed today is worth $100.00.00.00.

However, this value includes the value of the net cash flow (divHowever, this value includes the value of the net cash flow (dividends, idends, rents) that asset will pay between today and next year.rents) that asset will pay between today and next year.

Our development project wonOur development project won’’t produce those dividends, because it t produce those dividends, because it wonwon’’t produce a building until next year.t produce a building until next year.

So, we need a little more analysisSo, we need a little more analysis……Suppose that the underlying asset (the built property) has an exSuppose that the underlying asset (the built property) has an expected pected total return of 9%.total return of 9%.

If a similar building has a value today of $100.00, and an (ex dIf a similar building has a value today of $100.00, and an (ex dividend) ividend) value next year of either $113.21 (70% chance) or $78.62 (30% chvalue next year of either $113.21 (70% chance) or $78.62 (30% chance), ance), then the expected value next year is (0.7)113.21+(0.3)78.62 = $1then the expected value next year is (0.7)113.21+(0.3)78.62 = $102.83 02.83 (i.e., expected growth is (i.e., expected growth is E[gE[gVV]=2.83%).]=2.83%).

Thus, the PV today of a building that would not exist until nextThus, the PV today of a building that would not exist until next year year (i.e., PV of similar pre(i.e., PV of similar pre--existing building net of its cash flow between now existing building net of its cash flow between now and next year) is:and next year) is:

PV[VPV[V11] = V(0) = $102.83 / 1.09 = $94.34.] = V(0) = $102.83 / 1.09 = $94.34.(versus V0 = $100.00 for pre-existing bldg.)

27.3.1



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Now we can value the option by valuing the replicating portfolioNow we can value the option by valuing the replicating portfolio::

CC00 = (0.67)V(0) = (0.67)V(0) -- $51.21 $51.21

= (0.67)$94.34 = (0.67)$94.34 -- $51.21 $51.21

= $63.29 = $63.29 -- $51.21 $51.21

= $12.09.= $12.09.

Thus, our previous estimate of $13.54 (based on the 20% OCC) wasThus, our previous estimate of $13.54 (based on the 20% OCC) wasapparently not correct. The option is actually worth $1.45 less.apparently not correct. The option is actually worth $1.45 less.

27.3.1



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The general formula for the Replicating Portfolio in a Binomial The general formula for the Replicating Portfolio in a Binomial World is:World is:

Replicating Portfolio = NVReplicating Portfolio = NV--B, where:B, where:

““NN”” is is ““sharesshares”” (proportional value) of the underlying asset (built (proportional value) of the underlying asset (built property) to purchase, property) to purchase,

““BB”” is current (time 0) dollar value of bond to issue (borrow), andis current (time 0) dollar value of bond to issue (borrow), and::

N=(CuN=(Cu--Cd)/(VuCd)/(Vu--VdVd); and ); and

B=(NVdB=(NVd--Cd)/(1+rCd)/(1+rff).).

With: Cu = With: Cu = MAX[VuMAX[Vu--K, 0]; K, 0]; CdCd = = MAX[VdMAX[Vd--K, 0];K, 0];

Vu, Vu, VdVd, = , = ““upup”” & & ““downdown”” values of property to be built; K = values of property to be built; K = constrconstr cost.cost.

In the preceding example: In the preceding example: N = (23.21N = (23.21--0)/(113.210)/(113.21--78.62) = 23.21/34.59 = 0.67; and 78.62) = 23.21/34.59 = 0.67; and B = (0.67(78.62)B = (0.67(78.62)--0)/1.03 = $52.74/1.03 = $51.21.0)/1.03 = $52.74/1.03 = $51.21.



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Suppose we could sell the option for $13.54Suppose we could sell the option for $13.54……Then we could (with complete markets):Then we could (with complete markets):

• Sell the option (short) for $13.54, take in $13.54 cash.•Borrow $51.21 at 3% interest (with no possibility of default), thereby take in another $51.21 cash.• Use part of the resulting $64.75 proceeds to buy 0.67 units of a building just like the one to be built (minus its net rent for this coming year), for a price of (0.67)$94.34 = $63.29.• Our net cash flow at time 0 is: +$64.74 net cash flow at time 0 is: +$64.74 –– $63.29 = + $1.45.$63.29 = + $1.45.• A year from now, we face:

• In the ““upup”” outcome:• We must pay to the owner of the option we sold $23.21 = $113.21 - $90, the value of the development option.• We must pay off our loan for (1.03)$51.21 = $52.74.• We will sell our .67 share of the building for (.67)$113.21 = $75.95 cash proceeds.• Giving us a total net cash flow next year of $75.95 net cash flow next year of $75.95 –– ($23.21 + $52.74) = ($23.21 + $52.74) = $75.95 $75.95 -- $75.95 = 0.$75.95 = 0.

• In the ““downdown”” outcome: • We owe the owner of the option nothing, but we still owe the bank $52.74.• We sell our .67 share of the building for (.67)$78.62 = $52.74 cash proceeds.• Giving us a total net cash flow next year of 0.net cash flow next year of 0.

• Thus, we make a risklessriskless profitprofit at time 0 of +$1.45. +$1.45. (= $13.54 - $12.09.)

•• We could perform arbitrage for any option price other than $12.We could perform arbitrage for any option price other than $12.09.09.www.bsscommunitycollege.in www.bssnewgeneration.in www.bsslifeskillscollege.in


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Today Next Year

Development Option ValueC = Max[0,V-K]

PV[C1] = x“x” = unkown value,x = P0 , otherwise arbitrage..

C1up =113.21-90

= $23.21C1

down = 0(Don’t build)

Bond Value B = $51.21 B1 = (1+rf )B = (1.03)51.21 = $52.74

B1 = (1+rf )B = (1.03)51.21 = $52.74

Built Property Value PV[V1] = E[V1] / (1+OCC)= [(.7)113.21+(.3)78.62]/1.09= $102.83/1.09 =$94.34

V1up = $113.21 V1

down = $78.62

Replicating Portfolio:P = (N)V – B

P0 = (N) PV[V1] – B= (0.67)$94.34 - $51.21 = $63.29 - $51.21 = $12.09

P1up =(0.67)113.21 -

$52.74= $75.95 - $$52.74

= $23.21

P1down =(0.67)78.62 -

$52.74= $52.74 - $52.74

= $0

Here is another way of depicting what we have just suggested (Exh.27-3):

The replicating portfolio duplicates the option value in all futThe replicating portfolio duplicates the option value in all future scenarios, hence ure scenarios, hence its present value must be the same as the optionits present value must be the same as the option’’s present value: s present value: CC00..

Thus, the option is worth $12.09.Thus, the option is worth $12.09.

27.3.1



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We can now correct our decision tree:We can now correct our decision tree:

1 Yr1 Yr

ChoiceChoice

TodayToday

The correct OCC was not 20%, but rather 34.4%.The correct OCC was not 20%, but rather 34.4%.

We know this because this is the rate that gives the correct PV We know this because this is the rate that gives the correct PV of of the option: $12.09 = E[C] / (1+E[rthe option: $12.09 = E[C] / (1+E[rcc]) = $16.25 / 1.344.]) = $16.25 / 1.344.

In effect, we were able to derive the In effect, we were able to derive the option value without knowing the OCC. option value without knowing the OCC. If we want to know the OCC we can If we want to know the OCC we can ““back it outback it out”” from the option value.from the option value.

Build: Get113.21-90.00= $23.21

70%

30%





Get 100.00Get 100.00--88.24 = 88.24 = $11.76.$11.76.


PV = PV = 16.25/1.344 = 16.25/1.344 = 12.09.12.09.



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( ) ( ) ( )TD

TT

V

TT

C

TTT rE

LrE

VrELVCPV

][1][1][1][

+−

+=

+−

=

Note:

This options-based derivation of the OCC of developable land is completely consistent with Chapter 29’s formula for development project OCC:

Only in the circumstance where the option will definitely be developed next period (e.g., in the previous example, if the construction cost were $78.62 million instead of $90 million, the option would be worth$18.01 million and it would be “ripe” for immediate development):

In all cases, the result is to provide the same expected return risk premium per unit of risk across all the asset markets (land, buildings, bonds): the equilibrium condition within and across the relevant markets.

03.162.78$

09.183.102$

344.162.7883.102$01.18$ −=

−=



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Here is the corrected summary of the analysis of the developmentHere is the corrected summary of the analysis of the development project:project:The land is worth: The land is worth: MAX[$100.00 MAX[$100.00 –– $88.24, C$88.24, C00] = $12.09:] = $12.09:

34.4% OCC for the option34.4% OCC for the option

What is the value of this land today?What is the value of this land today? Answer: = Answer: = MAX[11.76, 12.09] = $12.09MAX[11.76, 12.09] = $12.09Should owner build now or wait?Should owner build now or wait? Answer: = Answer: = Wait. Wait. (100.00 (100.00 –– 88.24 88.24 –– 12.09 < 0.)12.09 < 0.)



Development Cost (exclu land) $88.24 $90.00 $90.00NPV of exercise $11.76 -$11.38 $23.21(Action) (Don’t build) (Build)Future Values 0 $23.21Expected Values $11.76 $16.25= Sum[ Probability X Outcome ] (1.0)11.76 (0.3)0 + (0.7)23.21PV(today) of Alternatives @ 34% $11.76 16.25 / 1.344 = $12.09



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The previously described option valuation of a development projeThe previously described option valuation of a development project is ct is completely consistent with the completely consistent with the ““Certainty Equivalent ValuationCertainty Equivalent Valuation”” form of the form of the DCF valuation model presented earlier in the Chapter 10 lecture DCF valuation model presented earlier in the Chapter 10 lecture in this in this course.course.The general 1The general 1--period Certainty Equivalent Valuation Formula is:period Certainty Equivalent Valuation Formula is:

( )

( ) ( )

( ) ( ) ( ) ( )( ) ( ) ( )( )

09.12$03.1

45.12$03.1

80.3$25.16$03.1

1636.021.23$25.16$03.1

21.23$25.16$05.1

%33.83%120%621.23$25.16$

%31)%34.94/62.78()%34.94/21.113(

%3%90$21.23$0)$3(.21.23)$7(.

:.,.

1%%

][][

1][

%67.36%6

0

10

100

==−

=

−=

−=

⎟⎠⎞

⎜⎝⎛

−−

=

+

⎟⎟⎠

⎞⎜⎜⎝

⎛−−

−−+=

+

⎟⎟⎠

⎞⎜⎜⎝

⎛

−−

−−

=+

=

C

exampleouringe

rVV

rrECCCE

rCCEQC

f

downup

fVdownup

f

27.3.2



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I’m hoping you developed some intuition for the certainty equivalence valuation model back in Chapter 10. But in case not, let’s try this . . .The certainty equivalent value next year is the downward adjusted value of the risky expected value for which the investment market would be indifferent between that value and a riskfree bond value of the same amount…

( )

f

downup

fVdownup

f rVV

rrECCCE

rCCEQC

+

⎟⎟⎠

⎞⎜⎜⎝

⎛

−−

−−

=+

=1

%%][

][

1][

10

100

The certainty equivalent value next year is the expected value minus a risk discount.

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛

−

−−

%%][

downup

fVdownup VV

rrECC

The risk discount consists of the amount of risk in the next year’s value as indicated by the range in the possible outcomes times…

times the market price of risk.

%%][

downup

fV

VVrrE

−

−The market price of risk is the market expected return risk premium per unit of return risk, the ratio of…

the market expected return risk premium divided by the

range in the corresponding return possible outcomes.



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Thus, we can derive the same present value of the option Thus, we can derive the same present value of the option through two completely consistent (indeed, through two completely consistent (indeed, mathematically equivalent) approaches:mathematically equivalent) approaches:

•• The The ““arbitrage analysisarbitrage analysis”” based on the based on the replicating portfolioreplicating portfolio, or;, or;

•• The certainty equivalent valuation model.The certainty equivalent valuation model.

The latter is more convenient for computations.The latter is more convenient for computations.



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27.3.3 What is fundamentally going on with this framework:

PV[VPV[V1 1 ]]=$94.34=$94.34

VV11upup==

$113.21$113.21

VV11downdown==

$78.62$78.62

pp = 0.7= 0.7

11--pp = 0.3= 0.3

Underlying asset (built property) outcome % range:

%3734.94$

62.78$21.113$=

−

PV[CPV[C1 1 ]]=$12.09=$12.09

CC11upup==

$23.21$23.21

CC11downdown==$0$0

pp = 0.7= 0.7

11--pp = 0.3= 0.3

Option (land) outcome % range:

%19209.12$

0$21.23$=

−

With With perfectperfect correlation between the two (land is correlation between the two (land is derivativederivative).).www.bsscommunitycollege.in www.bssnewgeneration.in www.bsslifeskillscollege.in


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27.3.3 What is fundamentally going on with this framework:

With With perfectperfect correlation between the two (land is correlation between the two (land is derivativederivative).).

Hence, relative risk exactly equals ratio of outcome ranges:Hence, relative risk exactly equals ratio of outcome ranges:

24.5%37%192

=

Option (land) is 5.24 times more risky than investment in the Option (land) is 5.24 times more risky than investment in the underlying asset (built property).underlying asset (built property).

Thus, option value must be such that Thus, option value must be such that EE[[rrCC] risk premium in ] risk premium in land is 5.24 times greater than that in built property.land is 5.24 times greater than that in built property.

Built property risk premium is: Built property risk premium is: RPRPVV = 9% = 9% -- 3% = 6%.3% = 6%.

Thus, land risk premium must be: Thus, land risk premium must be: RPRPCC = 6%*5.24 = 31.4%.= 6%*5.24 = 31.4%.

Thus landThus land’’s s EE[[rrCC] = ] = rrff + RP+ RPCC = 3% + 31.4% = 34.4%.= 3% + 31.4% = 34.4%.



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Risk

E[r]

rf = 3.0%

34.4%

9.0%

Built Property37% range

Devlpt Option192% range

E[RP]


27.3.3 What is fundamentally going on with this framework:The “price of risk” (the ex ante investment return risk premium per unit of risk) is being equated across the markets for land and built property:

Exh.27-4



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Note that the probabilities and expected future values used in tNote that the probabilities and expected future values used in this model his model are are ““realreal””, not , not ““riskrisk--neutral dynamicsneutral dynamics”” values. i.e., (0.7)113.21 + values. i.e., (0.7)113.21 + (0.3)78.62 = $102.83 is the real or true expected value of the t(0.3)78.62 = $102.83 is the real or true expected value of the too--bebe--built built building next year, and 70% and 30% are the true probabilities obuilding next year, and 70% and 30% are the true probabilities of the f the ““upup”” and and ““downdown”” outcomes.outcomes.

It is necessary in this formulation to know:It is necessary in this formulation to know:•• The expected total return (OCC) to the underlying asset (the The expected total return (OCC) to the underlying asset (the E[rE[rVV] ] = 9% in our example), and = 9% in our example), and •• The underlying assetThe underlying asset’’s cash payout rate (the s cash payout rate (the E[yE[yVV] = 6% in our ] = 6% in our example).example).

It is also possible to obtain an exactly equivalent solution usiIt is also possible to obtain an exactly equivalent solution using song so--called called ““riskrisk--neutral dynamicsneutral dynamics””, in which case it is not necessary to know the , in which case it is not necessary to know the OCC of the underlying asset. However, this poses little additionOCC of the underlying asset. However, this poses little additional al advantage in the case of real estate, and it results in a less iadvantage in the case of real estate, and it results in a less intuitive ntuitive formulation.formulation.

““RealReal”” vsvs ““RiskRisk--neutralneutral”” dynamics . . .dynamics . . .



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27.4 The Binomial Option Value Model27.4 The Binomial Option Value Model

Think of an individual binomial element (1 period, either “up” or “down”) as like a financial economic “molecule”: the smallest, simplest representation of the essential characteristics dealt with by financial economics: value over time with risk.

We can have as many periods of time as we want (individual “molecules”stitched together as in a “crystal”: as layers or rows & columns in a table, or nodes & branches in a “tree).

Each period can represent as short a span of calendar time as we want.We can have as many periods as we want.

Result:Result:Binomial “tree” can very realistically model actual evolution of values

over time.



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CD27.4 The Binomial Option Value ModelCD27.4 The Binomial Option Value Model

Here are the rules for constructing the underlying asset value tHere are the rules for constructing the underlying asset value tree. ree.

Let:Let:

•• rrVV = Expected total return rate on the underlying asset (built prop= Expected total return rate on the underlying asset (built property).erty).

•• yyVV = Payout rate (dividend yield or net rent yield).= Payout rate (dividend yield or net rent yield).

•• rrff = = RiskfreeRiskfree interest rateinterest rate

•• σσ = Annual volatility of underlying asset (instantaneous rate)*.= Annual volatility of underlying asset (instantaneous rate)*.

•• VVtt = Value of the underlying asset at time (end of period) t, = Value of the underlying asset at time (end of period) t, ex dividendex dividend(i.e., net of current cash payout, i.e., the value of the asset (i.e., net of current cash payout, i.e., the value of the asset itself based only itself based only on forwardon forward--looking cash flows beyond time t). The asset is assumed to looking cash flows beyond time t). The asset is assumed to pay out cash at a rate of pay out cash at a rate of yyVV every period: every period: yyVV = CF= CFt+1t+1 / V/ Vt+1t+1.**.**

All rates are simple periodic rates: All rates are simple periodic rates: rr = = i/mi/m, where , where rr is the simple periodic rate, is the simple periodic rate, ii is the nominal annual is the nominal annual rate, and rate, and mm is the number of periods per yearis the number of periods per year. . The implied effective The implied effective

annual rate (EAR) is thus given by: 1+EAR = (1+annual rate (EAR) is thus given by: 1+EAR = (1+rr))mm



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For example, in our previous illustrationFor example, in our previous illustration……

•• rrVV = 9%= 9%

•• yyVV = 6%= 6%

•• rrff = 3%= 3%

•• σσ = Let= Let’’s say this is 20%.s say this is 20%.

•• VVtt = $100 at time 0, E[V= $100 at time 0, E[Vt+1t+1] = $102.83 at time 1.] = $102.83 at time 1.

VV00==$100$100

VV11upup==

$113.21$113.21

+ CF1up = $6.79

= (.06)$113.21

VV11downdown==

$78.62$78.62

+ CF1down = $4.72

= (.06)$78.62

pp = 0.7= 0.7

11--pp = 0.3= 0.3

E[V1] = (1.09)$100/(1.06) = $102.83.

E[V1] = (0.7)$113.62 + (0.3)$78.62 = $102.83.

E[CF1] = (0.06)$102.83 = $6.17.

E[CF1] = (0.7)$6.79 + (0.3)$4.72 = $6.17.

“going-in cap rate” = $6.17 / $100 = 6.17%.

E[gV] = (1+rV)/(1+yV) = 1.09/1.06 – 1 = 2.83%= rV – (going-in cap rate) = 9% - 6.17%.

$100 = ($102.83 + $6.17) / 1.09




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Now define the 1Now define the 1--period period ““upup”” movement ratio as:movement ratio as:

u u = = VVupup / V(0) ./ V(0) . e.g., in our last example: e.g., in our last example: uu = $113.21 / $94.34 = 1.20.= $113.21 / $94.34 = 1.20.

For the binomial model to work, the For the binomial model to work, the ““downdown”” movement ratio must be the movement ratio must be the inverseinverse of the of the ““upup”” movement ratio:movement ratio:

d d = = VVdowndown / V(0) / V(0) = = 1 / u1 / u . e.g., in our last example: . e.g., in our last example: dd = $78.62 / $94.34 = = $78.62 / $94.34 = 0.833 = 1/1.20.0.833 = 1/1.20.

The magnitude of the The magnitude of the ““upup”” movement is determined so that the binomial movement is determined so that the binomial tree will converge to a tree will converge to a ““normalnormal”” (Gaussian) distribution of periodic (Gaussian) distribution of periodic returns with annual volatility returns with annual volatility σσ as the period lengths approach zero (as the period lengths approach zero (mm

∞∞ , or , or T/nT/n 0). This requires0). This requires::

nTu /1 σ+=where where TT is the total calendar time in the tree (in years) and is the total calendar time in the tree (in years) and nn is the is the total number of periods (hence, total number of periods (hence, T/nT/n is the fraction of a year in any is the fraction of a year in any one period, and one period, and mm = = n/Tn/T is the number of periods per year).is the number of periods per year).

In our previous example: T = 1, n = 1, and σ = 20%.




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The probability of the The probability of the ““upup”” move, move, pp, is determined so that the binomial , is determined so that the binomial tree will converge to a normal (Gaussian) distribution of periodtree will converge to a normal (Gaussian) distribution of periodic returns ic returns with a mean annual total return based on with a mean annual total return based on rrVV as the period lengths as the period lengths approach zero (approach zero (mm ∞∞ , or , or T/nT/n 0). [Or equivalently, an 0). [Or equivalently, an appreciation appreciation return of approximately: return of approximately: ggVV = (1+= (1+rrVV)/(1+)/(1+yyVV))--1.] This requires:1.] This requires:

( ) ( ) ( )( ) ( )nTnT

nTrdu

drp VV

/1/1/1/1/111

σσσ+−+

+−+=

−−+

=

The probability of the The probability of the ““downdown”” movement is of course just movement is of course just 1 1 –– pp ..

Note: These are Note: These are actualactual probabilities, not probabilities, not ““riskrisk--neutralneutral”” pseudopseudo--probabilities.probabilities.They produce a tree that reflects actual real underlying value dThey produce a tree that reflects actual real underlying value distributions.istributions.




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Example based on our previous illustrationExample based on our previous illustration……

( ) ( ) ( )( ) ( )

( ) 70.03667.02567.0

833.020.1833.009.1

20.1120.120.1109.1

/1/1/1/1/111

==−−

=−−

=

+−++−+

=−−+

=nTnT

nTrdu

drp VV

σσσ

The probability of the The probability of the ““downdown”” movement is of course just:movement is of course just:

1 1 –– p = 1 p = 1 –– 0.7 = 0.30.7 = 0.3 ..




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The binomial tree for the underlying asset exThe binomial tree for the underlying asset ex--dividend values is then dividend values is then constructed as follows.constructed as follows.

For any given value node with current (observable) exFor any given value node with current (observable) ex--dividend value dividend value VVtt, the subsequent , the subsequent ““upup”” and and ““downdown”” values in the two possible values in the two possible subsequent value nodes are:subsequent value nodes are:

( ) ( ) ( )

( ) ( )( )( )VtVtdown

t

VtVtup

t

ynTVydVV

yVnTyuVV

++=+=

++=+=

+

+

1/11

1/11

1

1

σ

σ




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The binomial tree for the underlying asset exThe binomial tree for the underlying asset ex--dividend values is then dividend values is then constructed as follows.constructed as follows.

For example in our previous illustrationFor example in our previous illustration……

( ) ( ) ( )

( ) ( )

( ) ( )( )( )

( ) ( ) 62.78$06.1100$833.0

1/11

21.113$06.1100$20.1

1/11

1

1

==

++=+=

==

++=+=

+

+

VtVtdown

t

VtVtup

t

ynTVydVV

yVnTyuVV

σ

σ




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Suppose:Suppose:Expected Expected total returntotal return on the underlying asset is on the underlying asset is 10%10%, with a cash , with a cash payoutpayoutrate of rate of 6%6%, and a , and a riskfreeriskfree interest rate of interest rate of 3%3% (all nominal annual rates).(all nominal annual rates).

Option expires inOption expires in TT = 1 year. = 1 year. nn = 12: There are 12 periods (beyond 0), of = 12: There are 12 periods (beyond 0), of one month each (1 year total). Hence:one month each (1 year total). Hence:

rrVV = 10%/12 = .833%= 10%/12 = .833% , , yyVV = 6%/12 = 0.5%= 6%/12 = 0.5% , , rrff = 3%/12 = 0.25%= 3%/12 = 0.25% ;;

ggVV = (1+= (1+rrVV)/(1+)/(1+yyVV))--1 = 1.00833/1.005 1 = 1.00833/1.005 –– 1 = 0.0033 = 1 = 0.0033 = 0.33%0.33%..

Suppose the volatility of the underlying asset (built property) Suppose the volatility of the underlying asset (built property) is is σσ = 15%.= 15%.

VV00 = $100, the time 0 value of the underlying asset (as if pre= $100, the time 0 value of the underlying asset (as if pre--existing).existing).

Thus: Thus: u u = [1+.15*SQRT(1/12)] = 1.0433= [1+.15*SQRT(1/12)] = 1.0433; ; dd = 1 / = 1 / uu = 1 / 1.0433 = 0.9585= 1 / 1.0433 = 0.9585..

VVupup = = uu($100)/(1+.005) = $104.33/(1.005) = $103.81.($100)/(1+.005) = $104.33/(1.005) = $103.81.

VVdowndown = = dd($100)/(1+.005) = $95.85/(1.005) = $95.37.($100)/(1+.005) = $95.85/(1.005) = $95.37.

pp = = ((1+.10/12)((1+.10/12)--1/(1+.15*SQRT(1/12)))/((1+.15*SQRT(1/12))1/(1+.15*SQRT(1/12)))/((1+.15*SQRT(1/12))--1/(1+.15*SQRT(1/12)))1/(1+.15*SQRT(1/12)))

== ((1.008331.00833 –– .9585.9585)/()/(1.04331.0433 –– .9585.9585) ) = 0.5877; = 0.5877; hence:hence: 1 1 –– p p = 0.4123.= 0.4123.

Numerical Example:Numerical Example:CD27.4 The Binomial Option Value ModelCD27.4 The Binomial Option Value Model



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Numerical Example (cont.)Numerical Example (cont.)……

VV00==$100$100

VV11upup==

$103.81$103.81

VV11downdown==

$95.37$95.37

pp = .5877= .5877

11--pp = .4123= .4123

Note that: Note that: V(0)V(0) = $100.33 / (1+(.10/12)) = $100.33/1.00833 = $99.50 = $100.33 / (1+(.10/12)) = $100.33/1.00833 = $99.50 ≠≠ $100 = $100 = VV00

Note that: E[Note that: E[VV11] = .5877(103.81) + .4123(95.37) = $100.33 = (1.0033)] = .5877(103.81) + .4123(95.37) = $100.33 = (1.0033)$100 = $100 = (1+(1+ggVV ))VV00

Equivalently: Equivalently: V(0)V(0) = = VV00 / (1+/ (1+yyVV) = $100 / (1+(.06/12)) = $100/1.005 = $99.50.) = $100 / (1+(.06/12)) = $100/1.005 = $99.50.



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VV00==$100$100

VV11upup==

$103.81$103.81

VV11downdown==

$95.37$95.37

pp = .5877= .5877

11--pp = .4123= .4123


Now consider the Now consider the ““downdown”” jump from jump from VV11upup , , and the and the ““upup”” jump fromjump from VV11

downdown (call (call this value this value ““VV1,21,2””, because it is in the 1, because it is in the 1stst row down from the top, 2row down from the top, 2ndnd column over column over from the left in the overall binomial tree) .from the left in the overall binomial tree) . . .. .

V1,2 = up from V1down = u($95.37)/(1+.06/12) = 1.0433(95.37)/1.005 = $99.01.

V1,2 = down from V1up = d($103.81)/(1+.06/12) = .9585(103.81)/1.005 = $99.01.

This is This is notnot a coincidence.a coincidence.

It is a general property of the It is a general property of the way we have constructed the way we have constructed the binomial tree. binomial tree. (constant u, d = 1/u.)

ItIt’’s the same value!s the same value!

VV1,21,2==$99.01$99.01

11--pp = .4123= .4123

pp = .5877= .5877



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VV00==$100$100

VV11upup==

$103.81$103.81

VV11downdown==

$95.37$95.37

pp = .5877= .5877

11--pp = .4123= .4123


Here is the tree up through the Here is the tree up through the VV0,20,2 , , VV1,21,2 , and , and VV2,22,2 value nodes .value nodes . . .. .

VV1,21,2==$99.01$99.01

11--pp = .4123= .4123

pp = .5877= .5877

We build the underlying asset value tree forward in this mannerWe build the underlying asset value tree forward in this manner……

V0,2 = up from V1up = u($ 103.81)/(1+.06/12) = 1.0433(103.81)/1.005 = $107.77.

V2,2 = down from V1up = d($95.37)/(1+.06/12) = .9585(95.37)/1.005 = $90.96.

VV2,22,2==$90.96$90.96

VV0,20,2==$107.77$107.77

11--pp = .4123= .4123

pp = .5877= .5877



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We build the underlying asset value tree forward in this mannerWe build the underlying asset value tree forward in this manner……

$116.58$110.77

$105.25 $104.20$100.00 $99.01

$94.07 $93.14$88.49

$83.25



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We build the underlying asset value tree forward in this mannerWe build the underlying asset value tree forward in this manner……$184.73

$175.52$166.77 $165.11

$158.45 $156.88$150.55 $149.06 $147.58

$143.05 $141.63 $140.22$135.91 $134.57 $133.23 $131.91

$129.14 $127.86 $126.59 $125.33$122.70 $121.48 $120.28 $119.08 $117.90

$116.58 $115.43 $114.28 $113.15 $112.02$110.77 $109.67 $108.58 $107.50 $106.44 $105.38

$105.25 $104.20 $103.17 $102.14 $101.13 $100.13$100.00 $99.01 $98.02 $97.05 $96.09 $95.13 $94.19

$94.07 $93.14 $92.21 $91.30 $90.39 $89.49$88.49 $87.62 $86.75 $85.89 $85.03 $84.19

$83.25 $82.42 $81.60 $80.79 $79.99$78.31 $77.53 $76.77 $76.00 $75.25

$73.67 $72.94 $72.21 $71.50$69.30 $68.61 $67.93 $67.26

$65.19 $64.55 $63.91$61.33 $60.72 $60.12

$57.69 $57.12$54.27 $53.73

$51.05$48.03



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Here is the 12Here is the 12--period, monthly periods (1 year) numerical example period, monthly periods (1 year) numerical example tree we have been working on (from Excel)tree we have been working on (from Excel)……

Notice the first element here, as Notice the first element here, as we previously calculated it.we previously calculated it.

Each node in the tree (each row, column cell in the table) Each node in the tree (each row, column cell in the table) represents a possible future represents a possible future ““state of the worldstate of the world””, as indicated by a , as indicated by a possible value of the underlying asset as of the given future tipossible value of the underlying asset as of the given future time me period (month in this case).period (month in this case).

V tree (net of payout, "ex dividend" values):Period ("j "): "n " =

0 1 2 3 4 5 6 7 8 9 10 11 12

V tree (net of payout, "ex dividend" values):100.00 103.81 107.77 111.87 116.14 120.56 125.16 129.93 134.88 140.02 145.36 150.90 156.65

95.37 99.01 102.78 106.70 110.76 114.99 119.37 123.92 128.64 133.54 138.63 143.9190.96 94.43 98.02 101.76 105.64 109.66 113.84 118.18 122.69 127.36 132.22

86.75 90.06 93.49 97.05 100.75 104.59 108.58 112.71 117.01 121.4782.74 85.89 89.16 92.56 96.09 99.75 103.55 107.50 111.60

78.91 81.92 85.04 88.28 91.64 95.13 98.76 102.5275.26 78.12 81.10 84.19 87.40 90.73 94.19

71.77 74.51 77.35 80.30 83.36 86.5368.45 71.06 73.77 76.58 79.50

65.29 67.77 70.36 73.0462.26 64.64 67.10

59.38 61.6556.64



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27.4 The Binomial Option Value Model27.4 The Binomial Option Value ModelAlthough the conditional probabilities are Although the conditional probabilities are pp = .5877 and = .5877 and 11--pp = .4123 going forward = .4123 going forward one period (one period (upup and and downdown) from any given node, over multiple periods the ) from any given node, over multiple periods the unconditional probabilities become bellunconditional probabilities become bell--shaped over all the possible outcomesshaped over all the possible outcomes……

Actually, although the model converges toward continuously-compounded return probabilities that are normally distributed, the asset value level probabilities are log-normally distributed (skewed bell shape).

Tree real probabilities (p based):Period ("j "): "n " =

0 1 2 3 4 5 6 7 8 9 10 11 121.0000 0.5877 0.3454 0.2030 0.1193 0.0701 0.0412 0.0242 0.0142 0.0084 0.0049 0.0029 0.0017

0.4123 0.4846 0.4272 0.3347 0.2459 0.1734 0.1189 0.0798 0.0528 0.0345 0.0223 0.01430.1700 0.2997 0.3523 0.3451 0.3042 0.2503 0.1961 0.1482 0.1088 0.0782 0.0551

0.0701 0.1648 0.2421 0.2846 0.2926 0.2752 0.2426 0.2036 0.1645 0.12890.0289 0.0849 0.1497 0.2053 0.2413 0.2553 0.2500 0.2309 0.2035

0.0119 0.0420 0.0864 0.1355 0.1791 0.2105 0.2268 0.22850.0049 0.0202 0.0475 0.0838 0.1231 0.1591 0.1870

0.0020 0.0095 0.0252 0.0494 0.0798 0.11250.0008 0.0044 0.0130 0.0280 0.0493

0.0003 0.0020 0.0065 0.01540.0001 0.0009 0.0032

0.0001 0.00040.0000

Period 12 Value Probabilities

0%

5%

10%

15%

20%

25%

$57 $62 $67 $73 $80 $87 $94 $103 $112 $121 $132 $144 $157



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CD27.4 The Binomial Option Value ModelCD27.4 The Binomial Option Value ModelDefine the tree as a table of rows and columns. The jth column is the number of periods after the present (time 0), where j = 0, 1, 2, …, n (where n is the total number of periods). The ith row is the number of “down” moves in the asset price since time 0, where i = 0, 1, 2, … , j . Each row, column cell (i, j) defines a “state of the world” j periods in the future. Vi,j is the value of the underlying asset in that state.

The ex ante probability (as of time 0) of any given state of the world i, j is given by:

( )iij ppiji

jjiprob −⎟⎟⎠

⎞⎜⎜⎝

⎛−

= − 1)!(!

!),( )(

where the symbol “!” indicates the “factorial” product operation: x! = 1*2*3* . . . *x.


0 1 2 3 4 5 6 7 8 9 10 11 12

"down" moves ("i"): V tree (net of payout, "ex dividend" values):0 100.00 103.81 107.77 111.87 116.14 120.56 125.16 129.93 134.88 140.02 145.36 150.90 156.651 95.37 99.01 102.78 106.70 110.76 114.99 119.37 123.92 128.64 133.54 138.63 143.912 90.96 94.43 98.02 101.76 105.64 109.66 113.84 118.18 122.69 127.36 132.223 86.75 90.06 93.49 97.05 100.75 104.59 108.58 112.71 117.01 121.474 82.74 85.89 89.16 92.56 96.09 99.75 103.55 107.50 111.605 78.91 81.92 85.04 88.28 91.64 95.13 98.76 102.526 75.26 78.12 81.10 84.19 87.40 90.73 94.197 71.77 74.51 77.35 80.30 83.36 86.538 68.45 71.06 73.77 76.58 79.509 65.29 67.77 70.36 73.0410 62.26 64.64 67.1011 59.38 61.6512 56.64



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In this numerical example, the Period 12 underlying asset valuesIn this numerical example, the Period 12 underlying asset values and and probabilities, indicated in the last column on the right in the probabilities, indicated in the last column on the right in the previous previous two slides, give:two slides, give:

EE00[V[V1212] = E] = E00[V(1 yr)] = $104.05[V(1 yr)] = $104.05

which is identical to: Vwhich is identical to: V00((1+((1+rrVV)/(1+)/(1+yyVV))))1212 = V= V00(1+(1+ggVV))1212 = $100(1.0033)= $100(1.0033)1212 = $104.05= $104.05, , And:And:

STD[VSTD[V1212]/V]/V00 = 1 yr Volatility = = 1 yr Volatility = ±±14.99%14.99%

which is very similar to the 15% simple annual volatility assumpwhich is very similar to the 15% simple annual volatility assumption.tion.

(If you(If you’’re curious, these statistics are found as followsre curious, these statistics are found as follows……))

( )

( ) ( ) %99.141)!12(!

!12][][

.,5877.0:

05.104$1)!12(!

!12][

0

12

0

)12(212012,012

12,

12

0

)12(12,120

±=⎥⎦

⎤⎢⎣

⎡−⎟⎟

⎠

⎞⎜⎜⎝

⎛−

−=

=

=−⎟⎟⎠

⎞⎜⎜⎝

⎛−

=

∑

∑

=

−

=

−

Vppii

VEVVVSTD

tabletheinfoundasareVandpwhere

ppii

VVE

i

iii

i

i

iii



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EE00[V[V1212] = $104.05 = V] = $104.05 = V00(1.0033)(1.0033)1212 = V= V00(1+(1+ggVV))1212 ..

STD[VSTD[V1212]/V]/V00 = = ±±14.99% 14.99% ≈≈ 15% = 15% = σσ

Value probabilities for the underlying asset (V) 12 periods intoValue probabilities for the underlying asset (V) 12 periods into the future . . .the future . . .

Period 12 Value Probabilities

0%

5%

10%

15%

20%

25%

$57 $62 $67 $73 $80 $87 $94 $103 $112 $121 $132 $144 $157




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Period ("j "): "n " =0 1 2 3 4 5 6 7 8 9 10 11 12

"down" moves ("i"): K Value Tree:0 80.00 80.13 80.27 80.40 80.53 80.67 80.80 80.94 81.07 81.21 81.34 81.48 81.611 80.13 80.27 80.40 80.53 80.67 80.80 80.94 81.07 81.21 81.34 81.48 81.612 80.27 80.40 80.53 80.67 80.80 80.94 81.07 81.21 81.34 81.48 81.613 80.40 80.53 80.67 80.80 80.94 81.07 81.21 81.34 81.48 81.614 80.53 80.67 80.80 80.94 81.07 81.21 81.34 81.48 81.615 80.67 80.80 80.94 81.07 81.21 81.34 81.48 81.616 80.80 80.94 81.07 81.21 81.34 81.48 81.617 80.94 81.07 81.21 81.34 81.48 81.618 81.07 81.21 81.34 81.48 81.619 81.21 81.34 81.48 81.6110 81.34 81.48 81.6111 81.48 81.6112 81.61

For each node (cell) in the underlying asset value tree (the For each node (cell) in the underlying asset value tree (the ““V TreeV Tree”” ) ) described previously, there will also be associated a projected described previously, there will also be associated a projected value of value of the the ““exercise priceexercise price”” for the option (the for the option (the construction costconstruction cost of the of the development project). development project).

We label this cost We label this cost KK. .

Assuming Assuming KK grows grows risklesslyrisklessly at 2%/yr nominal (0.1667%/mo), the table at 2%/yr nominal (0.1667%/mo), the table of of KKii, j, j values giving construction costs corresponding to the previous values giving construction costs corresponding to the previous VVi, ji, j values is as followsvalues is as follows……




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How to value a call option using the model . . .How to value a call option using the model . . .

While the underlying asset value and exercise price trees are While the underlying asset value and exercise price trees are constructed going forward in time as described previously, constructed going forward in time as described previously,

An option on the underlying asset is valued by working backward An option on the underlying asset is valued by working backward in in time, starting at the righttime, starting at the right--hand edge of the tree (option expiration) and hand edge of the tree (option expiration) and working back to the left.working back to the left.

The option can be valued one period at a time, at each node of tThe option can be valued one period at a time, at each node of the tree, he tree, based on the option values in the two subsequent possible nodes.based on the option values in the two subsequent possible nodes.

Starting in the last column (expiration period Starting in the last column (expiration period j j == nn ) one works ) one works backwards in time ultimately to the present (time 0 at period backwards in time ultimately to the present (time 0 at period jj = = 0 0 ).).

Each valuation in each node (Each valuation in each node (i , j i , j cell in the table) is a simple 1cell in the table) is a simple 1--period period binomial valuation using the certaintybinomial valuation using the certainty--equivalent present value model equivalent present value model discussed previously.discussed previously.




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The general formula and procedure for call option valuation is The general formula and procedure for call option valuation is thus as follows . . .thus as follows . . .

First, First, let:let:

VVi,ji,j = The ex= The ex--dividend underlying asset value in statedividend underlying asset value in state--ofof--thethe--world world i i at at time (period) time (period) jj, as enumerated in the binomial value tree described , as enumerated in the binomial value tree described previously (e.g., built property value).previously (e.g., built property value).

KKjj = The exercise price (construction cost) at time = The exercise price (construction cost) at time jj (known for certain in (known for certain in advance). i.e., paying advance). i.e., paying KKjj in period in period j j will produce in period will produce in period jj an asset worth an asset worth VVi,ji,j at that time (instantaneous construction).at that time (instantaneous construction).

Then in the terminal period Then in the terminal period j j == nn (in which the option expires), the call (in which the option expires), the call option is worth, in any given state whose underlying asset valueoption is worth, in any given state whose underlying asset value is is VVi,ni,n ::

)0,( ,, nnini KVMaxC −=




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For example, look at the top two values in the terminal column For example, look at the top two values in the terminal column j j = = nn = 12 = 12 of our previous tree, of our previous tree, VV0,120,12 == $156.65 and $156.65 and VV1,121,12 == $143.91 respectively.$143.91 respectively.

Label the value of the call option in each of these nodes: Label the value of the call option in each of these nodes: CC0,120,12 and and CC1,12 1,12 ..

Given that construction cost in month 12, Given that construction cost in month 12, KK1212 , is $81.61 (see previous , is $81.61 (see previous table), we thus have:table), we thus have:

CC0,120,12 = = Max(Max( $156.65 $156.65 -- $81.61, 0 $81.61, 0 ) ) = $75.04= $75.04

CC1,121,12 = = Max(Max( $143.91 $143.91 -- $81.61, 0 $81.61, 0 ) ) = $62.30= $62.30

Now consider the period Now consider the period jj = = nn--11 state from which these two state from which these two j j == nn value value states are each possible, and suppose (for now) that the option states are each possible, and suppose (for now) that the option cannot be cannot be exercised prior to its maturity at period exercised prior to its maturity at period nn ( ( ““European OptionEuropean Option”” ))……

For example, for the $156.65 and $143.91 values in period 12, thFor example, for the $156.65 and $143.91 values in period 12, this would is would be the state in period 11 in our previous example where be the state in period 11 in our previous example where VV0,110,11 is worth is worth $150.90.$150.90.




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0 1 2 3 4 5 6 7 8 9 10 11 12


VV0,110,11==$150.90$150.90

VV1212upup==

$156.65$156.65

VV1212downdown==

$143.91$143.91

CC0,11 0,11 = ?= ?

Max(156.65Max(156.65--81.61, 0) = 81.61, 0) =

$$75.0475.04

Max(143.91Max(143.91--81.61, 0) = 81.61, 0) =

$$62.3062.30




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The value of the call option in any state is a function of its tThe value of the call option in any state is a function of its two possible wo possible values in the subsequent period. The exact valuation formula is values in the subsequent period. The exact valuation formula is the same the same certaintycertainty--equivalence PV formula we have presented previously:*equivalence PV formula we have presented previously:*

( )

f

downt

upt

fVdownt

upttt

ftt

rVV

rrECCCE

rCCEQC

+

⎟⎟⎠

⎞⎜⎜⎝

⎛−−

−−=

+=

+++++

+

1%%

][][

)1(][

11111

1

Substituting our previouslySubstituting our previously--described binomial model parameters, this described binomial model parameters, this becomes:becomes:

( ) ( )( ) ( )nTnT

nTrp V

/11/1/111

σσσ+−+

+−+=

where the probability where the probability pp is as defined previously:is as defined previously:

( ) ( ) ( ) ( )f

fVjijijiji

ji rnTnT

rrCCCppC

C+

⎥⎦

⎤⎢⎣

⎡

+−+

−−−−+

=++++++

1/11/1

)1( 1,11,1,11,

,σσ




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In particular, for In particular, for CC0,110,11 , recalling our previous 1, recalling our previous 1--year monthly numerical year monthly numerical example input parameters of: example input parameters of: rrVV = 10%/12 = .833%= 10%/12 = .833% , , yyVV = 6%/12 = 0.5%= 6%/12 = 0.5% , , rrff = 3%/12 = 0.25%= 3%/12 = 0.25%, and , and σσ = 15%= 15%, we obtain:, we obtain:

( ) ( ) ( ) ( )( ) ( )

( ) ( )

( ) ( )[ ]( )

73.68$

0025.191.68$

0025.10688.073.12$78.69$

0025.1%48.8%583.030.6204.75)30.62(4123.)04.75(5877.

0025.1%85.95%33.104

%25.0%833.0412.5877.

)1(12/11112/11

4123.5877.

12,212,112,112,0

12,112,012,112,011,0

=

=

−=

⎟⎠

⎞⎜⎝

⎛⎥⎦⎤

⎢⎣⎡−−+=

⎟⎠

⎞⎜⎝

⎛⎥⎦⎤

⎢⎣⎡

−−

−−+=

+⎟⎟⎠

⎞⎜⎜⎝

⎛⎥⎦

⎤⎢⎣

⎡

+−+

−−−+=

CCCC

rrr

CCCCC ffV

σσ




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VV0,110,11==$150.90$150.90

VV1212upup==

$156.65$156.65

VV1212downdown==

$143.91$143.91

CC0,11 0,11 = = $68.73$68.73

CC0,120,12 ==

$75.03$75.03

CC1,121,12 ==

$62.30$62.30

( ) ( ) ( ) ( )( ) ( ) ( ) ( )

73.68$

0025.191.68$

)12/%31(12/1%151112/1%151

12/%312/%1030.6203.75)30.62(4123.)03.75(5877.

)1(12/1112/11

)1( 12,112,012,112,011,0

=

=

+⎟⎟⎠

⎞⎜⎜⎝

⎛⎥⎦

⎤⎢⎣

⎡

+−+−

−−+=

+⎟⎟⎠

⎞⎜⎜⎝

⎛⎥⎦

⎤⎢⎣

⎡

−−+

−−−−+= f

fV rrr

CCCppCCσσ

KK1212 = $81.61= $81.61

KK1111 = $81.48= $81.48




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Repeating this process within each column for Repeating this process within each column for ii = 0, 1, 2, = 0, 1, 2, ……, , jj , and then , and then across columns from right to left for across columns from right to left for jj = 11, 10, 9, = 11, 10, 9, ……, 0 , we eventually , 0 , we eventually obtain the value of the option as of the present time 0:obtain the value of the option as of the present time 0:

Period ("j "): "n " =0 1 2 3 4 5 6 7 8 9 10 11 12

"down" moves ("i"): Eurpoean Call Option Value Tree:0 15.76 19.23 23.06 27.20 31.60 36.23 41.07 46.13 51.41 56.94 62.71 68.73 75.031 12.09 15.20 18.72 22.60 26.78 31.19 35.83 40.67 45.72 51.01 56.53 62.302 8.81 11.48 14.63 18.21 22.15 26.36 30.79 35.42 40.26 45.32 50.603 5.97 8.15 10.85 14.06 17.72 21.72 25.96 30.39 35.02 39.854 3.64 5.27 7.44 10.19 13.50 17.26 21.32 25.55 29.985 1.90 2.97 4.51 6.67 9.51 12.98 16.86 20.916 0.77 1.31 2.21 3.64 5.81 8.87 12.587 0.18 0.35 0.68 1.32 2.55 4.928 0.00 0.00 0.00 0.00 0.009 0.00 0.00 0.00 0.0010 0.00 0.00 0.0011 0.00 0.0012 0.00

The European option is worth $15.76 in the present time 0.The European option is worth $15.76 in the present time 0.

Note here the values we calculated in the previous slides.*




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In our example, given that In our example, given that KK0,110,11 = $81.48, then if the land can be = $81.48, then if the land can be developed immediately at any time, it is worth in state developed immediately at any time, it is worth in state 0,110,11 ::

42.69$)73.68$,42.69($)73.68$,48.81$90.150($11,0 ==−= MaxMaxC

If the landowner can begin the development project (exercise theIf the landowner can begin the development project (exercise the option) option) at at anyany time ( time ( ““American optionAmerican option”” ), then the value of the land in any state ), then the value of the land in any state prior to option expiration is given by:prior to option expiration is given by:

( ) ( ) ( ) ( )

⎪⎪

⎭

⎪⎪

⎬

⎫

⎪⎪

⎩

⎪⎪

⎨

⎧

+

⎥⎦

⎤⎢⎣

⎡

+−+

−−−−+

−=++++++

f

fVjijijiji

jijiji rnTnT

rrCCCppC

KVMaxC1

/11/1)1(

,1,11,1,11,

,,,σσ

The flexibility to build the project at The flexibility to build the project at any timeany time prior to the end of the year prior to the end of the year ( ( ““American OptionAmerican Option”” instead of instead of ““European OptionEuropean Option”” ), makes the option ), makes the option worth more, namely, $20 at time 0 (instead of $15.76) . . .worth more, namely, $20 at time 0 (instead of $15.76) . . .




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Here is the complete Here is the complete American OptionAmerican Option land value tree, assuming as land value tree, assuming as before initial building value of: before initial building value of: VV00 = $100, initial construction cost: = $100, initial construction cost: KK0 0 = = $80, (deterministic) construction cost growth rate of 2%/yr $80, (deterministic) construction cost growth rate of 2%/yr (0.167%/month), and that the right to ever develop the land expi(0.167%/month), and that the right to ever develop the land expires res after 1 year. From Excel:after 1 year. From Excel:

An example Excel spreadsheet template for this binomial option mAn example Excel spreadsheet template for this binomial option model example is odel example is available for downloading from the course web site.available for downloading from the course web site.

Period ("j "): "n " =0 1 2 3 4 5 6 7 8 9 10 11 12

"down" moves ("i"): LAND Value tree:0 20.00 23.68 27.50 31.47 35.60 39.90 44.36 48.99 53.81 58.81 64.01 69.42 75.031 15.24 18.74 22.38 26.16 30.10 34.18 38.43 42.84 47.43 52.20 57.15 62.302 10.69 14.03 17.49 21.09 24.84 28.73 32.77 36.97 41.34 45.88 50.603 6.88 9.52 12.82 16.25 19.81 23.52 27.37 31.37 35.53 39.854 4.06 5.90 8.38 11.62 15.02 18.54 22.21 26.02 29.985 2.11 3.25 4.92 7.27 10.43 13.79 17.28 20.916 0.88 1.47 2.41 3.89 6.10 9.25 12.587 0.25 0.46 0.84 1.52 2.74 4.928 0.03 0.06 0.11 0.21 0.409 0.00 0.00 0.00 0.0010 0.00 0.00 0.0011 0.00 0.0012 0.00Note the value we

just calculated, here:




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Note that, as we have presented it, the option (land) valuation Note that, as we have presented it, the option (land) valuation formula formula appears to be a function of nine variables or parameters*:appears to be a function of nine variables or parameters*:

CCi,ji,j = = CC((VVi,ji,j , , KKi,ji,j , , rrVV , , rrff ,, yyVV , , ggKK , , σσ, , TT, , nn))

In general, In general, ceteris paribusceteris paribus (holding all other variables and parameters (holding all other variables and parameters constant), option value constant), option value increasesincreases as a function of: as a function of:

V , V , rrff , , σσ , , andand T.T.

And And decreasesdecreases as a function of:as a function of:

K , K , yyVV , and , and ggKK

Importantly (and very interestingly), note that the option valueImportantly (and very interestingly), note that the option value is:is:

UNAFFECTED BY THE UNDERLYING ASSET UNAFFECTED BY THE UNDERLYING ASSET REQUIRED RETURNREQUIRED RETURN , , rrVV OR THE GROWTH RATE,OR THE GROWTH RATE, ggVV

(holding constant the (holding constant the currentcurrent underlying asset VALUE, underlying asset VALUE, VVi,ji,j , and the , and the payout rate payout rate yyVV .).)




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Effect of Underlying Asset VolatilityEffect of Underlying Asset VolatilityThis is the same option as before only weThis is the same option as before only we’’ve increased the underlying ve increased the underlying asset volatility (asset volatility (σσ) from 15% to 25%.) from 15% to 25%.

Period ("j "): "n " =0 1 2 3 4 5 6 7 8 9 10 11 12

"down" moves ("i"): LAND Value tree:0 20.16 26.55 33.55 41.02 49.00 57.52 66.63 76.34 86.72 97.80 109.63 122.26 135.741 13.86 18.90 25.22 32.15 39.55 47.45 55.88 64.89 74.51 84.79 95.75 107.462 8.89 12.66 17.62 23.91 30.76 38.08 45.90 54.26 63.17 72.70 82.873 5.15 7.76 11.40 16.31 22.60 29.39 36.63 44.37 52.64 61.474 2.56 4.14 6.55 10.08 15.02 21.30 28.02 35.19 42.855 0.99 1.75 3.04 5.19 8.62 13.79 20.01 26.666 0.24 0.46 0.91 1.78 3.48 6.81 12.587 0.01 0.02 0.04 0.08 0.16 0.328 0.00 0.00 0.00 0.00 0.009 0.00 0.00 0.00 0.0010 0.00 0.00 0.0011 0.00 0.0012 0.00

Note the increase in value from $20.00 to $20.16

With 15% volatility, the option model called for optimal immediate exercise at time 0.

With 25% volatility, the model indicates that the option is more valuable held for speculation at time 0 instead of immediate exercise at that time.




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Period ("j "): "n " =0 1 2 3 4 5 6 7 8 9 10 11 12

"down" moves ("i"): Optimal exercise:0 exer exer exer exer exer exer exer exer exer exer exer exer exer1 exer exer exer exer exer exer exer exer exer exer exer exer2 exer exer exer exer exer exer exer exer exer exer exer3 hold exer exer exer exer exer exer exer exer exer4 hold hold hold exer exer exer exer exer exer5 hold hold hold hold exer exer exer exer6 hold hold hold hold hold exer exer7 hold hold hold hold hold exer8 hold hold hold hold hold9 hold hold hold hold10 hold hold hold11 hold hold12 hold

Notice that the option value model not only values the option, but also indicates in which states of the world it is optimal to exercise the option (build the development project). Here are the valuation and optimal exercise trees for the option with σσ back at the original 15%15% . . .

Period ("j "): "n " =0 1 2 3 4 5 6 7 8 9 10 11 12

"down" moves ("i"): LAND Value tree:0 20.00 23.68 27.50 31.47 35.60 39.90 44.36 48.99 53.81 58.81 64.01 69.42 75.031 15.24 18.74 22.38 26.16 30.10 34.18 38.43 42.84 47.43 52.20 57.15 62.302 10.69 14.03 17.49 21.09 24.84 28.73 32.77 36.97 41.34 45.88 50.603 6.88 9.52 12.82 16.25 19.81 23.52 27.37 31.37 35.53 39.854 4.06 5.90 8.38 11.62 15.02 18.54 22.21 26.02 29.985 2.11 3.25 4.92 7.27 10.43 13.79 17.28 20.916 0.88 1.47 2.41 3.89 6.10 9.25 12.587 0.25 0.46 0.84 1.52 2.74 4.928 0.03 0.06 0.11 0.21 0.409 0.00 0.00 0.00 0.0010 0.00 0.00 0.0011 0.00 0.0012 0.00




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Here is the same option only with σσ = 25%= 25% . . .Period ("j "): "n " =

0 1 2 3 4 5 6 7 8 9 10 11 12"down" moves ("i"): LAND Value tree:

0 20.16 26.55 33.55 41.02 49.00 57.52 66.63 76.34 86.72 97.80 109.63 122.26 135.741 13.86 18.90 25.22 32.15 39.55 47.45 55.88 64.89 74.51 84.79 95.75 107.462 8.89 12.66 17.62 23.91 30.76 38.08 45.90 54.26 63.17 72.70 82.873 5.15 7.76 11.40 16.31 22.60 29.39 36.63 44.37 52.64 61.474 2.56 4.14 6.55 10.08 15.02 21.30 28.02 35.19 42.855 0.99 1.75 3.04 5.19 8.62 13.79 20.01 26.666 0.24 0.46 0.91 1.78 3.48 6.81 12.587 0.01 0.02 0.04 0.08 0.16 0.328 0.00 0.00 0.00 0.00 0.009 0.00 0.00 0.00 0.0010 0.00 0.00 0.0011 0.00 0.0012 0.00

Notice that with greater underlying asset volatility, option exercise is held back, less likely. (Compare the “exer” cells in this table with the previous.)

Period ("j "): "n " =0 1 2 3 4 5 6 7 8 9 10 11 12

"down" moves ("i"): Optimal exercise:0 hold exer exer exer exer exer exer exer exer exer exer exer exer1 hold hold exer exer exer exer exer exer exer exer exer exer2 hold hold hold exer exer exer exer exer exer exer exer3 hold hold hold hold exer exer exer exer exer exer4 hold hold hold hold exer exer exer exer exer5 hold hold hold hold hold exer exer exer6 hold hold hold hold hold exer exer7 hold hold hold hold hold exer8 hold hold hold hold hold9 hold hold hold hold10 hold hold hold11 hold hold12 hold




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Period ("j "): "n " =0 1 2 3 4 5 6 7 8 9 10 11 12


With 15% volatility, immediate exercise.

Period ("j "): "n " =0 1 2 3 4 5 6 7 8 9 10 11 12

"down" moves ("i"): Optimal exercise:0 hold exer exer exer exer exer exer exer exer exer exer exer exer1 hold hold exer exer exer exer exer exer exer exer exer exer2 hold hold hold exer exer exer exer exer exer exer exer3 hold hold hold hold exer exer exer exer exer exer4 hold hold hold hold exer exer exer exer exer5 hold hold hold hold hold exer exer exer6 hold hold hold hold hold exer exer7 hold hold hold hold hold exer8 hold hold hold hold hold9 hold hold hold hold10 hold hold hold11 hold hold12 hold

With 25% volatility, delay construction.




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Risk & the OCCRisk & the OCCWhat are the implications of the option model for the amount of What are the implications of the option model for the amount of investment investment risk, and the corresponding riskrisk, and the corresponding risk--adjusted discount rate (OCC ) applicable adjusted discount rate (OCC ) applicable to the land? . . .to the land? . . .

For a finiteFor a finite--lived option, the risk and OCC will differ according to the lived option, the risk and OCC will differ according to the ““statestate--ofof--thethe--worldworld”” (the (the VV, and , and KK values, and the time until option values, and the time until option expiration). expiration).

But recall that the certaintyBut recall that the certainty--equivalence valuation we are employing here equivalence valuation we are employing here allows us to allows us to ““back outback out”” what is the OCC once we have computed the option what is the OCC once we have computed the option value. The formula to do this is obtained as follows:value. The formula to do this is obtained as follows:

( )][

][11

,1

][][1

][1

][

1

1,

,

111,

,

+

+

+++

+=+

⇒

+=

++=

+=

j

jjfji

ji

jj

Cf

jj

f

jji

CCEQCE

rOCC

OCCCE

RPErCE

rCCEQ

Cji




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Risk & the OCCRisk & the OCCThus, for any Thus, for any i, j i, j state of the world in the binomial tree, we can state of the world in the binomial tree, we can compute the OCC (and the implied amount of investment risk compute the OCC (and the implied amount of investment risk indicated by the corresponding risk premium in the OCC). indicated by the corresponding risk premium in the OCC).

Here is are the 1Here is are the 1--period (monthly) period (monthly) OCCsOCCs for our previous numerical for our previous numerical example example (1-yr finite option with σ = 15% and the other parameters as before) . . .. . .

Period ("j "):0 1 2 3 4 5 6 7 8 9 10 11

"down" moves ("i"): 1-Period Option Opportunity Cost of Capital:0 3.22% 2.84% 2.56% 2.35% 2.17% 2.03% 1.91% 1.81% 1.72% 1.65% 1.58% 1.52%1 3.98% 3.39% 2.97% 2.66% 2.42% 2.23% 2.08% 1.95% 1.84% 1.75% 1.67%2 4.94% 4.27% 3.58% 3.11% 2.77% 2.50% 2.30% 2.13% 2.00% 1.88%3 5.82% 5.34% 4.62% 3.81% 3.27% 2.88% 2.59% 2.37% 2.19%4 6.87% 6.40% 5.86% 5.03% 4.07% 3.45% 3.01% 2.69%5 8.34% 7.85% 7.28% 6.61% 5.54% 4.38% 3.65%6 10.46% 10.07% 9.57% 8.90% 7.92% 6.19%7 13.54% 13.54% 13.54% 13.54% 13.54%8 NA NA NA NA9 NA NA NA10 NA NA11 NA12

Note that the OCC is mathematically indeterminate in states of the world where the option has a certain value of zero (in all future possible states of the world and hence in the current state).*




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Period ("j "):0 1 2 3 4 5 6 7 8 9 10 11

"down" moves ("i"): Option Opportunity Cost of Capital per Annum (EAR):0 46.2% 40.0% 35.5% 32.1% 29.4% 27.2% 25.5% 24.0% 22.7% 21.7% 20.7% 19.9%1 59.8% 49.2% 42.1% 37.0% 33.3% 30.3% 28.0% 26.1% 24.5% 23.2% 22.0%2 78.3% 65.2% 52.6% 44.4% 38.7% 34.5% 31.3% 28.8% 26.8% 25.1%3 97.2% 86.7% 71.9% 56.6% 47.1% 40.6% 36.0% 32.4% 29.7%4 121.9% 110.5% 98.1% 80.2% 61.4% 50.2% 42.8% 37.5%5 161.6% 147.8% 132.4% 115.6% 91.1% 67.2% 53.8%6 229.8% 216.2% 199.4% 178.3% 149.7% 105.5%7 358.9% 358.9% 358.9% 358.9% 358.9%8 NA NA NA NA9 NA NA NA10 NA NA11 NA

Risk & the OCCRisk & the OCCHere are the per annum (effective annual rates) expected returnsHere are the per annum (effective annual rates) expected returnsimplied by the preceding periodic implied by the preceding periodic OCCsOCCs . . .. . .

Note: These OCCs are probably not very realistic (too high) for actual land investment, because of our assumption here of a 1-year finite life of the

development option. In reality, land development rights typically do not expire at the end of a year. (More on this shortly.)




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Risk & the OCCRisk & the OCCHow do these option How do these option OCCsOCCs compare to the compare to the ““Method 1Method 1”” ((““canonicalcanonical””) ) Formula for the OCC of a development project, introduced in the Formula for the OCC of a development project, introduced in the Chapter 29 lecture notes? . . .Chapter 29 lecture notes? . . .

Recall that the Method 1 Formula is as follows (where Recall that the Method 1 Formula is as follows (where TTCC is the time is the time required for construction):required for construction):

Recasting this in our current nomenclature with Recasting this in our current nomenclature with TTCC = 1 yr , this = 1 yr , this formula is:formula is: ( )( )

( ) ( ) 11][11][

][1

11,

−⎥⎥⎦

⎤

⎢⎢⎣

⎡

+−+

+−=

+

++

KrVErrKVE

rEVjjf

fjjjC ji

This formula will in fact be equivalent to the option OCC previoThis formula will in fact be equivalent to the option OCC previously usly computed in any state of the world where the option will definitcomputed in any state of the world where the option will definitely be ely be exercised in the next period. exercised in the next period. (Recall that the canonical formula assumes a definite commitment to go forward with the development project.)

( )( ) ( )( ) ( )

( )

1][1][1

][1][1][1

−⎥⎦

⎤⎢⎣

⎡

+−+++−

=C

CC

CCT

TT

VTT

D

TD

TVTT

C LrEVrErErELVrE




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Comparison of Comparison of ““canonicalcanonical”” OCC versus actual option OCC OCC versus actual option OCC (previous numerical example, 1st 4 periods only) . . .. . .

Period ("j "):0 1 2 3 4

"down" moves ("i"): "Canonical" ("Method 1") OCC Formula from Ch.29:0 3.22% 2.84% 2.56% 2.35% 2.17%1 3.98% 3.39% 2.97% 2.66%2 Not Valid 4.27% 3.58%3 Not Valid Not Valid4 Not Valid

Period ("j "):0 1 2 3 4

"down" moves ("i"): 1-Period Option Opportunity Cost of Capital:0 3.22% 2.84% 2.56% 2.35% 2.17%1 3.98% 3.39% 2.97% 2.66%2 4.94% 4.27% 3.58%3 5.82% 5.34%4 6.87%

Period ("j "):0 1 2 3 4

"down" moves ("i"): Optimal exercise:0 exer exer exer exer exer1 exer exer exer exer2 exer exer exer3 hold exer4 hold




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Problems with the Binomial ModelProblems with the Binomial Model

There are two major technical problems with the Binomial Model:There are two major technical problems with the Binomial Model:

1.1. Discrete time & values (the real world is continuous).Discrete time & values (the real world is continuous).

2.2. Finite expiration of the option (land is perpetual).Finite expiration of the option (land is perpetual).

Both of these can have significant effects on the option value aBoth of these can have significant effects on the option value and nd optimal exercise decision characteristics.optimal exercise decision characteristics.

The first problem (discreteness) can be addressed by making the The first problem (discreteness) can be addressed by making the periods periods of time very short (of time very short (mm ∞∞, , T/nT/n 0).0).

Perpetual expiration can be approximated by a long time horizon,Perpetual expiration can be approximated by a long time horizon, but but more accurate solution requires an entirely different type of momore accurate solution requires an entirely different type of model.del.

For modeling a simple option, sufficient for dealing with the For modeling a simple option, sufficient for dealing with the Wait OptionWait Option, , there is a simple solution to this problem:there is a simple solution to this problem:

A model of perpetual option value in continuous time that includA model of perpetual option value in continuous time that includes the es the value of the option to delay construction as well as a solution value of the option to delay construction as well as a solution to the to the decision problem of optimal development timing . . .decision problem of optimal development timing . . .



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27.5 The Samuelson27.5 The Samuelson--McKean Formula Applied to Land Value McKean Formula Applied to Land Value as a Development Optionas a Development Option

The simplest option valuation formula is also the first one deveThe simplest option valuation formula is also the first one developed loped (before (before BlackBlack--ScholesScholes), and the one that is most relevant to land valuation ), and the one that is most relevant to land valuation and optimal development timing:and optimal development timing:

The SamuelsonThe Samuelson--McKean FormulaMcKean Formula

Developed by Nobel Prize winning economist Paul Samuelson and hiDeveloped by Nobel Prize winning economist Paul Samuelson and his s mathematician partner Henry McKean, at MIT in 1965, as a model omathematician partner Henry McKean, at MIT in 1965, as a model of a f a ““perpetual American warrantperpetual American warrant””..

The SamuelsonThe Samuelson--McKean Model is consistent with the Binomial Model in McKean Model is consistent with the Binomial Model in that the latter would converge to the former if we could let that the latter would converge to the former if we could let TT ∞∞ and also and also T/nT/n 0. 0. (You can imagine how big a table this would require, since the (You can imagine how big a table this would require, since the binomial table has dimension binomial table has dimension nXnnXn, with approximately n, with approximately n22/2 elements in it .)/2 elements in it .)



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To see how this works, recall our replicating portfolio model ofTo see how this works, recall our replicating portfolio model of option valueoption value……

Today Next Year

Development Option Value C(0)=x“x” = unkown val.

C(t)UP=113.21-90 = $23.21

C(t)DOWN = 0(Don’t build)

Bond Value B = $51.21 B(t) = (1+rf )B = $52.74

B(t) = (1+rf )B = $52.74

Built Property Value V(0) = V0 / (1+yV) = $102.83/(1.09)

=$94.34

V(t)UP= $113.21 V(t)DOWN= $78.62

Replicating Portfolio:C(0) = (N)V(0) – B

C(0) = (N)V(0) – B = (0.7)$94.34 -$51.21 = $12.09

C(t)UP = (0.7)113.21 - $52.74 = $23.21

C(t)DOWN = (0.7)78.62 - $52.74 = 0

The Replicating Portfolio = NV-B, where: N=(Cu-Cd)/(Vu-Vd); B=(NVd-Cd)/(1+rf); and V = V(0) (not V0 ) . . .

BVVC

r

CVVVCC

VVVCCC

f

DOWNt

DOWNtDOWN

tUP

t

DOWNt

UPt

DOWNt

UPt

DOWNt

UPt −⎟

⎠⎞

⎜⎝⎛ΔΔ

=+

−⎟⎟⎠

⎞⎜⎜⎝

⎛−−

−⎟⎟⎠

⎞⎜⎜⎝

⎛−−

= )0(1

)0(0



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Note that as we approach continuous time (periods get very short), N becomes like the derivative of the option value with respect to the underlying asset value:Thus:

dtVdVdCV

CdVdC 22

21

2

2 σ∂∂+=

Combining our Replicating Portfolio formula C = NV – B with the above, and looking at changes over time (returns), we see:

dtVdB

dBdVdtVdVdC

VC

dVdC

VC

dVdC

2221

2221

2

2

2

2

σ

σ

∂∂

∂∂

−=⇒

−=+=

But we also know that the riskless bond value, B, given its Replicating Portfolio value of: B = NV – C, will change over time according to the riskfree interest rate, as:

( ) ( ) dtrCVdtrBdB fdVdC

f −==

We can also use the Taylor Series expansion from basic calculus (supplemented by some very advanced mathematics known as “Stochastic Calculus” ) to approximate the change in value of a (perpetual) option over time as:

dVdCN =

dBdVdBNdVdCBNVC dVdC −=−=⇒−= ,

Equating the above two expressions for dB, we obtain the following ordinary differential equation: ( )

02

2

2

2

2221

2221

=−+⇒

−=−=

∂∂

∂∂

CrVrV

dtrCVdtVdB

fdVdC

fVC

fdVdC

VC

σ

σ



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( ) ( )2

22221

dVCd

dVdC

ff VVrCr σ+=

The solution to this differential equation, combined with suitabThe solution to this differential equation, combined with suitable boundary le boundary conditions ( conditions ( C(V=0) = 0, C(V=C(V=0) = 0, C(V=∞∞) = V ) = V ) and) and the conditions of optimal the conditions of optimal exercise (expected exercise timing so as to maximize the presentexercise (expected exercise timing so as to maximize the present value of value of the option), gives the the option), gives the SamuelsonSamuelson--McKean FormulaMcKean Formula. .

This works as a model for land value because, like a perpetual AThis works as a model for land value because, like a perpetual American merican warrant, land never expires (warrant, land never expires (““perpetualperpetual””), and can be developed at any ), and can be developed at any time by its owner (exercise policy is time by its owner (exercise policy is ““AmericanAmerican””).).

Actually, the equation presented above ignores dividends and assumes a constant exercise price. To allow (more realistically for construction projects) for the

underlying asset to pay dividends (property net rent) and for construction costs to grow over time, some minor modifications must be made in the formula. These

are reflected in the model presented on subsequent slides.



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The SamuelsonThe Samuelson--McKean Model Applied to Land Value:McKean Model Applied to Land Value:

Let: Let: VV = Currently observable value of built property of the type that= Currently observable value of built property of the type that is the is the HBU for the land (underlying asset, what we have labeled HBU for the land (underlying asset, what we have labeled VV00 , not , not V(0)V(0) ).).

σσ = Volatility of (= Volatility of (Std.DevStd.Dev. of return to . of return to unleveredunlevered) ) individualindividual built properties built properties (= (= ““total risktotal risk””, not just systematic or non, not just systematic or non--diversifiable risk, includes diversifiable risk, includes idiosyncratic riskidiosyncratic risk: Typical range for real estate is 15% to 25% per year).: Typical range for real estate is 15% to 25% per year).

yyVV = Payout ratio of the built property (current cash yield rate, = Payout ratio of the built property (current cash yield rate, like like cap ratecap rateonly net of capital improvement reserve, typical real estate valonly net of capital improvement reserve, typical real estate values range from ues range from 4% to 12%).4% to 12%).

yyKK = = Construction cost Construction cost ““yieldyield”” rate (= rate (= rrff –– ggKK , where , where ggKK is the growth rate of is the growth rate of construction costs, typically approximately equal to inflation).construction costs, typically approximately equal to inflation).



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(3) The option (land) value is given by:(3) The option (land) value is given by:

Then the option value (and optimal exercise) formula has three sThen the option value (and optimal exercise) formula has three steps:teps:

(1) The (1) The ““option elasticityoption elasticity”” [[((dLAND/LAND)/(dV/VdLAND/LAND)/(dV/V))], ], ηη ((““etaeta””)), is given by:, is given by:

ηη == {{yyVV –– yyKK + + σσ22/2 + [(/2 + [(yyKK –– yyVV -- σσ22/2)/2)22 + 2y+ 2yKKσσ22]]1/21/2} / } / σσ22

(2) The option (2) The option critical valuecritical value ((““hurdle valuehurdle value””) of the built property at and ) of the built property at and above which it is optimal to immediately exercise the option (deabove which it is optimal to immediately exercise the option (develop the velop the land), labeled land), labeled V* V* , is:, is:

V*V* = = KKηη / (/ (ηη -- 1) 1)

The SamuelsonThe Samuelson--McKean Model Applied to Land Value:McKean Model Applied to Land Value:

( )

otherwiseKV

VVifVV-KV

= LAND

⎪⎪⎪

⎩

⎪⎪⎪

⎨

⎧

−

≤⎟⎠⎞

⎜⎝⎛

,

*,*

*η



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Example:Example:rrff = 3%, = 3%, yyVV = 6%, = 6%, σσ = 15%, = 15%, K = $80 (with K = $80 (with yyKK=1%,=1%, 2%growth) , V = $95, 2%growth) , V = $95,

ηη == {{yyVV –– yyKK + + σσ22/2 + [(/2 + [(yyKK –– yyVV –– σσ22/2)/2)22 + 2y+ 2yKKσσ22]]1/21/2} / } / σσ22

= {.06= {.06--.01+.15.01+.1522/2+[(.01/2+[(.01--.06.06-- .15.1522/2)/2)22+2(.01).15+2(.01).1522]]1/21/2}/.15}/.1522 = 5= 5.60..60.

V*V* == K[K[ηη/(/(ηη--1)] = $80[5.6/(5.61)] = $80[5.6/(5.6--1)] = $80(5.6/4.6) = $80(1.22) = 1)] = $80(5.6/4.6) = $80(1.22) = $97.38.$97.38.

LAND LAND == (V*(V*--K)(V/V*)K)(V/V*)ηη = ($97.38 = ($97.38 -- $80)($95/$97.38)$80)($95/$97.38)5.65.6 = = $15.13.$15.13.

In this example, In this example, Option Elasticity = 5.60, Hurdle Benefit/Cost Ratio = 1.22,Option Elasticity = 5.60, Hurdle Benefit/Cost Ratio = 1.22,Land Value = $0.16 per dollar of current built property value.Land Value = $0.16 per dollar of current built property value.

(Obviously you wouldn’t memorize this formula! Use the downloadable file from course web site.)

Note: In applying the SamNote: In applying the Sam--McKMcK Formula, in principle Formula, in principle VV and and KK should be should be defined based on the HBU that the site will ultimately be develodefined based on the HBU that the site will ultimately be developed for (not ped for (not

necessarily what it could immediately be developed for).*necessarily what it could immediately be developed for).*



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$0.00

$0.10

$0.20

$0.30

$0.40

$0.50

$0.60

$0.70

$0.00 $0.15 $0.30 $0.45 $0.60 $0.75 $0.90 $1.05 $1.20 $1.35 $1.50 $1.65

BUILT PROPERTY VALUE (V)

LAN

D (O

PTIO

N) V

ALU

E

Option Value Option Value at Expiration

NPV of Construction

LandValue

V*=$1.28"Hurdle"

DevlptOptimal

Here is a picture of what the SamuelsonHere is a picture of what the Samuelson--McKean Formula looks like:McKean Formula looks like:

Land value (LAND) is a monotonically increasing, convex function of the current HBU built property value (underlying asset value). Above the hurdle benefit/cost (V/K) ratio, the option should already be exercised, and its value is simply V-K.

Parameters in above chart are: σ = 15%, yV = 8%, yK = 5%.



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Both the option value, and the hurdle Both the option value, and the hurdle V/KV/K ratio, are ratio, are increasingincreasing functions of functions of the volatility (the volatility (σσ) and ) and decreasingdecreasing functions of the payout ratio (functions of the payout ratio (yy).).

$0.00

$0.10

$0.20

$0.30

$0.40

$0.50

$0.60

$0.70

$0.00 $0.15 $0.30 $0.45 $0.60 $0.75 $0.90 $1.05 $1.20 $1.35 $1.50 $1.65

BUILT PROPERTY VALUE (V)

LAN

D (O

PTIO

N) V

ALU

E (L

)

Opt Val @ 15% Vol Opt Val @ 20% Vol Option Value at Expiration

V* =$1.28

V* = $1.44

The hurdle benefit/cost ratio, and the land value as a fraction The hurdle benefit/cost ratio, and the land value as a fraction of the of the construction cost, are construction cost, are independentindependent of the of the scalescale of the site (in the sense of the of the site (in the sense of the size of the land parcel, holding HBU density constant).size of the land parcel, holding HBU density constant).

Assuming: yV = 8%, yK = 5%.



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Recall that with the Binomial Model there appeared to be a ““hurdle valuehurdle value””of the underlying asset above which it is optimal to exercise (develop) . . .

With the SamWith the Sam--McKMcK Model there is an explicit formula for this Model there is an explicit formula for this hurdle value . . .hurdle value . . .


0 1 2 3 4 5 6 7 8 9 10 11 12


Period ("j "): "n " =0 1 2 3 4 5 6 7 8 9 10 11 12


With 15% volatility, immediate exercise.

Here (with 15% volatility) the hurdle value of V seems to be about $90 (until the end).



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The The hurdle benefit/cost hurdle benefit/cost ratio:ratio:(V*/K)(V*/K) = = ηη / (/ (ηη--1)1)

is an interesting measure in its own right.is an interesting measure in its own right.

It tells you how much greater the anticipated completed new It tells you how much greater the anticipated completed new built property value (including land) must be than its built property value (including land) must be than its construction cost (excluding land), in order for it to be optimaconstruction cost (excluding land), in order for it to be optimal l to stop waiting to develop, and immediately begin to stop waiting to develop, and immediately begin (instantaneous) construction.(instantaneous) construction.

Expressing this in terms of the Expressing this in terms of the land value fractionland value fraction of the total of the total development project value at the time of optimal development, development project value at the time of optimal development, the optimal land value fraction is given by the inverse of the the optimal land value fraction is given by the inverse of the elasticity:elasticity:

ηηη 111

*1

**

=−

−=−=−

VK

VKV

e.g., Elasticity = 3 Hurdle B/C Ratio = 1.5 Optimal Land Fraction = 33%.www.bsscommunitycollege.in www.bssnewgeneration.in www.bsslifeskillscollege.in


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SamuelsonSamuelson--McKean Implications for Optimal DevelopmentMcKean Implications for Optimal Development

As noted, the option elasticity also determines the hurdle benefAs noted, the option elasticity also determines the hurdle benefit/cost it/cost ratio, ratio, V*/KV*/K, at which it is optimal to immediately begin development , at which it is optimal to immediately begin development whenever the current value of whenever the current value of VV and and KK equate to this ratio*:equate to this ratio*:

1*

−=ηη

KV

The hurdle benefit/cost ratio is thus an inverse function of theThe hurdle benefit/cost ratio is thus an inverse function of the option option elasticity: larger elasticity means a lower hurdle ratio.elasticity: larger elasticity means a lower hurdle ratio.



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SamuelsonSamuelson--McKean Implications for Optimal DevelopmentMcKean Implications for Optimal DevelopmentHurdle Ratio ( Hurdle Ratio ( V* / KV* / K ) as a function of underlying asset volatility ( ) as a function of underlying asset volatility ( σσ ):):

With: yV = 8%, yK = 2%.

1.00

1.05

1.10

1.15

1.20

1.25

1.30

1.35

1.40

1.45

1.50

10%

11%

12%

13%

14%

15%

16%

17%

18%

19%

20%

21%

22%

23%

24%

25%

Underlying Asset Volatility ("sigma")

Hur

dle

Rat

io (

V* /

K )



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SamuelsonSamuelson--McKean Implications for Optimal DevelopmentMcKean Implications for Optimal DevelopmentHurdle Ratio ( Hurdle Ratio ( V* / KV* / K )) as a function of underlying asset yield ( as a function of underlying asset yield ( yyVV ):):

With: σ = 15%, yK = 2%.

1.00

1.20

1.40

1.60

1.80

2.00

2.20

2% 3% 4% 5% 6% 7% 8% 9% 10%

11%

12%

Underlying Asset Yield ("y(V)"))

Hur

dle

Rat

io (

V* /

K )



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SamuelsonSamuelson--McKean Implications for Optimal DevelopmentMcKean Implications for Optimal DevelopmentHurdle Ratio ( Hurdle Ratio ( V* / KV* / K )) as a function of construction yield (as a function of construction yield (yyKK= = rrff –– ggKK ):):

With: yV = 8%, σ = 15%.

1.00

1.10

1.20

1.30

1.40

1.50

1.60

1.70

0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%

Construction Yield ("y(K)")

Hur

dle

Rat

io (

V* /

K )



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The The hurdle benefit/cost hurdle benefit/cost ratio (& ratio (& optimal land fraction)optimal land fraction) is:is:•• Greater the more volatile is the built property market (i.e., tGreater the more volatile is the built property market (i.e., the more he more uncertainty there is in the future value of built properties):uncertainty there is in the future value of built properties):

•• As long as you hold the option unexercised, greater volatility As long as you hold the option unexercised, greater volatility gives you gives you greater potential upside outcomes you can take advantage of whilgreater potential upside outcomes you can take advantage of while the option e the option flexibility allows you to avoid the greater downside outcomes imflexibility allows you to avoid the greater downside outcomes implied by the plied by the greater volatility.greater volatility.•• Uncertain and volatile property markets will dampen developmentUncertain and volatile property markets will dampen development, as , as developers wait until they can get built property values (based developers wait until they can get built property values (based on space market on space market rents) sufficiently above the construction cost exclusive of lanrents) sufficiently above the construction cost exclusive of land).d).

•• Lower the greater is the current cash yield (akin to Lower the greater is the current cash yield (akin to cap ratecap rate) being ) being provided by built properties:provided by built properties:

•• You You onlyonly start to get the net rent the property can generate when the start to get the net rent the property can generate when the building is complete, so the greater the current yield, the greabuilding is complete, so the greater the current yield, the greater the incentive ter the incentive to build sooner rather than later.to build sooner rather than later.•• Land value (site acquisition cost) will be a smaller fraction oLand value (site acquisition cost) will be a smaller fraction of total f total development cost (including construction) in locations where buidevelopment cost (including construction) in locations where built property lt property values tend to grow slower (holding risk constant, lower values tend to grow slower (holding risk constant, lower ““gg”” higher higher ““yy””, as , as g+yg+y=r, recalling Ch.9).=r, recalling Ch.9).



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Example:Example:In the U.S., land (site acquisition) is typically about 20% of tIn the U.S., land (site acquisition) is typically about 20% of the total he total development cost in most areas of the country, but often 50% in development cost in most areas of the country, but often 50% in major major metropolises on the East and West Coast. Why?...metropolises on the East and West Coast. Why?...

Big East & West Coast Cities Rest of U.S.

Property Mkt Volatility (σ) 20% 15%

Property Payout Rate (y) 5% 8%

Big East & West Coast Cities

Rest of U.S.

LAND/V* @ V=V* (optimal dvlpt)

46% 22%

Then the SamuelsonThen the Samuelson--McKean Formula gives the following difference in land McKean Formula gives the following difference in land value fraction of total developed property value at the time of value fraction of total developed property value at the time of optimal optimal development (based on the implied development (based on the implied V*/KV*/K hurdle ratio):hurdle ratio):

Suppose Suppose rfrf = 5%, and property market volatility and payout rates differ as = 5%, and property market volatility and payout rates differ as follows:follows:



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The The option elasticityoption elasticity measure, measure, ηη, is also interesting in its own right., is also interesting in its own right.

Prior to the point of optimal exercise (when the land is still Prior to the point of optimal exercise (when the land is still optimally held undeveloped for speculation), the elasticity telloptimally held undeveloped for speculation), the elasticity tells the s the percentage change in land value resulting from a given percentage change in land value resulting from a given percentage change in built property value (for the type of percentage change in built property value (for the type of property that would be the HBU of the land).property that would be the HBU of the land).

For a For a ““livelive”” option (below the hurdle ratio) the elasticity is:option (below the hurdle ratio) the elasticity is:

•• Independent of the size of the land parcel (for a given HBU Independent of the size of the land parcel (for a given HBU density);density);

•• Independent of the current value of the underlying asset (the Independent of the current value of the underlying asset (the state of the property market).*state of the property market).*

•• A decreasing function of the volatility in the property A decreasing function of the volatility in the property market.market.



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The option elasticity relates the volatility (and risk) of the The option elasticity relates the volatility (and risk) of the option (the undeveloped land investment) to the volatility (and option (the undeveloped land investment) to the volatility (and risk) of the underlying asset (the built property market for therisk) of the underlying asset (the built property market for theHBU of the site).HBU of the site).

Assuming Assuming risklessriskless construction costs:construction costs:

σσLANDLAND = = ησησV ,V ,

WhereWhere σσLANDLAND is the volatility of the undeveloped land.is the volatility of the undeveloped land.

Since the option return is perfectly correlated with the Since the option return is perfectly correlated with the underlying asset return, the option elasticity can therefore alsunderlying asset return, the option elasticity can therefore also o be used to relate the required expected investment return risk be used to relate the required expected investment return risk premium in undeveloped land to that in the HBU built property premium in undeveloped land to that in the HBU built property market:market:

RPRPLANDLAND = = ηηRPRPVV ..



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Example:Example:Built property expected return Built property expected return rrVV = 8%, Cash yield = 8%, Cash yield yyVV = 6%= 6%RiskfreeRiskfree interest rate = 4%, interest rate = 4%, Built property Built property RPRPVV = 4%.= 4%.Construction yield Construction yield yyKK = 2%.= 2%.

(Which might be determined as the 4% (Which might be determined as the 4% riskfreeriskfree rate minus a 2% likely rate minus a 2% likely construction cost growth rate: construction cost growth rate: yyKK = = rrff –– ggKK = 4% = 4% -- 2% = 2%.)2% = 2%.)

If built property volatility If built property volatility σσ = 15%, then: (= 15%, then: (σσ =.15, =.15, yyVV =.06, =.06, yyKK =.02) =.02) ηη = 4.9= 4.9..Thus,Thus, RPRPLANDLAND = = ηη((RPRPVV) ) = 4.9(4%) = 19.7% = 4.9(4%) = 19.7% Expected return (OCC) on land speculation investment =Expected return (OCC) on land speculation investment =

rrff + RP+ RPLANDLAND = 4% + 19.7% = 23= 4% + 19.7% = 23.7%..7%.

Based on the SamuelsonBased on the Samuelson--McKean assumptions, this required expected return for land McKean assumptions, this required expected return for land speculation would hold no matter how big or small the land parcespeculation would hold no matter how big or small the land parcel (for a given HBU l (for a given HBU density), or what the current state of the built property marketdensity), or what the current state of the built property market is, as long as is, as long as σσ, y, , y, rrff , , andandRPRPVV remain the same. The Samremain the same. The Sam--McKMcK Formula is a Formula is a ““constant elasticityconstant elasticity”” formula.formula.



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SamuelsonSamuelson--McKean Implications for Land OCCMcKean Implications for Land OCC

As noted, the option elasticity, As noted, the option elasticity, ηη , gives the ratio of the land risk to the , gives the ratio of the land risk to the underlying asset risk, hence the ratio of the land to underlyingunderlying asset risk, hence the ratio of the land to underlying asset asset expected risk premium in the opportunity cost of capital (in theexpected risk premium in the opportunity cost of capital (in theexpected investment return):expected investment return):

][][

V

C

RPERPE

=η

We also noted that for a We also noted that for a ““live optionlive option”” (not yet ripe for exercise) (not yet ripe for exercise) ηη is is independent ofindependent of both:both:

•• Scale (value of Scale (value of VV or of or of KK ), and), and•• Current benefit cost ratio (amount of Current benefit cost ratio (amount of ““operational operational leverageleverage”” in the construction project: in the construction project: V / KV / K

In fact, In fact, ηη is a function of only three variables: is a function of only three variables: σσ, , yyVV , and , and yyKK ..

This makes the option elasticity in the SamuelsonThis makes the option elasticity in the Samuelson--McKean Formula a McKean Formula a very useful tool for understanding and quantifying land investmevery useful tool for understanding and quantifying land investment nt risk and return requirements.risk and return requirements.



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SamuelsonSamuelson--McKean Implications for Land OCCMcKean Implications for Land OCCOption elasticity ( E[RPOption elasticity ( E[RPCC] / E[RP] / E[RPVV] ) as a function of underlying asset ] ) as a function of underlying asset volatility ( volatility ( σσ ):):

With: yV = 8%, yK = 2%.

0

2

4

6

8

10

12

14

10%

11%

12%

13%

14%

15%

16%

17%

18%

19%

20%

21%

22%

23%

24%

25%

Underlying Asset Volatility ("sigma")

Opt

ion

Elas

ticity

("et

a" )



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Option elasticity ( E[RPOption elasticity ( E[RPCC] / E[RP] / E[RPVV] ) as a function of underlying asset ] ) as a function of underlying asset yield ( yield ( yyVV ):):

With: σ = 15%, yK = 2%.

0

2

4

6

8

10

12

2.0%

3.0%

4.0%

5.0%

6.0%

7.0%

8.0%

9.0%

10.0

%

11.0

%

12.0

%

Underlying Asset Yield ("y(V)")

Opt

ion

Elas

ticity

("et

a" )




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Option elasticity ( E[RPOption elasticity ( E[RPCC] / E[RP] / E[RPVV] ) as a function of construction yield ] ) as a function of construction yield ((yyKK = = rrff –– ggKK ):):

With: yV = 8%, σ = 15%.


0

1

2

3

4

5

6

7

8

9

0.0%

1.0%

2.0%

3.0%

4.0%

5.0%

6.0%

7.0%

8.0%

9.0%

10.0

%

Construction Yield ("y(K)")

Opt

ion

Elas

ticity

("et

a" )



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CD27.5 Generalizing the SamuelsonCD27.5 Generalizing the Samuelson--McKean Model to allow McKean Model to allow for risky construction costs . . .for risky construction costs . . .

The SamThe Sam--McKMcK Model can allow for risky construction costs by use of a Model can allow for risky construction costs by use of a simple transformation: Value the option simple transformation: Value the option per dollar of construction costper dollar of construction cost, as , as follows:*follows:*

1.1. Divide the current underlying asset value by the current Divide the current underlying asset value by the current construction cost, replacing construction cost, replacing VV in the formula with in the formula with V/KV/K, and , and replacing replacing KK in the formula with in the formula with 11..

2.2. In computing the In computing the ““construction yieldconstruction yield””, , yyKK , use the expected , use the expected return on an asset with market risk equivalent to that of the return on an asset with market risk equivalent to that of the construction cost, instead of the construction cost, instead of the riskfreeriskfree rate. i.e., rate. i.e., yyKK = = rrKK –– ggKK= = rrff + + E[RPE[RPKK] ] –– ggKK ..

3.3. In computing In computing σσ, use the volatility of a portfolio of the underlying , use the volatility of a portfolio of the underlying asset minus the construction cost:asset minus the construction cost:

],[2][][ KVKV rrCOVrVARrVAR −+=σ

( This transformation is attributed to Fisher and Margrabe* .)www.bsscommunitycollege.in www.bssnewgeneration.in www.bsslifeskillscollege.in


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Summarizing up to now:Summarizing up to now:•• The Binomial Model can handle:The Binomial Model can handle:

•• FiniteFinite--lived development options (rights expire at a lived development options (rights expire at a specified future time), specified future time), ““AmericanAmerican”” oror……•• ““EuropeanEuropean”” development options (construction development options (construction prohibited prior to a given future point in time)prohibited prior to a given future point in time)

•• The SamuelsonThe Samuelson--McKean Model can handle:McKean Model can handle:•• The simple The simple ““Wait OptionWait Option”” for a perpetual for a perpetual ““AmericanAmerican””development option (typical development option (typical ““land valueland value”” problem).problem).

It remains for us to address two important considerations:It remains for us to address two important considerations:

•• Until now we have assumed instantaneous exercise: we need to Until now we have assumed instantaneous exercise: we need to consider the effect of construction time, consider the effect of construction time, akaaka ““time to buildtime to build”” ..

•• The The ““Phasing OptionPhasing Option””, in which the project is broken into , in which the project is broken into sequential sequential phasesphases rather than building it all at oncerather than building it all at once



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CD27.5 CD27.5 Time to Build . . .Time to Build . . .

With nonWith non--instantaneous construction, when you exercise the option to instantaneous construction, when you exercise the option to build in state of the world build in state of the world i, ji, j , you don, you don’’t get t get VVi,ji,j –– KKjj . .

You get the PV of the completed project: You get the PV of the completed project:

((EEi,ji,j[[VVj+TCj+TC])/(1+])/(1+rrVV))TCTC –– KKj+TCj+TC /(1+/(1+rrff))TCTC

where where TCTC is the number of periods it will take to complete construction.is the number of periods it will take to complete construction.

In the Binomial Model, if you exercise the option at time 0 whenIn the Binomial Model, if you exercise the option at time 0 when the the underlying asset has current observable value underlying asset has current observable value VV00 , then if the time to , then if the time to build is 1 period you will get:build is 1 period you will get:

( ) ( ) ( ) ( ) ( )KVfVfV

VV

fV yK

yV

rK

rVppV

rK

ryVdpyuVp

rK

rVEKVPV

+−

+=

+−

+−+

=+

−+

+−++=

+−

+=−

11111

11111

11][][ 0011,11,0100110

11

If the time to build is 2 periods, you will get:If the time to build is 2 periods, you will get:

( ) ( )( )( ) ( )

( ) ( ) ( ) ( )20

20

22

22,2

22,12,0

2

22

220

22 1111112

11][][

KVfVfV yK

yV

rK

rVpVppVp

rK

rVEKVPV

+−

+=

+−

+

−+−+=

+−

+=−



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For example, consider our previous underlying asset value tree For example, consider our previous underlying asset value tree and a timeand a time--toto--build of 2 months with build of 2 months with rrVV = 10%/yr = 0.833%/mo, = 10%/yr = 0.833%/mo, yyVV = 6%/yr = 0.5%/mo (= 6%/yr = 0.5%/mo ( ggVV = 0.33%/mo= 0.33%/mo)) ……

VV1,21,2==$99.01$99.01

VV00==$100$100

VV0,10,1==$103.81$103.81

VV1,11,1==$95.37$95.37

pp = = .5877.5877

11--pp = = .4123.4123

11--pp = = .4123.4123

pp = = .5877.5877

VV2,22,2==$90.96$90.96

VV0,20,2==$107.77$107.77

11--pp = = .4123.4123

pp = = .5877.5877


A decision at time 0 to build the asset A decision at time 0 to build the asset obtains an asset at month 2obtains an asset at month 2that is worth at that is worth at time 0: $99.01time 0: $99.01

( ) ( )

( ) ( )20

222

2

2

22

220

20

2

2

1005.100.100$01.99$

00833.166.100$

00833.1100$)0033.1(

00833.196.90)4123(.01.99)4123)(.5877(.277.107)5877(.

1][

1)1(][

V

VV

V

yV

rVE

rVgVPV

+=====

++=

+=

++

=



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Summarizing:Summarizing:

To account for time to build in the option model:To account for time to build in the option model:

•• In any state In any state i, ji, j where the option could be where the option could be exercised, replace the immediate exercise value exercised, replace the immediate exercise value VVi,ji,j –– KKjj with the present value as of time with the present value as of time jj of the of the exercise value exercise value TCTC periods later (where periods later (where TCTC is the is the required construction time) : required construction time) : PVPVi,ji,j [[VVj+TCj+TC –– KKj+TCj+TC], as ], as defined in the previous slides.defined in the previous slides.

•• In the SamuelsonIn the Samuelson--McKean Formula, replace the McKean Formula, replace the current value of the underlying asset, current value of the underlying asset, VVijij , with: , with: VVijij // (1 + (1 + yyVV))TCTC , and replace the exercise price , and replace the exercise price KKjjwith with KKjj // (1 + (1 + yyKK))TCTC ..



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The general effect of timeThe general effect of time--toto--build is:build is:

•• The value of the option is reduced below what it The value of the option is reduced below what it otherwise would be.otherwise would be.

•• The expected time until optimal exercise is The expected time until optimal exercise is increased beyond what it otherwise would be increased beyond what it otherwise would be (hurdle value of (hurdle value of VVtt as measured by current as measured by current observable price of preobservable price of pre--existing assets is increased):existing assets is increased):

• Condition of optimal exercise, where “Vt” is current observable price of identical pre-existing asset:

• η/(η-1) = (Vt /(1+yV)TC ) / (Kt/(1+yK)TC )

• Vt = Kt[η/(η-1)]((1+yV)/(1+yK))TC ,

• and normally: yV > yK .www.bsscommunitycollege.in www.bssnewgeneration.in www.bsslifeskillscollege.in


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Old GM 1e 28.2.2 The Land Development Option Contrasted with FinOld GM 1e 28.2.2 The Land Development Option Contrasted with Financial Options: ancial Options:

Distinguishing characteristics of the land Distinguishing characteristics of the land devlptdevlpt option:option:•• Perpetual (no Perpetual (no expiriationexpiriation):):

•• More flexibility (greater value),More flexibility (greater value),•• Only reason to exercise is to obtain operating cash flows.Only reason to exercise is to obtain operating cash flows.

•• ““Time to BuildTime to Build”” (exercise not immediate):(exercise not immediate):•• CanCan’’t observe exact att observe exact at--completion completion mktmkt valval of of underl.assetunderl.asset at at time exercise decision is made (added risk in exercise decision)time exercise decision is made (added risk in exercise decision)..

•• ““NoisyNoisy”” value observation of (even current) value observation of (even current) mktmkt valval of of underlunderl. asset. . asset. ((““thin thin mktmkt””, recall Ch.12,, recall Ch.12, also adds to risk of exercise decision):also adds to risk of exercise decision):

•• Possibly heterogeneous information about Possibly heterogeneous information about truetrue value of value of underlying asset (the tounderlying asset (the to--bebe--built property): Some built property): Some devlprsdevlprs may be may be more more knowledgableknowledgable than others. than others. (( Wait longer until exercise.)Wait longer until exercise.)

•• Exercise Exercise creates new real assetscreates new real assets that add to the supply side of the that add to the supply side of the space market (affecting space market (affecting mktmkt valval of all competing properties):of all competing properties):

•• Can increase risk of Can increase risk of notnot exercising (option may effectively exercising (option may effectively ““expireexpire”” if demand is absorbed by competing if demand is absorbed by competing devlptdevlpt projects).projects).



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27.6 What the real option theory of land development can tell us27.6 What the real option theory of land development can tell usabout the about the ““overbuilding phenomenonoverbuilding phenomenon””. . .. . .

What is the What is the ““overbuilding phenomenonoverbuilding phenomenon””?...?...

The widely observed tendency for commercial real estate The widely observed tendency for commercial real estate markets to periodically become markets to periodically become ““overbuiltoverbuilt””, that is, , that is, characterized by characterized by excess supplyexcess supply (abnormally high vacancy, (abnormally high vacancy, downward pressure on rents), due to excessive speculative downward pressure on rents), due to excessive speculative development of new buildings.development of new buildings.

Recall that in Chapter 2 we discussed an explanation for this Recall that in Chapter 2 we discussed an explanation for this ““cyclicalitycyclicality”” phenomenon using the phenomenon using the ““44--Quadrant DiagramQuadrant Diagram””, , based on the existence of based on the existence of myopic behaviormyopic behavior (not just lack of (not just lack of perfect foresight, but some degree of perfect foresight, but some degree of irrational expectationsirrational expectations) ) on the part of investors and developers in the system . . .on the part of investors and developers in the system . . .



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Real option theory offers several explanations for why/how Real option theory offers several explanations for why/how overbuilding can be due to completely overbuilding can be due to completely rationalrational (i.e., profit(i.e., profit--maximizing) behavior on the part of developers (landowners):maximizing) behavior on the part of developers (landowners):

1.1. ““CascadesCascades””: : Noisy observations of the Noisy observations of the mktmkt values of the underlying assets values of the underlying assets (comparable built properties), combined with heterogeneous devel(comparable built properties), combined with heterogeneous developer oper knowledge about the knowledge about the ““truetrue”” value, causes a value, causes a followfollow--thethe--leaderleader type effect, in type effect, in which developers wait longer than they otherwise would to develowhich developers wait longer than they otherwise would to develop, and p, and then they all rush in as soon as the first (presumably most knowthen they all rush in as soon as the first (presumably most knowledgeable) ledgeable) developer reveals his knowledge by commencing development.developer reveals his knowledge by commencing development.

2.2. ““Lumpy supply & first out of the gateLumpy supply & first out of the gate””:: Economies of scale in building Economies of scale in building size, combined with finite user demand and the fact that option size, combined with finite user demand and the fact that option exercise exercise creates real physical capital, leads to early exercise of the decreates real physical capital, leads to early exercise of the development velopment option to preclude loss (expiration) of the option if a competitoption to preclude loss (expiration) of the option if a competitor builds first.or builds first.

3.3. ““LongLong--term leasing optionterm leasing option””:: The cost of having empty space in a new The cost of having empty space in a new building may be less than it first appears in space markets charbuilding may be less than it first appears in space markets characterized by acterized by longlong--term leases, as it gives the landlord a term leases, as it gives the landlord a leasing optionleasing option, that has value , that has value prior to its prior to its ““exerciseexercise”” (in the signing of a lease contract): Volatility in the (in the signing of a lease contract): Volatility in the rental rental mktmkt may bring better longmay bring better long--term lease deals in the future.term lease deals in the future.



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Real Estate Finance 11.431/15.426J Fall 2006

Problem Set 2 (Ch13, 14)

1. The Donald Grump Corporation, a publicly-traded REIT, has expected total return to equity of 13%, average interest rate on their debt of 7.5%, and a Debt/Total Asset Value ratio of 40%. What is Grump’s (firm-level) average cost of capital? 2. Consider a commercial (non-residential) property that costs $1 Million with an initial before-tax yield of 8% (based on NOI), and an expected growth rate of 1% per year (in income and value). Ignoring capital improvements and selling expenses, develop a 10-year proforma for before-tax and after-tax property and equity cash flows. Assume a 40% income tax rate on ordinary income and 20% on capital gains, and financing of 70% of the property price with a 9% interest-only loan, and that land is worth 25% of the property value. Use the proforma to determine: (a)the ex ante before-tax IRR of the unlevered property investment; (b)the after-tax IRR of the unlevered property investment; (c) Compute the before-tax ex ante IRR of the levered investment in this property; and (d) the after-tax ex ante IRR of the levered equity in this property; and (e) the ratio of the AT/BT in the levered IRR, and note the difference between this ratio and the unlevered equivalent: (f) Do you think this is an argument for debt financing for this property investment for this investor? Why not? [Hint: Note that this problem here is simplified from 14.11, leaving out the questions about PV(DTS), which you can skip. I strongly recommend that you use Excel or your favorite computer spreadsheet to do this problem. It will be much faster that way, and good practice for your computer spreadsheet skills.] 3. The table below presents recent survey information regarding what professional investors state is their typical expected total returns for “institutional” and “non-institutional” commercial property of various types and locations. (This is from Exhibit 11-6a, on page 130, discussed in section 11.2.5 of Chapter 11.) Let’s ignore the fact that these expectations may be a bit exaggerated (as discussed in sections 11.2.3 and 11.2.4 on pp.127-129). Assuming a riskfree rate of 5% (short-term US T-bill yield in 1999), and based on the average across the types of properties in the table, how much more risk did investors in 1999 apparently perceive “non-institutional” property to be, as compared to “institutional” property? (That is, what is the ratio of the amount of risk in non-institutional property divided by that in institutional property?) In computing your answer, I suggest you copy/paste the data in the table below from the assignment Word file into Excel. This will be much quicker and less subject to error than doing the necessary computations by hand, even using a calculator. Going-in IRR (Exhibit 11-6a):

Property Type: Prop. Quality: Malls Strip Ctrs Indust. Apts CBD Office Suburb.Off. Hou.Off SF Off Institutional 11.14% 11.61% 11.14% 11.48% 11.28% 11.11% 11.78% 10.71% Non-institutional 13.50% 14.20% 12.18% 13.01% 13.69% 12.73% 13.75% 12.46% *From Korpacz Investor Survey, First Quarter 1999 4. (a) Assuming riskless debt, if the loan/value ratio is 75%, approximately how much more risk will there be in the equity return than if the loan/value ratio were 50%? Put another way: If the return to equity can vary per year within a range of ±15% with a 50% loan/value ratio, then within what range can it vary with an 75% loan/value ratio? (b) How much larger should the market's required risk premium be in the required return to equity with 75% debt as compared to 50% debt?



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5. A certain real estate limited partnership (LP) advertises that it has a target of matching the stock market in total return for its limited partner investors, before-taxes. (Suppose that the stock market risk premium is expected to be 6%.) The conservative office and warehouse properties which the partnership plans to acquire typically command risk premia in their before-tax expected returns of about 3.5 percent. Assuming riskless debt, what loan-to-value ratio must the LP plan to maintain in its property investments in order to have a good chance of meeting its stated target? 6. Answer the preceding question assuming the riskfree interest rate is 6% and the debt would have an interest rate of 8%. 7. (a) If the cap rate on a certain property is 9%, and loans are available at a mortgage constant of 10%, then approximately what is the expected income component of your before-tax return if you borrow 70% of the property price? (b) What if you only borrow 60%? 8. Answer part (a) of the preceding question, only now with respect to the growth component of the equity return, assuming the loan interest rate is 10% and the expected total return on the property is 9.5%. (b) What if the property cap rate were 10% instead of 9%? 9. The NOI is $850,000, the debt service is $600,000 of which $550,000 is interest, the depreciation expense is $350,000. What is the Before-tax Cash Flow to the equity investor (EBTCF) if there are no capital improvement expenditures or reversion items this period? 10. In the problem above, what is the after-tax cash flow to the equity investor if the income tax rate is 35%? 11. A non-residential commercial property which cost $500,000 is considered to have 30 percent of its total value attributable to land. What is the annual depreciation expense chargeable against taxable income? 12. Consider an apartment property which costs $400,000, of which $300,000 is structure value (the rest is land). Suppose an investor expects to hold this property for 5 years and then sell it for at least what she paid for it (without putting any significant capital into the property). If the investor's marginal income tax rate is 39%, and the capital gains tax rate applicable to depreciation recapture is 25%, what is the present value, as of the time of purchase, of the depreciation tax shields obtained directly by this investor during the 5-year expected holding period (including the payback in the reversion)? Assume taxes are paid annually, with the first tax payment in one year from present, and assume that DTS for this investor are effectively riskless, and the investor’s after-tax borrowing rate is 5%.



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Private Practice (A)

It wasn’t the first time. It was Friday afternoon and Duna Wright wished his classmates well as they again departed without him. Last Saturday it was to the Head of the Charles regatta followed by the Miracle of Science for burgers and beers. This weekend a rented SUV would guide the spirited group of budding real estate entrepreneurs to the brilliant fall foliage in northern New England. It was only a month ago that the offer of a (significantly reduced) weekly paycheck and full health benefits seemed too good to pass up. Yet Duna Wright was now starting to wish he’d never agreed to continue to help analyze investment deals for Ottathe Money Managers once he had left for graduate school in Cambridge.

On Monday morning Duna would need to email bids on three potential acquisition opportunities to his former boss, N.P. Venter. Duna had previously prepared a preliminary bid on one of the properties, Pace Place. But Venter had just informed him that, on behalf of one of their private clients, Ottathe Money Managers was a finalist in the bidding to acquire that property as well as two others that had recently been identified. Revising his previous bid for Pace Place would be relatively easy; it was preparing bids on two new properties, Ciller Centre and Rowe House, which concerned Duna the most.

N.P. Venter was notoriously impatient, and she was starting to get a bit concerned about Duna turning the new analyses around by Monday.

Pace Place

Pace Place is a 7-year-old multi-tenanted office building. It contains 200,000 square feet of net rentable area and is about 98% leased to more than a dozen tenants. The property is well located within its competitive market area and is considered desirable by office tenants.

Since Duna’s preparation of the preliminary bid, an additional lease was signed with an existing tenant to expand into the balance of the floor it occupies. The tenant will pay a gross market rental rate of $25 per square foot and has agreed to accept the additional space in as-is condition. Leases in that market are generally written for a term of five years, although longer leases from larger tenants are also quite common. An updated projection of property cash flow prepared by one of Ottathe’s junior analysts, Cameron Rogers, is presented in Exhibit 1.

This case was prepared by W. Tod McGrath for the purpose of class discussion. Characters and events are fictional. © MIT Center for Real Estate. Revised September 2006.



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Ciller Centre

Ciller Centre is a very well-located 12-year-old distribution building leased to two national firms. The leases are structured as “triple net” (NNN), meaning that, in addition to the annual base rent payable to the landlord, each tenant is responsible for the payment of its pro rata share of the property’s operating expenses and real estate taxes, which currently total $3.00 per rentable square foot. A reserve for the replacement of base building components has been estimated at $0.25 per square foot per year by Ottathe’s independent engineers, which, under the terms of the leases, cannot be passed through to the tenants.

Di Carlo Discounters occupies 60,000 rentable square feet in the building. It has three years remaining on its lease and is paying an annual NNN rent of $6.00 per rentable square foot. Di Carlo Discounters has been a tenant in the building since the day it was completed. It is in its second 5-year lease renewal term, and has two additional 5-year lease renewal options at 90% of fair market rental value.

Weikal Widgets occupies the remaining 40,000 square feet of net rentable area. It entered into a 7-year lease two years ago. It is currently paying an annual rent per square foot of $6.75 NNN. Weikal Widgets has two 5-year renewal options at 90% of fair market rental value.

Clayton Nash, a local commercial real estate broker, estimated for Venter that the current fair market NNN rent for the building was about $7.00 per rentable square foot. Nash also suggested that the 2% historic average annual rate of growth in market rents would be a prudent estimate of future market rent growth. Under the terms of the renewal options contained in each lease, any required expenditures for tenant improvements and/or leasing commissions would be the responsibility of the tenant.

Nash further advised that the probability of renewal for each tenant was somewhere between 50% and 100%. In the event of non-renewal, however, Nash felt that a replacement tenant could be identified and put under lease within 6 months of the termination of either of the existing leases, due to the early notification requirements contained therein. In such a situation, expenditures for landlord-funded tenant improvements and leasing commissions would arise. Current market allowances for such items were $5 PSF and $2 PSF, respectively, and were expected to escalate over time at a rate consistent with property operating expenses and taxes (about 2% per year).

Both Di Carlo Discounters and Weikal Widgets enjoy investment grade credit ratings of BBB-, implying that their corporate bondholders would expect to earn a return of about 6.5% if either firm issued 5-year bonds.

Rowe House

Rowe House is a newly-constructed 100-unit mixed income apartment complex. Upon full lease-up, 80 of the units will be rented at average market rents of $1,500 per month,

2



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and the remaining 20 affordable units will be rented at average low-income rents of $500 per month. The initial lease-up should be completed by the closing of the acquisition.

In exchange for contracting with his management subsidiary to manage the property for a market-based management fee, the developer has personally guaranteed that the property will generate annual effective gross income of at least $1,500,000 during the first two years of operations. The long-run average vacancy rate for market-rate units in the submarket in which the property is located has been about 6%; for affordable units, the long-run average vacancy rate has been about 2%.

According to N.P. Venter, rental rates on the 80 market-rate units can be expected to increase by about 2% per year, while rental rates on the 20 affordable units can be expected to increase by only about half as much. Annual operating expenses1 and property taxes are budgeted at $4,500 per unit per year and can be expected to increase by about 3% per year. The standard tenant lease is for one year and does not permit the landlord to pass through increases in operating expenses or property taxes.

Due Diligence

Before laying out the relevant cash flows to analyze, Duna Wright took a moment to consider some of the broader assumptions he would use to generate such cash flows. Specifically, he assumed that:

¾ Investment decisions would generally be made on the basis of 10-year discounted cash flow analyses;

¾ In recognition of the high degree of uncertainty associated with forecasting future asset values, estimates of future sales prices would be based on eleventh year projected net operating incomes capitalized at a rates consistent with currently applicable discount rates minus the projected compound average annual change in property before-tax cash flow over the 10-year holding period;

¾ Costs of sale would be 2% of the estimated future sales prices;

¾ Projected annual capital (replacement) reserve funding would be expended on each property in the year funded; and

¾ Due diligence and legal fees paid to third-parties would be approximately $100,000 if Ottathe Money Managers were selected as the preferred buyer (i.e., “awarded” the deal).

1 Consistent with multi-family industry practice, such operating expenses include Wheeler’s estimate of required annual replacement reserve funding of $300 per unit per year (escalated at 3% per annum) as an expense in calculating Net Operating Income.

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2 Based on the first year’s projected net operating income.

Required Investment Returns and Bid Prices

Venter had earlier instructed Duna to establish appropriate bid prices for each property using unlevered pre-tax cash flows in conjunction with pre-tax discount rates that were consistent with the expected total returns for unlevered fully-leased institutional quality properties.

That was a big help, thought Duna.

Duna knew, however, that prevailing market capitalization rates2 in the institutional property markets were in the 6% to 8% range, and that realistic growth expectations for operating cash flows and asset values were typically about 1% or so less than the expected rate of inflation. Duna also knew that the current yield on the 10-year U.S. Treasury Note was about 4.75% and the yield on the 10-year U.S. Inflation-Indexed Treasury Note was about 2.25%, which indicated to him that the U.S. debt markets expected an average annual rate of inflation of around 2.5% over the next ten years.

Duna understood that both the projected investment returns and bid prices applicable to each property would need to be presented in a summary matrix as part of a summary investment memorandum, which was not to exceed 3 pages of text. Included in the summary memorandum would be a discussion of (i) the projected annual net investment flows associated with investing in such properties, (ii) projected investment return performance attribution, (iii) suggested rank-ordering of preference for the three properties based on the client’s stated need to enhance its ability to service its increasing long-term (as opposed to near-term) annual financial obligations, and (iv) any specific risk factors or other issues worthy of mention. Supporting financial analyses would be attached as exhibits.

Due Process

It was Friday night. The phone rang. It was Venter. She was anxious.

The client had called late in the afternoon to say it really wanted to get money invested quickly in good properties that could be acquired at prices that would deliver fair risk-adjusted investment returns. Based on the potential acquisition and investment management fees payable to Ottathe Money Managers in connection with such acquisitions, Venter wanted to get the client’s money invested quickly, too.

Venter made a point of thanking Duna again for all his help and, in her typically pretentious fashion, made a point to confirm that their new compensation and benefits agreement was comforting to Duna during his quest for higher education. You know, that they both really valued the commitment the other had made, and all that sort of stuff. Duna flinched a little on the other end of the phone, but politely agreed. It wasn’t the first time.

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Exhibit 1

Projection of Property Before-Tax Cash Flow

Pace Place

Year 1

Year 2

Year 3

Year 4

Year 5

Year 6

Year 7

Year 8

Year 9

Year 10

Year 11

Gross Rental Revenues

Less Vacancy Plus Expense Reimbursements

$4,323,000 (88,000) 287,000

$4,467,000 (90,000) 311,000

$4,512,000 (94,000) 336,000

$4,876,000 (602,000) 175,000

$4,912,000 (123,000) 201,000

$4,995,000 (136,000) 228,000

$5,147,000 (147,000) 256,000

$5,209,000 (160,000) 285,000

$5,536,000 (685,000) 156,000

$5,662,000 (303,000) 186,000

$5,988,000(189,000)217,000

Effective Gross Income 4,522,000 4,688,000 4,754,000 4,449,000 4,990,000 5,087,000 5,256,000 5,334,000 5,007,000 5,545,000 6,016,000

Less Operating Expenses Less Property Taxes

(1,300,000) (800,000)

(1,339,000) (824,000)

(1,379,000) (849,000)

(1,391,000) (874,000)

(1,463,000) (900,000)

(1,507,000) (927,000)

(1,552,000) (955,000)

(1,599,000) (984,000)

(1,615,000) (1,014,000)

(1,696,000) (1,044,000)

(1,747,000)(1,075,000)

Net Operating Income 2,422,000 2,525,000 2,526,000 2,184,000 2,627,000 2,653,000 2,749,000 2,751,000 2,378,000 2,805,000 3,194,000

Less Tenant Improvements Less Leasing Commissions Less Capital Reserve Funding

0 0

(100,000)

0 0

(100,000)

0 0

(100,000)

(456,000) (98,000)

(100,000)

0 0

(100,000)

0 0

(100,000)

0 0

(100,000)

0 0

(100,000)

(613,000) (141,000) (100,000)

00

(100,000)

Property Before-Tax Cash Flow $2,322,000 $2,425,000 $2,426,000 $1,530,000 $2,527,000 $2,553,000 $2,649,000 $2,651,000 $1,524,000 $2,705,000



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Private Practice (B)

It wouldn’t be the last time. Duna Wright glared at the caller ID number that seemed to have burned itself into the display of his cell phone. N.P. Venter had just left another voice message.

Reconsideration

To Duna’s surprise, Venter’s tone on the message sounded uncharacteristically disappointed, even a little embarrassed. She informed Duna that Ottathe Money Managers’ pension client had phoned to say it was no longer interested in pursuing additional real estate acquisitions; instead, it now considered itself a net seller of real estate based on the portfolio rebalancing recommendations recently approved by the plan’s investment committee. A recent decline in the value of the plan’s stock holdings had significantly reduced the aggregate value of the plan’s assets. Real estate, which had been performing well and increasing in value, was now over-allocated.

Venter was cautioned that Ottathe Money Managers could expect to lose some assets under management as well as the attendant annual asset management fees. And word traveled quickly: the investment sales brokers were already circling.

Rebound

But that’s not why N.P. Venter was calling. She actually needed more analysis done on the three properties that were still on the short list to acquire. A long-time client of the firm, the Barman Baskin Berger Partnership (BBBP) – which had also been humbled by the volatility and decline of the broader equity markets − had just come to realize that real estate might be a prudent addition to their ailing equity investment portfolio. According to Aaron Quinn, the trustee of this large family investment partnership, BBBP was interested in investing between $5 and $20 million, although such parameters were more guidelines than constraints.

N.P. Venter had dealt with Aaron Quinn for decades. She knew that the dozen-or-so beneficiaries of the partnership were financially comfortable, yet tax sensitive. She also knew that Quinn wouldn’t commit to any investment position in anything until he

This case was prepared by W. Tod McGrath for the purpose of class discussion. Characters and events are fictional. © MIT Center for Real Estate. Revised October 2006.



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completely understood the tax treatment of the investment, the magnitude and timing of the expected after-tax cash flows, and the resulting expected investment return. That’s why N.P. Venter needed Duna to re-run the numbers again. This weekend.

Reaction and Review

Infringed upon, but intrigued. Since Duna only had tentative plans with friends for the weekend, he didn’t particularly mind staying in Cambridge and crunching some more numbers. More importantly, he’d just finished a riveting lecture on federal incometaxation and was actually itching to apply some of the concepts he’d learned.

His instructor had presented the major federal income tax concepts and accounting methods applicable to commercial real estate investments. Duna’s review of his lecture notes highlighted the following:

¾ For purposes of preliminary analyses, each property’s depreciable basis could be estimated as the assessed value (for property tax purposes) of its improvements, excluding the assessed value of the land. Assessed values of the improvements on each property had been identified as follows:

o Pace Place $28,275,000 o Ciller Centre $ 5,850,000 o Rowe House $11,825,000

¾ Closing costs (due diligence and legal fees) as well as future capital expenditures relating to both tenant and building improvements would be added to the cost basis of each property and then depreciated for tax accounting purposes over the property’s applicable depreciable life (39 years for Pace Place and Ciller Centre; 27.5 years for Rowe House);

¾ Future capital expenditures relating to leasing commissions would be added to the cost basis of the property and then amortized for tax accounting purposes over the term of the lease1; and

¾ Taxable income from real estate investments would be subject to the following marginal federal income tax rates:

o Ordinary income (loss) 35% o Gain-on-sale attributable to previously-

claimed depreciation deductions 25% o Remaining taxable gain-on-sale 15%

Duna understood that the beneficiaries of BBBP paid income taxes at such marginal rates.

1 Duna assumed that (i) any future leases signed at Pace Place and Ciller Centre would be for terms of five years and (ii) renewal probabilities at each building would be 50% and 75%, respectively.

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2 The instructor tried to further impress Duna by explaining that he could similarly double-check his calculation of adjusted tax basis by adding together the balances of the owners’ tax capital account and the outstanding loan(s). After thanking him for his insights, Duna wondered why some people couldn’t just geta life.

Based on the foregoing parameters and the projection of property before-tax cash flow he had previously prepared (see Exhibit 1), Duna began to prepare a projection of property taxable income (loss) from operations for Pace Place (see Exhibit 2). Duna knew that the penultimate line on Exhibit 2 was nothing more than an accounting fiction, the result of following many arbitrary although (arguably) consistent tax accounting principles and rules prescribed by the Internal Revenue Service. His instructor had pejoratively described them in class as sanctioned lies that benefited taxpayers. Duna was still thinking a bit about what that really meant. But one thing was quite clear: the accounting fiction known as taxable income was important to know how to calculate because that’s the measure of income that taxpayers pay tax on. Duna needed to get that calculation right, along with the likely amount of annual federal income tax owed.

And that went for taxable gain on sale, too. Duna knew that the inherent deferral of income taxes associated with annual “non-cash” deductions such as depreciation and cost amortization came to a bitter end when an asset was sold. Not only did the investment value of tax deferral end upon sale, but the IRS then “got even.” It had recently been explained in class that the concept of a property’s adjusted tax basis is the mechanism by which the IRS keeps track of all of the non-cash deductions previously provided to taxpayers, and that the IRS uses that tracking mechanism to get even by requiring taxpayers to recognize taxable income upon sale equal to the amount of non-cash deductions previously claimed.

Applying the logic presented in class, Duna prepared Exhibit 3 to estimate both the resulting taxable gain on sale and the corresponding federal income tax liability. To double-check his calculations, Duna also laid out the capital account analysis procedure his real estate finance instructor had showed him after class. The instructor said that if the difference between the property’s projected net sale price and adjusted tax basis was equal to the difference between the owners’ projected tax capital account balance before the sale and the amount of the projected before-tax cash distribution in connection with the sale, then the calculation of taxable gain on sale was correct. The fundamental accounting result that needed to be achieved was that, after accounting for both the projected cash distribution and taxable gain on sale, the owners’ tax capital account equaled zero. Apparently the instructor was some sort of closet accountant or something.2

Redial

As he was about to pull together his after-tax analysis of Pace Place, his cell phone rang. N.P. Venter had one more request. The developer of Rowe House had just informed her that he had received a financing commitment from the state housing finance agency for a 30-year interest-only loan for any amount between 50% and 80% of the value of the property. The interest rate on the loan was 5.5%, a full 100 basis points below an

3



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3 Loan points paid in connection with arranging financing on the properties would be added to the cost basis of each property and then amortized for tax accounting purposes over the term-to-maturity of the respective loans.

equivalent market-rate loan. Loan fees equal to one point would be charged by the agency. The loan officers at the housing finance agency were quick to point out that because the property met the minimum threshold of 20% affordable units, the owners ofthe project would automatically qualify to claim about $95,000 of the so-called 4% Low Income Housing Tax Credits (LIHTC) each year for a period of 10 years. Kim Lee, the developer of the property, was now instructing each of her 3 short-listed bidders that she expected their final bids to incorporate the value of both the below-market financing and the LIHTCs.

“That’s not a problem, is it?” queried Venter.

Duna acknowledged that it would be relatively straightforward to incorporate such financing assumptions into his analyses, and further suggested that he could make equivalent market-rate financing assumptions in connection with his analyses of Pace Place and Ciller Centre. Venter thought that might be a good idea and further instructed Duna to assume the following:

¾ market-based interest rates of 6.5%, compounded monthly; ¾ 30-year amortization terms with monthly payments; ¾ 10-year terms-to-maturity; ¾ loan fees of one point; ¾ loan-to-value ratios of both 50% and 80%; and ¾ loan closing costs of about $75,000 (although the loan from the state housing

finance agency would likely be double that figure).

Redux

Duna knew that his first task would be to prepare a loan payment and amortization schedule for each property (see Exhibit 4). In terms of applying loan-to-value or leverage ratios, Duna figured it might make sense to initially value each property based on an arbitrary (albeit consistent) unlevered before-tax discount rate of 8.5%. Duna knew that that assumption would be questioned by both Venter and Quinn, but was prepared to argue that it was within a reasonable market range for such properties.

Next, Duna would need to incorporate the resulting annual debt service payment obligations into his previous schedules of property before-tax cash flow, taxable income (loss) from operations, and taxable gain on sale (see Exhibits 5, 6 & 7). Duna knew that he would also need to incorporate allowable tax deductions for cost amortization of capitalized loan points3 and loan closing costs.

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4 Due to (i) their compliance requirements under the Community Reinvestment Act (which affordablehousing investments help satisfy), (ii) the relatively favorable financial accounting treatment (booked as earnings under GAAP) afforded Low Income Housing Tax Credits, and (iii) 20 years of empirical evidence that 99+% of the LIHTC’s projected to be received by LIHTC fund investors actually have been.

Duna also knew he would have to pull all of these component analyses together into consolidated schedules of projected net investment flows on before- and after-tax and levered and unlevered bases (see Exhibit 8).

Finally, with regard to Rowe House, Duna recalled that if an investor were to acquire Rowe House and then sell it prior to the end of fifteen years (the so-called “tax credit compliance period”), one-third of the Low Income Housing Tax Credits previously claimed by such investor would be “recaptured” by the IRS in the form of an additional tax liability assessed upon sale. However, if the property were held for more than 10 years, the amount of the tax penalty would be reduced by one fifth for each year of continued ownership beyond 10 years (i.e., by the end of 15 years, the tax penalty would be zero). Duna was also aware that an investor could post a bond with the IRS in lieu of paying such recapture taxes − and avoid recapture tax all together upon a disposition of the property within the 15-year tax credit compliance period − provided the property continued to be rented in compliance with the existing affordability restrictions. For purposes of his analyses, Duna decided to assume that the cost of any such “recapture bond” would be de minimis.

Reflection

Duna had a lot to think about. On one level, Venter’s latest request for analysis involved nothing more than additional cash flow mechanics (schedules, revisions, etc.). Duna was fine with that; that’s what they paid him to do.

But on a more intellectual and strategic level, Duna knew he had some hard thinking to do about taxes, leverage, risk, and return. For example, while he understood that commercial banks4 were the typical investors in affordable housing developments nationwide, he was surprised to read in a recent affordable housing investment fund prospectus that acceptable levered after-tax investment returns were apparently below 10% − and for highly levered investment positions. He wondered aloud if that level of after-tax investment return should be applicable to, or appropriate for, BBBP.

In his quick estimation, he thought that the operating risks of each of the three prospective acquisitions seemed essentially equivalent. Yet he knew he needed to decide how, if at all, debt and taxes should affect required investment returns and resulting bid prices (asset values). And he needed to decide that quickly. After all, the sellers were demanding best-and-final offers, and Venter was growing increasingly hungry for additional acquisition fees, asset management fees, and client commendations.

It wouldn’t be the last time.

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Exhibit 1

Projection of Property Before-Tax Cash Flow

Pace Place

Year 1

Year 2

Year 3

Year 4

Year 5

Year 6

Year 7

Year 8

Year 9

Year 10

Year 11



$4,323,000 (88,000) 287,000

$4,467,000 (90,000) 311,000

$4,512,000 (94,000) 336,000

$4,876,000 (602,000) 175,000

$4,912,000 (123,000) 201,000

$4,995,000 (136,000) 228,000

$5,147,000 (147,000) 256,000

$5,209,000 (160,000) 285,000

$5,536,000 (685,000) 156,000

$5,662,000 (303,000) 186,000

$5,988,000(189,000)217,000



(1,300,000) (800,000)

(1,339,000) (824,000)

(1,379,000) (849,000)

(1,391,000) (874,000)

(1,463,000) (900,000)

(1,507,000) (927,000)

(1,552,000) (955,000)

(1,599,000) (984,000)

(1,615,000) (1,014,000)

(1,696,000) (1,044,000)

(1,747,000)(1,075,000)


Less Tenant Improvements Less Leasing Commissions Less Capital Reserve Funding

0 0

(100,000)

0 0

(100,000)

0 0

(100,000)

(456,000) (98,000)

(100,000)

0 0

(100,000)

0 0

(100,000)

0 0

(100,000)

0 0

(100,000)

(613,000) (141,000) (100,000)

00

(100,000)

Property Before-Tax Cash Flow $2,322,000 $2,425,000 $2,426,000 $1,530,000 $2,527,000 $2,553,000 $2,649,000 $2,651,000 $1,524,000 $2,705,000



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Exhibit 2

Projection of Property Taxable Income (Loss) From Operations

Pace Place

Year 1

Year 2

Year 3

Year 4

Year 5

Year 6

Year 7

Year 8

Year 9

Year 10

Year 11



$4,323,000 (88,000) 287,000

$4,467,000 (90,000) 311,000

$4,512,000 (94,000) 336,000

$4,876,000 (602,000) 175,000

$4,912,000 (123,000) 201,000

$4,995,000 (136,000) 228,000

$5,147,000 (147,000) 256,000

$5,209,000 (160,000) 285,000

$5,536,000 (685,000) 156,000

$5,662,000 (303,000) 186,000

$5,988,000(189,000)217,000



(1,300,000) (800,000)

(1,339,000) (824,000)

(1,379,000) (849,000)

(1,391,000) (874,000)

(1,463,000) (900,000)

(1,507,000) (927,000)

(1,552,000) (955,000)

(1,599,000) (984,000)

(1,615,000) (1,014,000)

(1,696,000) (1,044,000)

(1,747,000)(1,075,000)


Less Depreciation

Building Tenant Improvements Capital Reserve Expenditures Due Diligence / Legal Fees Less Cost Amortization

Leasing Commissions

(725,000) 0 0

(3,000)

0

(725,000) 0

(3,000) (3,000)

0

(725,000) 0

(6,000) (3,000)

0

(725,000) 0

(9,000) (3,000)

0

(725,000) (12,000) (12,000) (3,000)

(20,000)

(725,000) (12,000) (15,000) (3,000)

(20,000)

(725,000) (12,000) (18,000) (3,000)

(20,000)

(725,000) (12,000) (21,000) (3,000)

(20,000)

(725,000) (204,000) (24,000) (3,000)

(20,000)

(725,000)(22,000)(27,000)(3,000)

(28,000)

Taxable Income (Loss) $1,694,000 $1,794,000 $1,792,000 $1,447,000 $1,855,000 $1,878,000 $1,971,000 $1,970,000 $1,402,000 $2,000,000

Tax Savings (Liability) @ 35.0% ($593,000) ($628,000) ($627,000) ($506,000) ($649,000) ($657,000) ($690,000) ($690,000) ($491,000) ($700,000)



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Exhibit 3

Projection of Taxable Gain on Sale

Pace Place

Projected Sale Price * $46,971,000 Less Cost of Sale @ 2% (939,000)

Net Sale Price $46,032,000

Acquisition Cost ** $35,545,000 Due Diligence / Legal Fees 100,000 Tenant Improvements 1,069,000 Leasing Commissions 239,000 Other Capital Expenditures 1,000,000

Accumulated Depreciation (7,689,000) Accumulated Cost Amortization (128,000)

Less Adjusted Basis (Net Book Value) 30,136,000

Taxable Gain on Sale $15,896,000

Gain Attributable to Straight-Line Depreciation Tax @ 25% $1,922,000

$7,689,000

All Other Taxable Gain Tax @ 15% $1,231,000

$8,207,000

* Projected Year 11 NOI capitalized at ** Based on before-tax unlevered IRR of

6.8%8.5%

Tax Basis Capital Account Analysis

(1) (2) (3) (4) (5) (6) (7) (8)

[ + ] [ - ] [ + or - ] [ 1+2+3+4 ] [ - ] [ -5 - 6 ] [ 5+6+7 ]

Year

Beginning Capital

Account Balance

Cash Contributions

Cash Distributions

From Operations

Taxable Income (Loss) From

Operations

Capital Account Balance

Before Sale

Cash Distribution Upon Sale

Resulting Taxable

Gain on Sale

Ending Capital

Account Balance

0 1 2 3 4 5 6 7 8 9

10

$0 35,645,000 35,017,000 34,386,000 33,752,000 33,669,000 32,997,000 32,322,000 31,644,000 30,963,000 30,841,000

$35,645,000 0 0 0 0 0 0 0 0 0 0

$0 (2,322,000) (2,425,000) (2,426,000) (1,530,000) (2,527,000) (2,553,000) (2,649,000) (2,651,000) (1,524,000) (2,705,000)

$0 1,694,000 1,794,000 1,792,000 1,447,000 1,855,000 1,878,000 1,971,000 1,970,000 1,402,000 2,000,000

$35,645,000 35,017,000 34,386,000 33,752,000 33,669,000 32,997,000 32,322,000 31,644,000 30,963,000 30,841,000 30,136,000

$0 0 0 0 0 0 0 0 0 0

(46,032,000)

$0 0 0 0 0 0 0 0 0 0

15,896,000

$35,645,000 35,017,000 34,386,000 33,752,000 33,669,000 32,997,000 32,322,000 31,644,000 30,963,000 30,841,000

0



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Exhibit 4

Loan Amortization Schedule

Pace Place

Loan Amount $17,772,500 Interest Rate 6.50% Compounding Periods / Year 12 Payments / Year 12 Amortization Term (Years) 30 Term-to-Maturity 10

Periodic Payment $112,334.29 Annual Payment $1,348,011 Points 1.00 Closing Costs Lender $50,000 Borrower $75,000

Beginning Principal Ending Year Balance Payment Interest Amortization Balance

0 $17,772,500 1 $17,772,500 $1,348,011 $1,149,364 $198,648 17,573,852 2 17,573,852 1,348,011 1,136,060 211,952 17,361,901 3 17,361,901 1,348,011 1,121,865 226,146 17,135,754 4 17,135,754 1,348,011 1,106,720 241,292 16,894,463 5 16,894,463 1,348,011 1,090,560 257,452 16,637,011 6 16,637,011 1,348,011 1,073,318 274,694 16,362,317 7 16,362,317 1,348,011 1,054,921 293,090 16,069,227 8 16,069,227 1,348,011 1,035,292 312,719 15,756,508 9 15,756,508 1,348,011 1,014,349 333,662 15,422,846

10 15,422,846 1,348,011 992,003 356,008 15,066,837 11 0 0 0 0 0 12 0 0 0 0 0 13 0 0 0 0 0 14 0 0 0 0 0 15 0 0 0 0 0 16 0 0 0 0 0 17 0 0 0 0 0 18 0 0 0 0 0 19 0 0 0 0 0 20 0 0 0 0 0 21 0 0 0 0 0 22 0 0 0 0 0 23 0 0 0 0 0 24 0 0 0 0 0 25 0 0 0 0 0 26 0 0 0 0 0 27 0 0 0 0 0 28 0 0 0 0 0 29 0 0 0 0 0 30 0 0 0 0 0



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Exhibit 5

Projection of Equity Before-Tax Cash Flow

Pace Place

Year Year Year Year Year Year Year Year Year Year Year 1 2 3 4 5 6 7 8 9 10 11

Gross Rental Revenues $4,323,000 $4,467,000 $4,512,000 $4,876,000 $4,912,000 $4,995,000 $5,147,000 $5,209,000 $5,536,000 $5,662,000 $5,988,000

Less Vacancy (88,000) (90,000) (94,000) (602,000) (123,000) (136,000) (147,000) (160,000) (685,000) (303,000) (189,000)

Plus Expense Reimbursements 287,000 311,000 336,000 175,000 201,000 228,000 256,000 285,000 156,000 186,000 217,000


Less Operating Expenses (1,300,000) (1,339,000) (1,379,000) (1,391,000) (1,463,000) (1,507,000) (1,552,000) (1,599,000) (1,615,000) (1,696,000) (1,747,000)

Less Property Taxes (800,000) (824,000) (849,000) (874,000) (900,000) (927,000) (955,000) (984,000) (1,014,000) (1,044,000) (1,075,000)


Less Tenant Improvements 0 0 0 (456,000) 0 0 0 0 (613,000) 0

Less Leasing Commissions 0 0 0 (98,000) 0 0 0 0 (141,000) 0

Less Capital Reserve Funding (100,000) (100,000) (100,000) (100,000) (100,000) (100,000) (100,000) (100,000) (100,000) (100,000)

Property Before-Tax Cash Flow 2,322,000 2,425,000 2,426,000 1,530,000 2,527,000 2,553,000 2,649,000 2,651,000 1,524,000 2,705,000

Less Debt Service (1,348,000) (1,348,000) (1,348,000) (1,348,000) (1,348,000) (1,348,000) (1,348,000) (1,348,000) (1,348,000) (1,348,000)

Equity Before-Tax Cash Flow $974,000 $1,077,000 $1,078,000 $182,000 $1,179,000 $1,205,000 $1,301,000 $1,303,000 $176,000 $1,357,000



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Exhibit 6

Projection of Taxable Income (Loss) From Operations

Pace Place

Year 1

Year 2

Year 3

Year 4

Year 5

Year 6

Year 7

Year 8

Year 9

Year 10

Year 11



$4,323,000 (88,000) 287,000

$4,467,000 (90,000) 311,000

$4,512,000 (94,000) 336,000

$4,876,000 (602,000) 175,000

$4,912,000 (123,000) 201,000

$4,995,000 (136,000) 228,000

$5,147,000 (147,000) 256,000

$5,209,000 (160,000) 285,000

$5,536,000 (685,000) 156,000

$5,662,000 (303,000) 186,000

$5,988,000(189,000)217,000



(1,300,000) (800,000)

(1,339,000) (824,000)

(1,379,000) (849,000)

(1,391,000) (874,000)

(1,463,000) (900,000)

(1,507,000) (927,000)

(1,552,000) (955,000)

(1,599,000) (984,000)

(1,615,000) (1,014,000)

(1,696,000) (1,044,000)

(1,747,000)(1,075,000)


Less Interest Expense Less Depreciation

Building Tenant Improvements Capital Reserve Expenditures Due Diligence / Legal Fees Less Cost Amortization

Leasing Commissions Loan Points Loan Closing Costs

(1,149,000)

(725,000) 0 0

(3,000)

0 (18,000) (8,000)

(1,136,000)

(725,000) 0

(3,000) (3,000)

0 (18,000) (8,000)

(1,122,000)

(725,000) 0

(6,000) (3,000)

0 (18,000) (8,000)

(1,107,000)

(725,000) 0

(9,000) (3,000)

0 (18,000) (8,000)

(1,091,000)

(725,000) (12,000) (12,000) (3,000)

(20,000) (18,000) (8,000)

(1,073,000)

(725,000) (12,000) (15,000) (3,000)

(20,000) (18,000) (8,000)

(1,055,000)

(725,000) (12,000) (18,000) (3,000)

(20,000) (18,000) (8,000)

(1,035,000)

(725,000) (12,000) (21,000) (3,000)

(20,000) (18,000) (8,000)

(1,014,000)

(725,000) (204,000) (24,000) (3,000)

(20,000) (18,000) (8,000)

(992,000)

(725,000)(22,000)(27,000)(3,000)

(28,000)(18,000)(8,000)

Taxable Income (Loss) $519,000 $632,000 $644,000 $314,000 $738,000 $779,000 $890,000 $909,000 $362,000 $982,000

Tax Savings (Liability) @ 35% ($182,000) ($221,000) ($225,000) ($110,000) ($258,000) ($273,000) ($312,000) ($318,000) ($127,000) ($344,000)



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Exhibit 7

Projection of Taxable Gain on Sale

Pace Place

Projected Sale Price * Less Cost of Sale @

Net Sale Price

2% $46,971,000

(939,000)

$46,032,000

Acquisition Cost ** Due Diligence / Legal Fees Tenant Improvements Leasing Commissions Other Capital Expenditures Loan Points Loan Closing Costs

Accumulated Depreciation Accumulated Cost Amortization

Less Adjusted Basis (Net Book Value)

$35,545,000 100,000

1,069,000 239,000

1,000,000 178,000 75,000

(7,689,000) (388,000)

30,129,000

Taxable Gain on Sale $15,903,000

Gain Attributable to Straight-Line Depreciation Tax @ 25% $1,922,000

$7,689,000

All Other Taxable Gain Tax @ 15% $1,232,000

$8,214,000

* Projected Year 11 NOI capitalized at ** Based on before-tax unlevered IRR of

6.8%8.5%

Tax Basis Capital Account Analysis

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

[ + ] [ - ] [ + or - ] [ 1+2+3+4 ] [ - ] [ -5 - 6 ] [ 5+6+7 ] [ 5+9 ]

Year

Beginning Capital

Account Balance

Cash Contributions

Cash Distributions

From Operations

Taxable Income (Loss) From

Operations

Capital Account Balance

Before Sale

Cash Distribution Upon Sale

Resulting Taxable

Gain on Sale

Ending Capital

Account Balance

Outstanding Loan

Balance

Adjusted Tax

Basis

0 1 2 3 4 5 6 7 8 9

10

$0 18,126,000 17,671,000 17,226,000 16,792,000 16,924,000 16,483,000 16,057,000 15,646,000 15,252,000 15,438,000

$18,126,000 0 0 0 0 0 0 0 0 0 0

$0 (974,000)

(1,077,000) (1,078,000)

(182,000) (1,179,000) (1,205,000) (1,301,000) (1,303,000)

(176,000) (1,357,000)

$0 519,000 632,000 644,000 314,000 738,000 779,000 890,000 909,000 362,000 982,000

$18,126,000 17,671,000 17,226,000 16,792,000 16,924,000 16,483,000 16,057,000 15,646,000 15,252,000 15,438,000 15,063,000

$0 0 0 0 0 0 0 0 0 0

(30,965,000)

$0 0 0 0 0 0 0 0 0 0

15,902,000

$18,126,000 17,671,000 17,226,000 16,792,000 16,924,000 16,483,000 16,057,000 15,646,000 15,252,000 15,438,000

0

$17,773,000 17,574,000 17,362,000 17,136,000 16,894,000 16,637,000 16,362,000 16,069,000 15,757,000 15,423,000 15,067,000

$35,899,000 35,245,000 34,588,000 33,928,000 33,818,000 33,120,000 32,419,000 31,715,000 31,009,000 30,861,000 30,130,000

Note: Totals may not add due to rounding.



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Exhibit 8

Pace Place: Summary of Projected Net Investment Flows and Return Metrics

Unlevered Before-Tax OCC 8.5%

Resulting Property Before-Tax Bid Price $35,545,000

Resulting Acquisition Cap Rate 6.5%

Resulting Cash-on-Cash Return 5.4%

Leverage Ratio 2 : 1

Due Gross Loan Tax Savings Tax Savings Net Diligence / Loan Points / PBTCF: Debt (Liability): PBTCF: Loan (Liability): Investment Projected Effective

Year Legal Fees Bid Price Proceeds Closing Costs Operations Service Operations Sale Repayment Sale Flows IRR Tax Rate

Unlevered Before-Tax Cash Flows

0 ($100,000) ($35,545,000) ($35,645,000) 1 2,322,000 2,322,000 2 2,425,000 2,425,000 3 2,426,000 2,426,000 4 1,530,000 1,530,000 5 2,527,000 2,527,000 6 2,553,000 2,553,000 7 2,649,000 2,649,000 8 2,651,000 2,651,000 9 1,524,000 1,524,000

10 2,705,000 46,032,000 48,737,000

8.5%

Unlevered After-Tax Cash Flows

0 ($100,000) ($35,545,000) ($35,645,000) 1 2,322,000 (593,000) 1,729,000 2 2,425,000 (628,000) 1,797,000 3 2,426,000 (627,000) 1,799,000 4 1,530,000 (506,000) 1,024,000 5 2,527,000 (649,000) 1,878,000 6 2,553,000 (657,000) 1,896,000 7 2,649,000 (690,000) 1,959,000 8 2,651,000 (690,000) 1,961,000 9 1,524,000 (491,000) 1,033,000

10 2,705,000 (700,000) 46,032,000 (3,153,000) 44,884,000

6.3% 26%

Levered Before-Tax Cash Flows

0 ($100,000) ($35,545,000) $17,772,500 ($253,000) ($18,126,000) 1 2,322,000 (1,348,000) 974,000 2 2,425,000 (1,348,000) 1,077,000 3 2,426,000 (1,348,000) 1,078,000 4 1,530,000 (1,348,000) 182,000 5 2,527,000 (1,348,000) 1,179,000 6 2,553,000 (1,348,000) 1,205,000 7 2,649,000 (1,348,000) 1,301,000 8 2,651,000 (1,348,000) 1,303,000 9 1,524,000 (1,348,000) 176,000

10 2,705,000 (1,348,000) 46,032,000 (15,067,000) 32,322,000

9.9%

Levered After-Tax Cash Flows

7.8%0 ($100,000) ($35,545,000) $17,772,500 ($253,000) ($18,126,000) 1 2,322,000 (1,348,000) (182,000) 792,000 2 2,425,000 (1,348,000) (221,000) 856,000 3 2,426,000 (1,348,000) (225,000) 853,000 4 1,530,000 (1,348,000) (110,000) 72,000 5 2,527,000 (1,348,000) (258,000) 921,000 6 2,553,000 (1,348,000) (273,000) 932,000 7 2,649,000 (1,348,000) (312,000) 989,000 8 2,651,000 (1,348,000) (318,000) 985,000 9 1,524,000 (1,348,000) (127,000) 49,000

10 2,705,000 (1,348,000) (344,000) 46,032,000 (15,067,000) (3,154,000) 28,824,000

20%



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One Lincoln Street (A)

After more than six months of seemingly daily e-mails, conference calls, and presentations, John Hynes still couldn’t believe what he was hearing on the other end of the phone from Frank Mattson, a Real Estate Investment Officer for Midwest State Teachers Retirement System (“STRS”).

“Wait a minute. I know it looks like a good deal. But John, I’ve tried to be clear from the start: we’re a public pension fund. Our policies are we only invest in fully entitled land and, even then, we don’t build on spec. We need at least 25% pre-leasing. And I still want to talk to you about that residual profit split.

All I can say right now is get me those revised unlevered cash flows and maybe I can bring the issues up at the Investment Committee meeting this week. But don’t get too optimistic – we learned our lesson the last go-round, and it wasn’t pretty.

I’ve got to get home for dinner or my kids are going to forget my name. I’ll be in earlytomorrow. Thanks, partner.”

“O.K. then, Frank, I guess we’ll talk in the morning. Bye.”

As he released the call from his speaker phone, John Hynes muttered angrily:

“Spare me that partner crap, please! Partners take risks.”

John knew his discussions with Frank needed to evolve. He just worried that he didn’t have much time.

Context

John B. Hynes, III was the Senior Vice President and Principal in charge of the Boston office for Gale & Wentworth LLC (“G&W”), a diversified real estate investment and services firm. Gale & Wentworth owned approximately 12 million square feet of suburban office properties and provided fee-based services to another 17.5 million square feet of such product. Gale & Wentworth had offices in seven states and the United Kingdom, employing over 350 people.

This case was prepared by W. Tod McGrath for the purpose of class discussion. The case describes an actual situation, but in the interests of confidentiality, certain names and other identifying information have been changed. The situation described herein is not intended to illustrate either effective of ineffective handling of a fiduciary situation. Revised October 2003.



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John Hynes was G&W’s newest addition to its senior management team. A lifelong Bostonian and real estate professional, John was transitioning from a successful career in commercial brokerage back to one centered on real estate investment, development, and management. John had been there before. From 1983 to 1992, he directed Lincoln Property Company’s Boston office as its Operating Partner and developed approximately 850,000 square feet of office space in Boston and Chelsea, Massachusetts.

John’s primary responsibility at G&W was to use its resources and network of relationships to expand its presence in the Boston office market. John knew that the principal resource available to him was the $50 million in capital that had recently been raised in MSGW III, G&W’s latest opportunity fund co-sponsored with Morgan Stanley Real Estate. Similar to its two predecessor funds, MSGW III had been launched to acquire (with leverage) about $200 million of “value added” real estate (i.e., largely empty buildings in improving markets). Levered investment returns were targeted at about 25%, down considerably from the 40%+ returns achieved in MSGW’s first fund.

G&W had recently finished investing MSGW II, the second opportunity fund it co-sponsored with Morgan Stanley. This fund was subscribed in 1997 with $50 million of equity and, somewhat unexpectedly, became fully invested in a single transaction with the levered acquisition of a national portfolio of office properties known as the Chubb Portfolio.

John was well aware that it had become increasingly difficult to find existing investment opportunities that both matched MSGW III’s investment objectives and could deliver the targeted level of investment returns. In many respects, the Boston market as of mid 1999 didn’t seem to offer a great deal of promise in terms of opportunistic investing. Over the past 5 years, the vacancy rate for Class A & B space in the City of Boston had dropped from 13% to less than 4% and asking rental rates had more than doubled (Exhibit 1). John knew he was late to the party, but also felt that a dynamic metro area such as Boston would continue to offer smart investment opportunities over time.

Others thought so, too. That’s how John came to meet Frank Mattson.

STRS

From the standpoint of commercial real estate investment, STRS was one of the mostprogressive public pension plan sponsors in the country. Unlike most of its peers, STRS had made a conscious decision to internally staff its real estate investment function as opposed to outsourcing such responsibilities to third-party pension investment managers. More significantly, perhaps, STRS was willing to venture a little further out on the risk/reward frontier than most other plan sponsors.

But STRS appetite for risk was buffered by a strategic decision to concentrate their investment in only about 10 MSAs nationwide. The rationale for such concentration stemmed from the practical requirements of both internal management efficiency and depth of external investment resources (i.e., joint venture partners) in the private property markets.

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To be blunt, in order not to be preyed upon in the quirky and inefficient private real estate equity markets, STRS Real Estate Investment Committee wanted to make sure they were aligning themselves only with the most reputable partners and only in those markets with the most depth, stability, and transparency. STRS had come to regard Boston as one of those markets.

As of mid 1999, STRS commercial real estate portfolio had a market value in excess of $5.5 billion and funding commitments for another $700 million. Although the portfolio was generally well diversified across property types, geographic regions, and investment structures, Frank Mattson believed that additional investment exposure to the higher cost, supply-constrained Northeast property markets was desirable. As he continued to follow the rapid escalation of rents and asset values in the Northeast, he began to more formally explore investment opportunities in Boston, both for STRS on its own and with selected joint-venture partners. Early in 1999, G&W had been recommended to him as a possible source for investment opportunities by his contacts at Morgan Stanley Real Estate, with whom STRS had previous investment experience. Frank Mattson wasted no time in calling for a meeting with John Hynes, and soon the two were scavenging the Boston metro area looking for deals.

Unfortunately, after many months of search and due diligence, neither had identified a prospective investment that met their objectives. For John, “opportunistic” acquisitions seemed to be ancient history; for Frank, “core” investments in fully-leased office buildings were generating initial unlevered cash returns of only about 7.0% to 7.5% (Exhibit 2) and expected unlevered IRRs in the 9.0% to 9.5% range. Frank was more than a little dismayed to find that even 30 year old buildings (with a host of issues related to functional obsolescence) were trading at cap rates in the 7.50% to 7.75% range.

A strong appetite to invest, enthusiasm for the Boston market, and an underwhelming array of acquisition opportunities: it was no surprise that Frank and John’s discussions quickly turned to development.

The 4% vacancy rate in Boston’s downtown office market had prompted five new office developments totaling approximately 2.7 million square feet to break ground in time for tenants to take occupancy between 2000 and 2002 (Exhibit 3). These five developments included:

¾ World Trade Center East¾ World Trade Center West ¾ 10 Saint James Avenue ¾ 470 Atlantic Avenue ¾ 111 Huntington Avenue

Across these five developments, approximately 1.7 million square feet (60%) had been pre-leased and the remainder was in high demand by a dozen or so legal, financial services, and professional services firms which were strapped for available expansion space. Recently signed leases were generally in the $50.00 to $60.00 per rentable square foot range. Based on the nature of development timelines in Boston, it was pretty clear that the next wave of available supply couldn’t be delivered until 2003 or 2004. What seemed to be holding the

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other proposed developments back from a groundbreaking was a combination of inadequate entitlements and pre-leasing commitments.

John believed that the next building to break ground would have a first-mover advantage that would effectively cause the remaining proposed developments to stop and watch. While Frank certainly wasn’t prepared to base his investment strategy on that premise, he did feel strongly that each of the other proposed developments would need significant amounts of equity capital to move forward and, in some cases, additional development expertise. After carefully reviewing the location, development program, and sponsorship of each of the remaining development opportunities, One Lincoln Street quickly emerged as the front runner in terms of a realistic investment opportunity.

One Lincoln Street

One Lincoln Street was a proposed 36-storey office development located in the Financial District of downtown Boston on a site bordered by Lincoln, Bedford, Kingston, and Essex Streets. The development program consisted of approximately 1 million rentable square feet of office space, 15,000 rentable square feet of retail space, some below-grade storage space, and a five-level underground parking garage totaling 345,000 square feet with 725 parking spaces (parking for 900 cars with valet service). The development was projected to cost approximately $330 million if built on an “all cash” basis (Exhibit 4).

The development was ostensibly controlled by Columbia Plaza Associates (“CPA”), a minority-owned development consortium which had originally received developer designation for the project by the Boston Redevelopment Authority (“BRA”) back in the late ‘80’s. More specifically, the BRA had awarded CPA the right to acquire two parcels of land owned by the City of Boston. The first parcel was the 27,000 square foot site of the nearly condemned Kingston-Bedford Public Parking Garage located on the northern half of the block bounded by Bedford, Kingston, Essex and Columbia Streets. The second parcel was an adjacent 20,000 square foot surface parking lot. The acquisition of two other privately-owned parcels of land totaling approximately 16,000 square feet was needed to complete the development plan.

But all of that was supposed to have happened a decade ago. The city was now growing increasingly frustrated, and it had conveyed its frustration to CPA. Understanding the political realities of the need to show progress and, perhaps more importantly, as a condition to the extension of CPA’s designation as developer, CPA had recently entered into a preliminary joint-venture agreement with a local Boston developer who was responsible for arranging the debt and equity financing for the project as well as the acquisition of the privately-owned land parcels. But none of those development milestones had been achieved and John had just been able to confirm with city officials that the preliminary joint-venture agreement previously approved by the BRA was set to expire within 30 days. That’s all he needed to hear.

John immediately called the managing partner of CPA and asked if they could meet. Unfortunately, he was rather clinically informed that, under the terms of its existing joint-

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venture agreement, CPA was precluded from discussing any aspect of ownership in the proposed development with any other party. John wasn’t exactly sure what that meant − and he wasn’t exactly sure that he cared. Within 72 hours of his phone call with CPA, he had flown to New York and put the two privately-owned parcels under agreement for $22 million. The terms of sale were simple: $2 million upon execution of the purchase and sale agreement (which was fully refundable within the negotiated 30-day “due diligence” period) and the remaining $20 million at closing, which was also scheduled to occur in 30 days.

John knew that control of the privately-owned land parcels was essential to the proposed development becoming a reality. Without that site area, the land assemblage was inadequate for large-scale development. No one knew that better than CPA. John also knew that the BRA would be hesitant to even threaten to use its power of eminent domain in order to complete the assemblage for CPA. They’d had that chance for over a decade, and never bit.

As the purchase and sale agreement was being executed, John placed his second call to CPA, this time introducing himself as their new partner. He followed that call with one to Frank Mattson, suggesting that he may have found what they were looking for.

A few weeks passed and the preliminary joint-venture agreement between CPA and their local development partner expired. It was August of 1999. Within a matter of days, John had reached agreement with both CPA and his money source, MSGW III, to conditionally move forward with the project subject to the approval of the Mayor of Boston and the BRA Board.

Morgan Stanley

Investment approvals from MSGW were ultimately granted by Morgan Stanley Real Estate −guys who liked to ask a lot of questions. Question number one to John was something like:

“You don’t really think we’re going to go hard on a dollar without all the approvals, do you?”

John smiled nervously but assured them that he fully understood the investment objectives of MSGW III and that the necessary approvals would be in place before the due diligence period expired. Another phone call was quickly placed; this time to the mayor’s office. John needed a meeting, and fast.

Two weeks remained before the due diligence period expired. Everything seemed to be moving forward (as well as could be expected) until John received a call from the Mayor’s office informing him that, while the Mayor would support the project moving ahead, the Director of the BRA had suddenly resigned and the BRA Board meeting scheduled for later that week would need to be postponed for at least another two weeks. Breathing somewhat anxiously into his cell phone, John placed a call to the owner of the private land parcels. Twenty minutes later, he had negotiated both an extension of the due diligence period until the day after the rescheduled BRA Board meeting and an extension of the closing date until the end of the year. Price tag: $500,000 plus a $2 million contingent purchase payment if

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lease commitments for 250,000 square feet of space in the new development were executed within 12 months of the closing. Simple enough.

His next call was to his partners at Morgan Stanley. He updated them on his various discussions and politely reminded them that G&W had invested 10% of the capital ($5 million) into MSGW III and that there was no way they could realistically move forward on the deal without going hard on the $2 million deposit after the BRA Board vote. As John had painfully become aware, the venture still needed a handful of miscellaneous city (and state) permits in order to break ground. The good news was that the Mayor had agreed to try to expedite the issuance of all remaining permits by the closing of the purchase and sale agreement. The mayor had an obvious incentive to cooperate; the acquisition of the city-owned parcels had been negotiated to occur on the same day. Price tag: $15 million, half payable at closing, half payable approximately three years thereafter upon certificate of occupancy for the first tenant.

After listening to John’s pitch, reviewing the pro forma financial information relating to the operations of the development (Exhibit 5), and reflecting on the real estate investment climate in downtown Boston, Morgan Stanley not only signed on to going hard on the $2 million deposit, but funding for an additional $5 million of required design, professional, and permitting costs as well. And all by years end. John ended the call feeling a strange mix of elation and dread. Although he got the green light to proceed, Morgan Stanley not-so-politely reminded him that no more than 50% of the equity raised in their fund could be invested in any one asset.

John immediately thought of his new buddy Frank.

Venture Structure

After a few perfunctory meetings and conference calls, John cut to the chase and proposed the following deal structure to Frank for his review and recommendation to STRS Real Estate Investment Committee.

¾ A new joint-venture between MSGW, STRS and CPA would be formed to undertake the development. The venture would initially fund equity capital in an amount equal to the greater of $175 million or 50% of the total development cost. The remaining capital required to complete construction and lease-up would be borrowed under a construction loan with a commercial lender. Upon maturity of the construction loan, the venture would likely (although not necessarily) redeem it with additional equity.

¾ Of the equity capital required, MSGW would contribute 10% and STRS would contribute 90%. CPA had no obligation (or desire or ability) to contribute additional capital to the venture. In fact, as part of its understanding with John, CPA was entitled to a $5 million reimbursement at closing for previous expenditures made and services performed since the late ‘80’s.

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¾ MSGW and STRS would each receive an annually compounded 11% cumulative preferred return1 on their invested equity capital. Once such preferred returns were paid, MSGW, STRS, and CPA would receive 34%, 51%, and 15%, respectively, of any remaining cash flows. STRS would control a majority of the voting interests in the venture.

¾ Construction and permanent financing commitments would be approved by STRS in its sole discretion.

The bottom line was that Frank liked what he heard, both from a financial and managerial (control) standpoint. Frank had previously stressed to John the importance that STRS placed, for example, on the monitoring role an experienced construction lender performed during the construction period. He was pleased that John had wisely offered up − without posturing or pretense − exclusive approval rights to STRS on all project financings. After all, STRS was putting up 90% of the equity.

With regard to requiring the use of a construction lender during the construction stage, Frank realized he would have to review the cash flow impact of such use on the development and operating budgets. He also knew from recent experience that the venture would be required to expend available equity capital on project expenditures prior to draws being approved by the construction lender under the construction loan. The venture would also have to guarantee completion of the development to the construction lender.

Frank conservatively expected to be able to negotiate a construction loan with a term-to-maturity of up to four years, quarterly interest-only payments, and a fixed interest rate no higher than 8%, compounded quarterly. He estimated that the construction lender would charge $2 million in fees at closing and would require an additional $200,000 per year of direct expense reimbursement for inspections during the three-year base building construction period. John had previously provided Frank with an annual and quarterly breakdown of expected construction period expenditures on hard construction and soft development costs (Exhibit 6), which Frank assumed would occur ratably throughout each quarter. With that information in hand, Frank prepared a pro forma construction loan disbursement and interest schedule (Exhibit 7).

That essentially left Frank needing to do what he liked to do best: calculating and evaluating the expected cash flows and investment returns from the venture to each venturer in accordance with the proposed distribution priorities. Although Frank already felt comfortable with the development and operating budgets John had prepared for the property, he knew he

1 Cumulative preferred returns, in this context, are calculated similar to the way cumulative preferred dividends are paid on preferred stock. Specifically, MSGW and STRS must each be paid 100% of the 11% preferred return payable on their respective equity investments before any return (cash distribution) is paid to CPA; in addition, MSGW and STRS are each entitled to receive the full repayment of their cumulative equity investment (including any earned but unpaid preferred return thereon) from the proceeds of the sale of the development before any payment is made to CPA. MSGW and STRS are entitled to such return preferences on a pari passubasis.

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would need to make a few assumptions regarding capital events and related market-based investment parameters. In particular, Frank assumed that

¾ The property could be sold at the end of its tenth year of stabilized operations for a price equal to its then current net operating income capitalized at 7.5%. Frank reasoned that in Year 10 (not unlike in the Boston market at the time), the owner of the property would likely be on the verge of receiving significant increases in base rental revenues through lease renewals at market rental rates. Using a 7.5% capitalization rate to arrive at an expected sale price for the property seemed to be as good a guess as any, particularly in light of current market conditions.

¾ Transaction costs for an asset this size would be no more than 1.25%.

Frank understood that, for presentation purposes to STRS Real Estate Investment Committee, he would principally focus on the expected unlevered cash flows and investment returns (IRRs) both to the venture as a whole and to STRS individually. Analyses of potential levered investment returns would not be presented because he was uncomfortable trying to forecast permanent financing rates four years into the future. Moreover, one of the committee members was a real estate academic who undoubtedly would feel the need to comment on both the appropriateness of investing on a levered basis and any estimation of future interest rates. Frank was aware that permanent financing rates for current 10-year fundings to properties that meet conventional loan underwriting criteria were in the 7.5% range, about 200 basis points over 10-year Treasury Bonds and about 300 basis points over 90-day Treasury Bills.

But Frank also understood that the proposed investment in One Lincoln Street was more than just a little different than what STRS had seen in a while. Even for an institution that prided itself on taking the long view of real estate investment, four years of consecutive cash outflows was a long time indeed. He mused that, for any number of reasons, he might not even be around to see it completed.

But that got Frank thinking, from a practical standpoint, about when and how STRS could get out of the deal and what the project might be worth upon construction completion and lease-up. He figured he should be prepared to discuss those issues since they seemed particularly relevant for this investment. He also knew that if he were inclined to recommend the investment for approval, he would have to step off the curb and justify it from the standpoint of it adequately compensating STRS for bearing the risks associated with both construction and lease-up.

Even though he knew the venture would obtain a guaranteed maximum price contract fromtheir chosen general contractor, their construction lender would require a completion guarantee that would, in all likelihood, devolve into negotiations over the venturers guaranteeing individual line item costs in the development budget. Frank knew that based on the magnitude of the overall construction budget, STRS would have to be the front line guarantor on the construction loan. Frank also knew that STRS would require significant backup guarantees from Morgan Stanley (corporately) for certain budgeted line items, and that Morgan Stanley would in turn require Gale & Wentworth to provide certain backup

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guarantees. After all, it was G&W who sourced the deal and who had presumably vetted the thousands of assumptions that went into it. John had already informed Frank that $5 million of G&W’s $9 million share of the budgeted development fees were being proposed to be deposited into escrow accounts to ensure performance under its guarantees. Frank wondered whether or not Morgan Stanley would feel that was enough.

Regardless, he knew he needed to give the issue of risk-adjusted investment returns a lot more thought in order to formalize his analyses and recommendations. He needed to think hard about how to price construction and lease-up risk in real estate development.

Update

It was September 1999. In the afternoon before the regularly scheduled monthly Real Estate Investment Committee meeting, Frank’s assistant pulled him out of a staff meeting and informed him that John Hynes was on the phone and needed to talk.

John had just gotten off the phone with Morgan Stanley and Morgan Stanley had given himan ultimatum of sorts. It seemed that Morgan Stanley was getting a bit uncomfortable with the thought of carrying through with the development phase. By their calculations, they would need to invest in excess of $40 million over the next few months in order to close on the City-owned and privately-owned land parcels and to pay CPA and the venture’s permitting, design, and legal consultants. In the context of managing MSGW III in the near term, that was becoming a problem.

But the guys at Morgan were smart, although maybe too smart from John’s perspective. Their message to John was simple: get STRS, or someone else, on board right now to fund 90% of the equity requirements of the development or the day after the closing on the land parcels they were going to flip the site with its as-is entitlements to a large Boston-based REIT they had recently done some investment banking work for. Price tag: $60 million. Morgan told John – unequivocally − that they were prepared to execute such an agreement within 60 days. They also gratuitously reminded John that, as their partner, G&W could pocket their share of the profits if they did decide to sell. John wasn’t interested in selling.

So John’s message to Frank was equally simple: STRS had 15 days to get investment committee approval for the deal and 45 days to completely document the transaction. In addition, assuming that all of the entitlements were in place at the time of the land closings, there would be no pre-leasing contingencies or other thresholds to be met that would permit STRS to defer funding its 90% equity share. They didn’t have time for that. STRS was either in or out. Welcome to the real world of high stakes real estate development.

Crunch Time

Frank had personally invested a lot of time looking at this deal. And he realized that even if his analyses supported a recommendation to pursue it, he would still have to be particularly

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persuasive to gain Investment Committee approval the following day. They hadn’t even considered a deal like this for over a decade.

The thought of having to prepare both his analyses and remarks in one evening started to make him feel a bit anxious. And it really didn’t help to have John jump off the call saying,

“I’ve got to get home for dinner or my kids are going to forget my name. Get back to metomorrow as soon as you can and tell me how the meeting went. And, Frank, I wouldn’t eventhink about coming back to me on that residual profit split. It is what it is.

Hey, partner, remember: pre-leasing is for sissies.”

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Exhibit 1

Boston Office Market: Statistical Overview

Annual Change Annual Change Annual Change Annual Change Class A Class B Class A Class B Total Occupied Vacancy Asking Asking

Year Supply Sq.Ft. % Supply Sq.Ft. % Supply Sq.Ft. % Space Sq.Ft. % Rate Rents PSF Rents PSF

1975 14,166,000 3,813,000 36.8% 380,000 15,000 4.1% 14,546,000 15,000 0.1% 12,328,000 15,000 0.1% 15.2% $14.00 $6.50 1976 15,406,000 1,240,000 8.8% 753,000 373,000 98.2% 16,159,000 1,613,000 11.1% 13,816,000 1,488,000 12.1% 14.5% $12.00 $6.50 1977 16,465,000 1,059,000 6.9% 847,000 94,000 12.5% 17,312,000 1,153,000 7.1% 15,105,000 1,289,000 9.3% 12.7% $12.00 $6.50 1978 16,465,000 0 0.0% 1,388,000 541,000 63.9% 17,853,000 541,000 3.1% 16,157,000 1,052,000 7.0% 9.5% $14.00 $6.50 1979 16,465,000 0 0.0% 1,766,000 378,000 27.2% 18,231,000 378,000 2.1% 17,092,000 935,000 5.8% 6.2% $16.00 $8.00 1980 16,465,000 0 0.0% 2,590,000 824,000 46.7% 19,055,000 824,000 4.5% 18,388,000 1,296,000 7.6% 3.5% $20.00 $10.00 1981 17,475,000 1,010,000 6.1% 3,914,000 1,324,000 51.1% 21,389,000 2,334,000 12.2% 20,373,000 1,985,000 10.8% 4.8% $22.00 $12.00 1982 17,612,000 137,000 0.8% 5,506,000 1,592,000 40.7% 23,118,000 1,729,000 8.1% 22,309,000 1,936,000 9.5% 3.5% $25.00 $16.00 1983 17,812,000 200,000 1.1% 6,493,000 987,000 17.9% 24,305,000 1,187,000 5.1% 23,394,000 1,085,000 4.9% 3.7% $30.00 $22.00 1984 21,722,000 3,910,000 22.0% 7,884,000 1,391,000 21.4% 29,606,000 5,301,000 21.8% 26,201,000 2,807,000 12.0% 11.5% $35.00 $24.00 1985 22,491,000 769,000 3.5% 8,825,000 941,000 11.9% 31,316,000 1,710,000 5.8% 28,341,000 2,140,000 8.2% 9.5% $38.00 $26.00 1986 22,641,000 150,000 0.7% 12,154,000 3,329,000 37.7% 34,795,000 3,479,000 11.1% 31,316,000 2,975,000 10.5% 10.0% $42.00 $26.00 1987 24,280,000 1,639,000 7.2% 13,187,000 1,033,000 8.5% 37,467,000 2,672,000 7.7% 33,720,000 2,404,000 7.7% 10.0% $44.00 $28.00 1988 27,510,000 3,230,000 13.3% 14,577,000 1,390,000 10.5% 42,087,000 4,620,000 12.3% 36,195,000 2,475,000 7.3% 14.0% $50.00 $30.00 1989 28,220,000 710,000 2.6% 15,091,000 514,000 3.5% 43,311,000 1,224,000 2.9% 36,381,000 186,000 0.5% 16.0% $55.00 $30.00 1990 30,085,000 1,865,000 6.6% 15,894,000 803,000 5.3% 45,979,000 2,668,000 6.2% 38,048,000 1,667,000 4.6% 17.2% $40.00 $25.00 1991 30,335,000 250,000 0.8% 16,022,000 128,000 0.8% 46,357,000 378,000 0.8% 37,549,000 (499,000) -1.3% 19.0% $30.00 $20.00 1992 30,835,000 500,000 1.6% 16,077,000 55,000 0.3% 46,912,000 555,000 1.2% 38,937,000 1,388,000 3.7% 17.0% $25.00 $18.00 1993 31,585,000 750,000 2.4% 16,077,000 0 0.0% 47,662,000 750,000 1.6% 40,465,000 1,528,000 3.9% 15.1% $26.00 $18.00 1994 31,585,000 0 0.0% 16,077,000 0 0.0% 47,662,000 0 0.0% 41,466,000 1,001,000 2.5% 13.0% $27.00 $20.00 1995 31,005,000 (580,000) -1.8% 16,172,000 95,000 0.6% 47,177,000 (485,000) -1.0% 42,223,000 757,000 1.8% 10.5% $30.00 $24.00 1996 31,005,000 0 0.0% 16,422,000 250,000 1.5% 47,427,000 250,000 0.5% 43,870,000 1,647,000 3.9% 7.5% $34.00 $26.00 1997 31,585,000 580,000 1.9% 16,305,000 (117,000) -0.7% 47,890,000 463,000 1.0% 45,017,000 1,147,000 2.6% 6.0% $40.00 $30.00 1998 31,585,000 0 0.0% 16,305,000 0 0.0% 47,890,000 0 0.0% 45,903,000 886,000 2.0% 4.1% $50.00 $34.00 1999 32,185,000 600,000 1.9% 16,595,000 290,000 1.8% 48,780,000 890,000 1.9% 46,951,000 1,048,000 2.3% 3.7% $60.00 $35.00



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Exhibit 2

Boston Office Market: Recent Building Sales

Year Net Built/ Rentable Sale Cap

Building Rehabbed Floors Area Date % Leased Buyer Seller Price Price/SF Rate

One Boston Place 1970 41 779,000 Dec-99 95% Gerald Hines Interests Lend Lease $200,000,000 $257 7.75% 99 High Street 1971 32 731,000 Dec-99 99% Boston Capital Keystone-Centrose Associates 168,500,000 231 7.71% 75 State Street 1988 31 770,000 Oct-98 100% World Financial Properties Lend Lease 311,000,000 404 7.40% 745 Atlantic Atlantic 1987 11 168,000 Oct-99 100% Lend Lease Tishman Speyer 39,500,000 235 7.00% 399 Boylston Street 1983 13 255,000 Nov-98 90% CentreMark Met Life 52,000,000 204 7.50% 265 Franklin Street 1985 20 329,000 Apr-99 100% Westbrook Ptrs / Divco West Shuwa Investments 70,000,000 213 7.70% 260 Franklin Street 1985 23 349,000 Jan-00 100% Heitman / State of Florida JMB / TIAA 76,000,000 218 7.00% 125 High Street (1) 1990 30 1,438,000 May-99 100% Jamestown Tishman Speyer 496,600,000 345 7.75% 116 Huntington Avenue 1990 15 261,000 Jun-99 100% IDX Partners IDX 55,200,000 211 6.95% 100 Summer Street 1974 32 1,020,000 Mar-98 80% Equity Office Properties Blue Cross Blue Shield / Emerik 225,000,000 221 7.50%

Totals / Averages 6,100,000 $1,693,800,000 $278 7.43%

Note: (1) 76% ownership interest.



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Exhibit 3

Boston Office Market: Development Pipeline

Building District Developer

Net Rentable

Area Status Leased Space

Completion Date 1999 2000

Delivery of New Supply

2001 2002 2003 2004 2005

Lafayette Corporate Center Financial Amerimar 600,000 Under Constr. 600,000 1999 600,000

Landmark Center Fenway Abbey Group 950,000 Under Constr. 750,000 1999 950,000

World Trade Center East Seaport Drew / Fidelity 500,000 Under Constr. 500,000 2000 500,000

10 Saint James Back Bay Millenium 585,000 Under Constr. 450,000 2001 585,000

470 Atlantic Avenue Financial Modern Cont. 335,000 Under Constr. 0 2001 335,000

111 Huntington Avenue Back Bay Boston Properties 850,000 Under Constr. 550,000 2001 850,000

World Trade Center West Seaport Drew / Fidelity 500,000 Under Constr. 175,000 2002 500,000

One Lincoln Street Financial Gale & Wentworth 1,000,000 Proposed 0 2003 1,000,000

Seaport Center Seaport Chiofaro 500,000 Proposed 500,000 2003 500,000

Two Financial Center Financial Rose Associates 250,000 Proposed 0 2003 250,000

131 Dartmouth Street Back Bay Sullivan & Assoc. 350,000 Proposed 0 2003 350,000

33 Arch Street Financial Krulewich 600,000 Proposed 0 2004 600,000

700 Boyston Street Back Bay Boston Properties 150,000 Proposed 0 2004 150,000

650 Atlantic Avenue Financial Hines / Tufts 1,250,000 Proposed 0 2005 1,250,000

One Fan Pier Seaport Pritzger / S&S 750,000 Proposed 0 2005 750,000

Total New Supply 9,170,000 3,525,000 1,550,000 500,000 1,770,000 500,000 2,100,000 750,000 2,000,000

Preleased 1,350,000 500,000 1,000,000 175,000 500,000 0 0

% Preleased 87% 100% 56% 35% 24% 0% 0%



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Exhibit 4

ONE LINCOLN STREET DEVELOPMENT BUDGET

Cost Per Cost Per % of Sq.Ft. of Sq.Ft. of Total

Line Item Cost GBA NRA Cost SITE ACQUISITION:

BRA Parcel $15,000,000 $13.95 $14.79 4.5% O'Connor Parcel 24,500,000 22.79 24.16 7.4% CPA Entitlement Cost Reimbursement 5,000,000 4.65 4.93 1.5% Legal (Due Diligence) 250,000 0.23 0.25 0.1% Legal (Closing, Title Insurance, Misc.) 600,000 0.56 0.59 0.2%

Total Site Acquisition 45,350,000 42.19 44.72 13.7%

HARD CONSTRUCTION COSTS: Base Building: Guaranteed Maximum Price 162,975,000 151.60 160.70 49.3% Tenant Improvements 55,335,000 51.47 54.56 16.7% Window Coverings 250,000 0.23 0.25 0.1% Allowance for Common Corridors 1,000,000 0.93 0.99 0.3% Parking Garage Equipment 100,000 0.09 0.10 0.0% Abutter Improvement Allowance 500,000 0.47 0.49 0.2% Bell Atlantic Conduit Relocation 1,700,000 1.58 1.68 0.5% Building Security Equipment 250,000 0.23 0.25 0.1% FF&E / Interior Artwork 500,000 0.47 0.49 0.2% Landscaping 500,000 0.47 0.49 0.2%

Total Hard Construction Costs 223,110,000 207.54 219.99 67.5%

SOFT DEVELOPMENT COSTS: Architectural & Engineering 7,200,000 6.70 7.10 2.2% Space Planning 300,000 0.28 0.30 0.1% Construction Coordination Website 270,000 0.25 0.27 0.1% Building Permit 1,600,000 1.49 1.58 0.5% Other Permits 100,000 0.09 0.10 0.0% MEPA EIR, Consulting Fees 200,000 0.19 0.20 0.1% Builder's Risk Insurance 525,000 0.49 0.52 0.2% Bonds to City 250,000 0.23 0.25 0.1% Testing & Inspections 800,000 0.74 0.79 0.2% Legal (Contracts) 75,000 0.07 0.07 0.0% Legal (Approvals) 350,000 0.33 0.35 0.1% Legal (Leasing) 1,000,000 0.93 0.99 0.3% Leasing Commissions 8,113,000 7.55 8.00 2.5% Real Estate Taxes During Construction 2,500,000 2.33 2.47 0.8% Advertising & Marketing 1,000,000 0.93 0.99 0.3% Linkage & Public Benefits: Neighborhood Housing Trust 1,900,000 1.77 1.87 0.6% Neighborhood Jobs Trust 852,000 0.79 0.84 0.3% Chinatown Childcare 1,250,000 1.16 1.23 0.4% Dudley Street Initiative 50,000 0.05 0.05 0.0% Community Development Fund 10,000,000 9.30 9.86 3.0%

Owners's Representative 200,000 0.19 0.20 0.1% Development Fee: CPA 1,500,000 1.40 1.48 0.5% Development Fee: G&W 9,000,000 8.37 8.87 2.7% Contingency 13,000,000 12.09 12.82 3.9%

Total Soft Development Costs 62,035,000 57.71 61.17 18.8%

TOTAL DEVELOPMENT COSTS $330,495,000 $307.44 $325.87 100.0%



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Exhibit 5

ONE LINCOLN STREET PROJECTED NET OPERATING INCOME AND CASH FLOW FROM OPERATIONS

( $ in Thousands)

Calendar Years Ending: 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013

Base Rental Revenue $53,141 $53,141 $53,141 $53,141 $53,141 $54,435 $56,008 $58,012 $60,425 $60,425 $66,309 Absorption and Turnover Vacancy (21,736) 0 0 0 0 (3,477) 0 (3,939) 0 0 (3,568)

Scheduled Base Rental Revenue 31,405 53,141 53,141 53,141 53,141 50,958 56,008 54,073 60,425 60,425 62,741

Operating Expense Reimbursement 120 434 716 1,007 1,306 1,399 1,468 1,461 1,419 1,766 1,151 Real Estate Tax Reimbursement 120 434 716 1,007 1,306 1,399 1,468 1,461 1,419 1,766 1,151 Parking Garage Revenue (net) 4,000 5,000 5,150 5,305 5,464 5,628 5,796 5,970 6,149 6,334 6,524 General Vacancy 0 (2,950) (2,986) (3,023) (3,061) (3,143) (3,237) (3,345) (3,471) (3,514) (3,757)

Effective Gross Income 35,645 56,059 56,737 57,437 58,156 56,241 61,503 59,620 65,941 66,777 67,810

Operating Expenses (9,128) (9,401) (9,683) (9,974) (10,273) (10,582) (10,899) (11,226) (11,563) (11,910) (12,267) Real Estate Taxes (9,128) (9,401) (9,683) (9,974) (10,273) (10,582) (10,899) (11,226) (11,563) (11,910) (12,267)

NET OPERATING INCOME 17,389 37,257 37,371 37,489 37,610 35,077 39,705 37,168 42,815 42,957 43,276

Tenant Improvements (55,335) 0 0 0 0 (7,496) 0 (8,478) 0 0 (9,096) Leasing Commissions (4,057) 0 0 0 0 (1,874) 0 (2,119) 0 0 (2,326) Capital Reserve (152) (157) (161) (166) (171) (176) (182) (187) (193) (198) (204)

PROPERTY BEFORE-TAX CASH FLOW ($42,155) $37,100 $37,210 $37,323 $37,439 $25,531 $39,523 $26,384 $42,622 $42,759 $31,650



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Exhibit 6

ONE LINCOLN STREET CONSTRUCTION PERIOD FUNDING SCHEDULE

2000 2001 2002 2003 Totals

Base Building Costs Tenant Improvements Other Hard Construction Costs Linkage & Public Benefits Leasing Commissions Developer Fees Other Soft Development Costs

$14,430,000

2,200,000 4,326,000

2,140,000 13,684,000

$79,200,000

426,000 4,056,000 2,188,000 6,996,000

$65,350,000

2,203,000 5,725,000

$3,995,000 55,335,000 2,600,000 9,300,000 4,057,000 3,969,000 2,965,000

$162,975,000 55,335,000 4,800,000

14,052,000 8,113,000

10,500,000 29,370,000

Total Funding Requirements $36,780,000 $92,866,000 $73,278,000 $82,221,000 $285,145,000

SUPPORTING QUARTERLY DETAIL

Quarter Base Building Tenant

Improvements Other Hard

Construction Linkage &

Public Benefits Leasing

Commissions Developer Fees Other Soft

Development

2000.1 2000.2 2000.3 2000.4 2001.1 2001.2 2001.3 2001.4 2002.1 2002.2 2002.3 2002.4 2003.1 2003.2 2003.3 2003.4

2,030,000 3,146,000 9,254,000

16,005,000 18,047,000 19,424,000 25,724,000 19,912,000 20,223,000 14,851,000 10,365,000 1,701,000 1,134,000

673,000 486,000

32,960,000 4,421,000 5,181,000

12,773,000

500,000 1,700,000

1,623,000 457,000 386,000 134,000

3,150,000 1,126,000

50,000

426,000

6,800,000 1,500,000 1,000,000

1,014,000 1,014,000 1,014,000 1,014,000

1,014,000 1,014,000 1,014,000 1,015,000

525,000 525,000

1,090,000 525,000 525,000 525,000 613,000 525,000 525,000 525,000 628,000 525,000 525,000 525,000

2,394,000

4,983,000 3,574,000 3,106,000 2,021,000 1,478,000 1,623,000 1,816,000 2,079,000 1,734,000 1,398,000 1,467,000 1,126,000

896,000 734,000 691,000 644,000

Totals $162,975,000 $55,335,000 $4,800,000 $14,052,000 $8,113,000 $10,500,000 $29,370,000



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Exhibit 7

ONE LINCOLN STREET CONSTRUCTION PERIOD INTEREST SCHEDULE

Gross Construction Period Equity Funding

Less Site Acquisition Less Financing & Inspection Fees Less Construction Loan Interest Net Construction Period Equity Funding

$175,000,000(45,350,000)

(2,600,000)(16,312,000) 110,738,000

Annual Construction Interest Rate

(compounded quarterly)

8.00%

Quarter

Beginning Debt

Balance Required Funding

Equity Funding

Debt Funding *

Interest Expense

Interest Paid

Ending Debt

Balance

2000.1 2000.2 2000.3 2000.4 2001.1 2001.2 2001.3 2001.4 2002.1 2002.2 2002.3 2002.4 2003.1 2003.2 2003.3 2003.4

$0 0 0 0 0 0 0 0

18,908,000 41,079,000 63,225,000 80,068,000 92,187,000

130,906,000 145,991,000 155,961,000

$4,983,000 9,279,000 8,403,000

14,115,000 19,022,000 21,209,000 23,205,000 29,430,000 22,171,000 22,146,000 16,843,000 12,119,000 38,719,000 15,085,000

9,970,000 18,446,000

$4,983,000 9,279,000 8,403,000

14,115,000 19,022,000 21,209,000 23,205,000 10,522,000

0 0 0 0 0 0 0 0

$0 0 0 0 0 0 0

18,908,000 22,171,000 22,146,000 16,843,000 12,119,000 38,719,000 15,085,000

9,970,000 18,446,000

$0 0 0 0 0 0 0

189,000 600,000

1,043,000 1,433,000 1,723,000 2,231,000 2,769,000 3,020,000 3,304,000

$0 0 0 0 0 0 0

(189,000) (600,000)

(1,043,000) (1,433,000) (1,723,000) (2,231,000) (2,769,000) (3,020,000) (3,304,000)

$0 0 0 0 0 0 0

18,908,000 41,079,000 63,225,000 80,068,000 92,187,000

130,906,000 145,991,000 155,961,000 174,407,000

$285,145,000 $110,738,000 $174,407,000 $16,312,000 ($16,312,000)

* Assumed To Occur Ratably Throughout the Quarter.



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Real Estate Finance & Investment T.A.: Jong Yoon Lim & Chip Weintraub 11.431/15.426J

Problem Set 1 To be discussed Sept. 20 during recitation

PART C and D are REQUIRED (ARGUS Tutorial)

PART A: Chapter 8 Please use your calculator to do all even-numbered study questions at the end of Geltner-Miller Chapter 8 EXCEPT

#s 20,26,32,36. You only need to hand in the answers. Note, these problems are similar to the preceding odd-numbered questions are answered at the end of the book (pp.851-852). Calculator steps for solving the odd-numbered problems are available on the course web site in the folder of materials.

We also encourage you to get familiar with using Excel to solve these types of problems. An Excel file with formulas and functions for solving the odd-numbered Chapter 8 questions will be made available for downloading from the course web site.

The Chapter 8 PowerPoint lecture notes which should also be available for downloading from the course web site may also be helpful as a tutorial for students not familiar with solving PV math problems and the use of business calculators and computer spreadsheets for solving such problems. PART B: Chapter 10 Note that you can use the standard MS Windows “Copy/Paste” procedure (select material, click “copy” or type ctrl-c, then click “paste” or type ctrl-v) to copy/paste figures from a MS Word document table into a MS Excel worksheet. If you download the MS Word file of this homework assignment from the course web site, you can use this ability to quickly copy the data for problems 1 & 2 below into an Excel worksheet, which is probably the best way to do these problems. 1. The table below shows two 10-year cash flow projections (in $ millions, including reversion) for the same property. The upper row is the projection that will be presented by the broker trying to sell the building; the bottom row is the realistic expectations. Suppose that it would be relatively easy for any potential buyers to ascertain that the most likely current market value for the property is about $10 million. (a) What going-in IRR (blended rate) will equate the presented cash flow projection to the observable $10 million present value (as of Year 0)? (b) What rate will equate the realistic projection to that same present value? (c) What is the most likely amount of “disappointment” in the ex post rate of return earned by an investor who buys this property believing the broker’s cash flow projection (i.e., difference in presented vs realistic return)?



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Y ear 1 2 3 4 5 6 7 8 9 10 Presented seller’s broker

$1.0000 $1.0250 $1.0506 $1.0769 $1.1038 $1.1314 $1.1597 $1.1887 $1.2184 $13.0501

Realistic $1.0000 $1.0000 $1.0000 $1.0000 $1.0000 $1.0000 $1.0000 $1.0000 $1.0000 $11.0000 2. The projected cash flows (including reversion) are shown in the table below for Property A and Property B. (a) If both properties sell at cap rates (initial and terminal cash yields) of 8%, what is the expected total return on a 10-year investment in each property? (b) If the 8% cap rate represents a fair market value for each property, then which property is the more risky investment (and how do you know)? (c) What is the annual growth rate in operating cash flows for each building during the first nine years? (d) How is this growth rate related to the (constant) cap rate and the investor’s expected total return (IRR) in each property? Annual net cash flow projections for two properties ($ millions) Year 1 2 3 4 5 6 7 8 9 10 A $1.0000 $1.0050 $1.0100 $1.0151 $1.0202 $1.0253 $1.0304 $1.0355 $1.0407 $14.185 B $1.0000 $1.0200 $1.0404 $1.0612 $1.0824 $1.1041 $1.1262 $1.1487 $1.1717 $16.433 3. In a certain market the typical lease is net to the landlord with a term of five years, and rents typically grow 2% per year, both within leases (due to built-in step-ups) and in the prevailing market rents charged on new leases. Properties typically have a single tenant, and are sold with a new lease just signed (i.e., five years of contractual cash flows). Tenants typically can borrow at 9%, and the going-in cap rate prevailing in the property market is 8% (initial cash yield). Assuming annual cash flows in arrears and no vacancy between leases, what is the implied inter-lease and reversion discount rate? 4. (This problem is based on the Ch.10 Appendix.) A 10-year property investment is characterized by the net cash flow stream indicated in the table below (including initial investment and reversion at the end of year 10). Compute the: (a) Overall total IRR; (b) Initial cash yield component; (c) Cash flow growth component; (d) Yield-change component; and (e) Interaction effect.

Yr 0 1 2 3 4 5 6 7 8 9 10 11 (1) Actual Oper.CF $1,000 $1,030 $900 $1,061 $1,093 $1,126 $850 $1,159 $1,194 $1,230 $1,267 (2) Actual Capital CF -10,000 $0 $0 $0 $0 $0 $0 $0 $0 $0 $13,050 (3) Actual Total CF (=1+2) -10,000 $1,000 $1,030 $900 $1,061 $1,093 $1,126 $850 $1,159 $1,194 $14,280 REQUIRED: Part C- CASH FLOW PRO FORMA



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In this assignment you are to develop a multi-year cash flow proforma projection for an office building with multiple long-term leases, using an Excel spreadsheet (you will duplicate something similar to this exercise in Part D using Argus software). The office building is Rentleg Plaza, which has 30,000 net rentable square feet divided into two office suites. Suite 100 is 20,000 SF and is leased out under a 5-year lease signed 2 years ago (3 more years left on the lease) at $15.00/SF (per year). (Suppose it is the end of 2000, so the lease expires in 3 years at the end of 2003.) The other office, Suite 200, is 10,000 SF and is currently vacant.

In the land where Rentleg Plaza is located, the past few years have seen the office market soften greatly due to excess supply of newly-built space. As a result, rents have fallen. The currently typical rental rate in the market for buildings like Rentleg Plaza is $14.00/SF on 5-year leases, with concessions amounting to one month free rent up front for each year of lease term (e.g., a 5-year lease would get the first 5 months rent free). In these conditions, you expect Suite 200 will not lease up for a year (i.e., expected occupancy after 12 months, at the beginning of 2002, in a 5-year lease running through 2006), and will require $10/SF Tenant Improvement ("Tenant Finishing") expenditures by the landlord at that time.

With virtually no new office building development on the horizon, it is likely that the present modest growth in office demand will bring the rental market back into equilibrium within, say, 3 years, so that by 2003 we will be back into something like equilibrium. In these circumstances, it is reasonable to forecast no growth in (nominal) rental rates in the market for the next two years (2000-2002) followed by a rent growth "spike" of, let's say, 20%, in 2003, with then no further growth in rents for the next few years beyond that time. We would also expect the rent concessions (e.g., the free rent up front) to disappear from typical market deals by 2003.

Suppose it is reasonable to assume that when the lease on Suite 100 expires, there is only a 50% chance the existing tenant will renew. If they do not renew, there will be 6 months vacancy in the space, and it will require $10.00/SF in tenant improvement expenditures (TI) paid for by the landlord (plus a 6% commission to a leasing broker) to obtain a new tenant. On the other hand, if the current tenant does renew (50% probability), it will only require $3.00/SF in TI plus a 3% brokerage commission. (The brokerage commissions are paid by the landlord, up front at the time the lease is signed, based on the entire (undiscounted) cumulative revenue of the lease, less free rent concessions. For example a 5% commission on a 10-year, $10.00/SF lease, would be $5.00/SF if there were no concessions, or $4.50/SF if there was 1-year free rent.)

The type of lease that is common in the market in which Rentleg Plaza competes is what is known as a "gross" or "full service" lease, with an "expense stop". This means that the landlord pays the building operating expenses, except that the tenant must pay their pro-rata share of any expenses over and above a "stop" amount specified in the lease. The "stop" amount is typically defined at or near the annual operating expenses (per SF) which the building was experiencing as of the time when the lease was signed. The expense stop on the existing lease in Suite 100 is $4.00/SF.

The current operating expenses of the building (projected for 2001) would be $4.81/SF if the building were fully occupied all year. However, the building is expected to be 33% vacant during the year, which will keep operating expenses down a bit. In fact, 19% of the operating expenses are "variable", that is, directly proportional to occupancy, while the remaining 81% are "fixed" (independent of



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occupancy). Thus, the 2001 projected expenses are $135,161 [calculated as: 30,000*$4.81*(.81+(2/3)*.19)]. Operating expenses are expected to grow at the rate of 4% per year.

In addition to normal operating expenses and the previously noted leasing and tenant improvement expenditures, there is also expected to be $1.00/SF/yr of general capital improvement expenditures.

Assuming reversion at the end of year 5, with a sale price equal to 10 times the following year's expected Net Operating Income (NOI), and at a discount rate of 12% per annum, you should be able to verify using your proforma that Rentleg Plaza has a present value of $2,292,810.

In developing your Excel spreadsheet proforma, you should use the format indicated by the table on the following page, and employ the guidelines indicated in the footnotes to compute the tagged numbers. This is the type of pro forma that a broker would typically take to a potential investor, or a borrower would take to a lender. (Keep in mind that a real world pro forma is typically 10 years, not 5, and buildings often have dozens of spaces and leases (not just two), as well as several individual operating expense line items. Nevertheless, this simple example should be sufficient to help you to understand the basic “nuts and bolts”.) Rentleg Plaza, 5-year Pro Forma Cash Flow Projection:

Year: 2000 2001 2002 2003 2004 2005 2006Market Rent $nnnn $nnnn $nnnn $nnnn $nnnn $nnnnPotential Gross Revenue: Rent Roll: Suite 100 $nnnn $nnnn $nnnn $nnnn $nnnn $nnnn Suite 200 $nnnn $nnnn $nnnn $nnnn $nnnn $nnnn Total $nnnn $nnnn $nnnn $nnnn $nnnn $nnnn Vacancy ($nnnn)1 ($nnnn)2 Abatements ($nnnn)3 Reimbursements: Suite 100 $nnnn4 $nnnn4 $nnnn4 $05 $nnnn5 $nnnn5

Suite 200 $nnnn6 $nnnn6 $nnnn6 $nnnn6 $nnnn6

Total $nnnn $nnnn $nnnn $nnnn $nnnn $nnnnTotal Revenue $nnnn $nnnn $nnnn $nnnn $nnnn $nnnn Operating Expenses $135,161 $nnnn $nnnn $nnnn7 $nnnn $nnnn



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NOI: $nnnn $nnnn $nnnn $nnnn $nnnn $nnnnLeasing & Capital Expenditures: TI $nnnn $nnnn8 Commissions $nnnn9 $nnnn10 Cap. Expenditures $nnnn $nnnn $nnnn $nnnn $nnnn Total $nnnn $nnnn $nnnn $nnnn $nnnn Operating PBTCF $nnnn $nnnn $nnnn $nnnn $nnnn Reversion $nnnn11

PBTCF $nnnn $nnnn $nnnn $nnnn $nnnn Present Value @12%: $2,292,810

12

_____________________________________________________________________________ 1Based on Suite 200 vacant all year. 2Based on Suite 100 expected vacancy (50%*6mo = 25% of Potential Gross Revenue from Suite 100). 3Based on free rent concession of 5 months offered to new lease in Suite 200. 4Based on expense stop of $4.00/SF in the existing lease in Suite 100. 5Based on expense stop in new lease exactly equal to projected operating expenses per SF in 2004. 6Based on expense stop of $5.00/SF in the new lease in Suite 200. 7Reflects expected vacancy of 50%*6 mo = 0.25yr in Suite 100 in 2004. 8Reflects expected renewal probability: (50%*$10/SF + 50%*$3/SF)*20,000 SF. 9Reflects free rent concession: 0.06*(5*14 - (5/12)*14)*10,000. 10Reflects expected renewal probability: (50%*0.06 + 50%*0.03)*(5*$16.80/SF)*20,000 SF. 11Reflects selling broker's commission of 5% taken from sales price equal to 10 times next year projected NOI. 12Assumes first cash flow occurs 1 year from present.



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REQUIRED: Part D – ARGUS TUTORIAL

ARGUS is a software package produced by ARGUS Financial Software of Houston, TX. It provides a relatively user-friendly and simple environment to enter information about the current leases in a building, and about the rental market in which the building is situated (user judgement), from which ARGUS then calculates the implied future cash flow from the building. You can also enter loan parameters. ARGUS will tell you cash flows before and after debt service. You can easily do sensitivity analysis (compare the cash flow and present value impacts of different lease or rental and expense assumptions or scenarios) by making different versions of the same building (use the "make another" option in the "file" menu in the ARGUS toolbar).

The purpose of this assignment is to familiarize you with a type of computer software known as "lease-by-lease" analysis packages. These types of programs are in widespread use among commercial property investment analysts, advisors, lenders, property managers, and appraisers. Some familiarity with such programs is therefore part of the preparation we need to give you in this course.

In this assignment you will walk through an example which, though greatly simplified, contains some the essential features of a typical medium size class A- or B+ office building investment, as of the early 1990s. (This period is chosen to allow you to see the effect of a slack market, where current market rents are below long-run equilibrium levels, and analysts must try to project when equilibrium will be restored.)

There are three parts to this assignment. The first part you have already done in Part C. There you prepared a simple spreadsheet to reflect the pro-forma future cash flows of a simple example office building. There you used a general-purpose electronic spreadsheet (EXCEL), so the calculations used to compute the projected cash flows were (or should be by now) completely "transparent" to you (in the formulas of the Excel spreadsheet). Based on that assignment, you should be able to understand what ARGUS is doing in the current assignment (behind the scenes, for ARGUS is a bit of a "black box" -- its calculations are not readily apparent). In effect, this second part of the assignment is simply an ARGUS "tutorial" in which I will step you through some of the basics of ARGUS, by walking through the same example office building as in Part C. In the second part of the Argus exercise you will be asked to change the input assumptions and report your findings. I: Background: Review of Example Office Building ProForma The office building is Rentleg Plaza, which has 30,000 net rentable square feet divided into two office suites. Suite 100 is 20,000 SF and is leased out under a 5-year lease signed 2 years ago (3 more years left on the lease) at $15.00/SF (per year). (Suppose it is the end of 2000, so the lease expires in 3 years at the end of 2003.) The other office, Suite 200, is 10,000 SF and is currently vacant. In the land where Rentleg Plaza is located, the past few years have seen the office market softened greatly due to excess supply of newly-built space. As a result, rents have fallen. The currently typical rental rate in the market for buildings like Rentleg Plaza is $14.00/SF on 5-



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year leases, with concessions amounting to one month free rent up front for each year of lease term (e.g., a 5-year lease would get the first 5 months rent free). In these conditions, you expect Suite 200 will not lease up for a year (i.e., expected occupancy after 12 months, at the beginning of 2002, in a 5-year lease running through 2006), and will require $10/SF Tenant Improvement ("Tenant Finishing") expenditures by the landlord at that time. With virtually no new office building development on the horizon, it is likely that the present modest growth in office demand will bring the rental market back into equilibrium within, say, 3 years, so that by 2003 we will be back into something like equilibrium. In these circumstances, it is reasonable to forecast no growth in (nominal) rental rates in the market for the next two years (2000-2002) followed by a rent growth "spike" of, let's say, 20%, in 2003, with then no further growth in rents for the next few years beyond that time. We would also expect the rent concessions (e.g., the free rent up front) to disappear from typical market deals by 2003. Suppose it is reasonable to assume that when the lease on Suite 100 expires, there is only a 50% chance the existing tenant will renew. If they do not renew, there will be 6 months vacancy in the space, and it will require $10.00/SF in tenant improvement expenditures (TI) paid for by the landlord (plus a 6% commission to a leasing broker) to obtain a new tenant. On the other hand, if the current tenant does renew (50% probability), it will only require $3.00/SF in TI plus a 3% brokerage commission. (The brokerage commissions are paid by the landlord, up front at the time the lease is signed, based on the entire (undiscounted) cumulative revenue of the lease, less free rent concessions. For example a 5% commission on a 10-year, $10.00/SF lease, would be $5.00/SF if there were no concessions, or $4.50/SF if there was 1-year free rent.) The type of lease that is common in the market in which Rentleg Plaza competes is what is known as a "gross" or "full service" lease, with an "expense stop". This means that the landlord pays the building operating expenses, except that the tenant must pay their pro-rata share of any expenses over and above a "stop" amount specified in the lease. The "stop" amount is typically defined at or near the annual operating expenses (per SF) which the building was experiencing as of the time when the lease was signed. The expense stop on the existing lease in Suite 100 is $4.00/SF. The current operating expenses of the building (projected for 2001) would be $4.81/SF if the building were fully occupied all year. However, the building is expected to be 33% vacant during the year, which will keep operating expenses down a bit. In fact, 19% of the operating expenses are "variable", that is, directly proportional to occupancy, while the remaining 81% are "fixed" (independent of occupancy). Thus, the 2001 projected expenses are $135,161 [calculated as: 30,000*$4.81*(.81+(2/3)*.19)]. Operating expenses are expected to grow at the rate of 4% per year.



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In addition to normal operating expenses and the previously noted leasing and tenant improvement expenditures, there is also expected to be $1.00/SF/yr of general capital improvement expenditures. The following table presents the pro-forma developed on an Excel spreadsheet (downloadable from the course website as “431f02_ps4ANS.xls”). Assuming reversion at the end of year 5, with a sale price equal to 10 times the following year's expected Net Operating Income (NOI), and at a discount rate of 12% per annum, Rentleg Plaza has a present value of $2,292,810. Rentleg Plaza, 5-year Pro Forma Cash Flow Projection:

Year: 2000 2001 2002 2003 2004 2005 2006Market Rent $14.00 $14.00 $14.00 $16.80 $16.80 $16.80Potential Gross Revenue: Rent Roll: Suite 100 $300,000 $300,000 $300,000 $336,000 $336,000 $336,000 Suite 200 $140,000 $140,000 $140,000 $140,000 $140,000 $140,000 Total $440,000 $440,000 $440,000 $476,000 $476,000 $476,000 Vacancy ($140,00

0)1($84,000)

2

Abatements ($58,333)3

Reimbursements: Suite 100 $10,1074 $20,0484 $24,0504 $05 $7,7555 $12,2575

Suite 200 $246 $2,0256 $2,3936 $6,2706 $8,5216

Total $10,107 $20,072 $26,075 $2,393 $14,025 $20,778Total Revenue $310,107 $401,739 $466,075 $394,393 $490,025 $496,778 Operating Expenses

$135,161 $150,072 $156,075 $157,1787

$168,811 $175,563



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NOI: $174,946 $251,667 $310,000 $237,215 $321,215 $321,215Leasing & Capital Expenditures: TI $100,000 $130,000

8

Commissions $38,5009 $75,60010 Cap. Expenditures

$30,000 $30,000 $30,000 $30,000 $30,000

Total $30,000 $168,500 $30,000 $235,600 $30,000 Operating PBTCF $144,946 $83,167 $280,000 $1,615 $291,215 Rever sion $3,051,5

4111

PBTCF $144,946 $83,167 $280,000 $1,615 $3,342,755

Present Value @12%:

$2,292,81012

_____________________________________________________________________________ 1Based on Suite 200 vacant all year. 2Based on Suite 100 expected vacancy (50%*6mo = 25% of Potential Gross Revenue from Suite 100). 3Based on free rent concession of 5 months offered to new lease in Suite 200. 4Based on expense stop of $4.00/SF in the existing lease in Suite 100. 5Based on expense stop in new lease exactly equal to projected operating expenses per SF in 2004. 6Based on expense stop of $5.00/SF in the new lease in Suite 200. 7Reflects expected vacancy of 50%*6 mo = 0.25yr in Suite 100 in 2004. 8Reflects expected renewal probability: (50%*$10/SF + 50%*$3/SF)*20,000 SF. 9Reflects free rent concession: 0.06*(5*14 - (5/12)*14)*10,000. 10Reflects expected renewal probability: (50%*0.06 + 50%*0.03)*(5*$16.80/SF)*20,000 SF. 11Reflects selling broker's commission of 5% taken from sales price equal to 10 times next year projected NOI.



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12Assumes first cash flow occurs 1 year from present. II: Tutorial This tutorial should take you 1 to 2 hours. You don't need to do it all in one sitting. Note: This tutorial may be based on an earlier version of Argus. If so, then there may be slight differences compared to the exact steps described here, but you should be able to translate these steps into the new version.

Click on the ARGUS icon. To begin to create an ARGUS file on a new property select the File popdown menu and New... . To instead open a pre-existing ARGUS file, you would select Open..., or to make a new version of an existing file, select Make a Copy. If the “New” window comes up, give your file a name (such as the first four letters of your last name followed by the numeral “1” to indicate that this is the first scenario of version of the pro-forma for this building). Don't forget to change the path to A: or whatever path you want so that the ARGUS file you will be creating will be saved where you want it to be. In the Property Description window which comes enter the property name, “Rentleg Plaza”. (The Description menu is found in the Property popdown menu in the main menu, if it does not come up automatically.) If this were a real property, you would then enter the rest of the actual information (address, etc.). Our example property is of the "office/industrial" type. Click on “OK”. One of the useful features of ARGUS is that it explains, at the bottom of the window, the nature of the input item where your cursor is located on the screen. Always read this information before entering the input. Recall that we are working with a 30,000 square foot office building. So, in the Property menu, Area Measures window, select “Property Size” and “Edit...” and then enter 30000 in the “size” box. Click on OK and then close the Area Measures box to get back to the main menu. Now within the Property popdown click on the Timing menu. Assume the analysis period starts at the beginning of 01/2001 (1/01). We will do a 5-year analysis from 1/01 (end of the first year is obviously 12/01). Go back to the main menu and select Property, Inflation Rates... menu and edit General Inflation. Assume a general inflation rate of 4% per year for all the years in the analysis. Note, however, that we could have entered different inflation rates for each year, and also that this general inflation rate can be overridden for specific variables later on.



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Now from the Property popdown of the Main Menu select Reimbursable Expenses. (Note that in our building the leases are of the Expense-Stop type.) To have this type of lease, we need to use the Reimbursable Expense Menu. (However, ARGUS has the ability to handle a wide variety of lease types, including purely gross leases where there is no expense stop, for which we would use the Non-Reimbursable Expenses Menu.) In the Reimbursable Expense Menu press the insert button to describe the expense categories in the property. To simplify matters we have assumed our example building has only a single all-encompassing category of operating expenses, which you should label "General Expenses" in the "Name" column. More realistically there would be several categories of expenses, each with possibly different percents fixed and inflation rates. Enter the amount of $4.81/SF/Yr as the current expense Amount (units is $/Area). This $4.81/SF would be the expense amount if the building were fully occupied, so select “Property Size” in the Area box. Enter 81 in the %Fixed item, to reflect the assumption that 81% of the expenses are fixed while 19% are directly proportional to building occupancy. In reality, this percentage would vary with different categories of expenses. For example, property taxes and insurance expenses are usually assumed to be 100% fixed, while many other expenses, such as maintenance & repair, utilities, management, are at least partially variable (depending on the nature of the building, e.g., how much common area or security needs). (This 81% assumption will give projected operating expenses of approximately $4.50/SF in 2001 with the building 2/3 occupied -- Reimbursement based on actual occupancy, so as to agree with our example assumptions.) We assume that expenses would grow at the general inflation rate of 4% per year on a constant-occupancy basis, so we don't need to enter any special inflation assumptions in the "Inflation" box. Note that the “gross up for reimbursements” box should not be checked in our case. The expense stops on our leases will be based on actual building operating expenses no matter how full or vacant the building is. (The alternative, to “gross up”, would adjust the expense calculation to reflect what the expenses would be if the building were fully occupied, for purposes of computing the expense stop on new leases and for calculating the reimbursable expenses.) Now go to the Capital Expenditures menu in the Property popdown. Recall that in the example there are general building improvement expenditures of $30,000 per year, every year. We can get ARGUS to reflect this pattern of capital improvement expenditure by inserting a capital expense item and entering 30000 in the amount item, "$ Amount" in the units item, "year" in the frequency item, 100 in the %Fixed item, and 0 in inflation. Now in the Main Menu now select the Yield popdown and get into the Property Purchase & Resale menu. Leave the "Initial Purchase Price" blank (you would only fill this in if you wanted to have ARGUS determine the IRR of property at a given price). The most common way to calculate the resale price is to Capitalize Net Operating Income the property will be earning at the time of the resale, so select this option. The assumed going out cap rate is 10 percent, with 5 percent resale commission. Check the box to Apply Rate to following year income. Make sure the box for "calculate resale all years" is left blank (not checked). Click OK to get back to the Main Menu.



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From the Main Menu select the Market popdown and the Market Leasing Assumptions menu. It is in the Market Leasing Assumptions Menu that you tell ARGUS what to assume about the future rental market in which your property is situated. Conceivably, you might want to identify more than one sub-market in which your building operates. For example, some of your space might be "Class A" while other parts of your building might be "Class B". Or, you might have some retail space, some office space, and/or some warehouse space in your building. Or, more commonly, there might be a particular space in the building which is oddly shaped or sized, so that it is difficult to lease out at the same rate as the rest of the building (and/or, it would typically remain vacant longer between tenants). ARGUS thus allows you to specify more than one Market Leasing Assumption Category. In the Rent Roll Menu (which we will get to in a minute), you will then tell ARGUS which category of market assumptions to apply to which space in the building. Thus, when you select the Market Leasing Assumptions Menu, you have the choice of creating a new category or editing and existing category. Initially, you will select the New button. In the example all the spaces are in the same sub-market and are equally easy to lease, so we will identify only one market leasing category, which we will call "OfficeMkt". When you initially enter the Market Leasing Assumptions Menu, you must name the Market Assumption Category as "OfficeMkt". Now fill in the table in the Market Leasing Assumptions Menu with the appropriate assumptions to reflect the assumptions in the example. The renewal probability is 50 percent under Renewal Mkt column, the current market rent is $14.00/SF, so enter 14 under the New Market column. You can leave the market rent row blank for the subsequent columns to the right ("Renewal Mkt", "Term 2", etc), as we will be taking care of that in the "Inflation Rates..." menu. Enter 6 in the Months Vacant row under New Market, 10 dollars in the Tenant Improvements item under the New Market, but only 3 dollars for that item under the Renewal Market column. Enter 6 percent Leasing Commissions for the New market, but only 3 percent for the Renewal Mkt. Enter 5 months in the Rent Abatement item for the New Market column, but 0 for the Renewal Mkt. For a new file click on “Overrides” to bring up the subsequent lease terms inputs. The only item for which you need to worry about entering assumptions for the subsequent terms (Term 2, Term 3,...) is the Rent Abatement item, for recall that we assumed there would be no further rent abatements after the Suite 200 lease, so enter 0 in all the subsequent Terms. In the bottom part of the Market Leasing Assumptions Menu we tell ARGUS what type of leases we are dealing with in both the current and future market. Enter Base Stop in the Reimbursement category so ARGUS knows we are in a market where expense-stop leases are the norm. Finally, enter 5 in the Term Lengths category to indicate the typical length of leases in the market. To deal with the expected inflation or growth rate in the market rent, we need to go back into the Inflation Rates under Property and edit the “Market Rent” inflation rate assumption (unless we were simply going to use the default inflation assumption of 4% entered in the General Inflatioln menu, which in this case we are not). Consistent with our example, we assume 0% growth in the market rent for the next 3 years (so years 2001 through 2003 will all have market rents of $14.00/SF, note that “Year 1” is 2001), reflecting the current over-



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built soft leasing market. Then we assumed a rent growth "spike" consisting of a 1-year 20% increase in 2004 (year 4), followed by 0 growth again after that. (Actually, it might be more realistic to assume a small positive growth rate after the rent spike, assuming that the rental market would then be back at long-run equilibrium, we might assume a growth rate 1 or 2 percent less than the general inflation rate. But let's stick with our existing example for comparability.) Thus, in the market rent inflation rates you have: 0, 0, 20, 0, 0, 0. Now from the Main Menu select the Tenants popdown and get into the Rent Roll menu. In the Rent Roll Menu you tell ARGUS what leases or spaces exist in the building, and what rental rates, lease terms and rental market leasing assumption categories apply to those leases or spaces. In the example there were two spaces in the building (suites 100 and 200), the latter of which was vacant as of the beginning of the analysis period. While it is possible to treat vacant space in the Rent Roll Menu (by entering a future date in the "Start Date" column, reflecting the time expected until the space will lease), it is generally easier to treat large vacant spaces in the Space Absorption Menu. So we only enter the one lease, the existing tenant in Suite 100, in the Rent Roll Menu. Recall from the example, we assumed that lease had been signed a couple of years ago at $15.00/SF, with 3 years remaining on the lease (through the end of 2003), and an expense stop at $4.00/SF. Press the insert button in the Rent Roll menu. You can leave the tenant name blank, but fill in the suite# as 100, of the office type, with 20000 SF. The lease began 2 years ago on 1/99 and ends in three more years at 12/03. The Base Rent is $15/SF/Yr, with no rent changes, retail space, abatements, or leasing costs (as these are all water over the dam for the existing lease, and will be dealt with subsequently by the market leasing assumptions we entered in the Market Leasing Assumptions menu). In the Reimbursements item enter 4 dollars to reflect the expense stop in the existing lease. In the Market Leasing column we tell ARGUS to use Market Leasing Assumption "OfficeMkt" Category we previously defined in the Market Leasing Assumptions Menu for the Suite 100 space. Upon Expiration, the lease will be subject to the Market.. This means that, upon the expiration of the existing lease on Suite 100, ARGUS will apply the rental market leasing assumptions described in the "OfficeMkt" Category. From the Main Menu next select Space Absorption from the Tenants popdown. In the Space Absorption Menu you tell ARGUS about major areas of space in your building that are currently vacant. ARGUS will automatically have these spaces "leased up" at a rate (over a time period) which you indicate in this menu. Depending on your judgement about the current rental market your building finds itself in, you may wish to have the space leased up rapidly or slowly, immediately or after a delay. The rate of lease-up should also depend on the rent to be charged (and concessions to be given) for the space, in relation to what is typically prevailing in the market today. In our example building, there was one vacant space, Suite 200 (10,000 SF). We assumed Suite 200 would remain vacant for the entire first year, and then be leased out in a 5-year lease at the prevailing market rent of $14.00/SF (with one month free rent for each year of lease term) with an expense stop approximately equal to the second year's expenses of $5.00/SF. This is indicated in the Space Absorption Menu much as the Rent Roll menu was, only with some differences to reflect the vacant Suite 200 space. Insert a space description line for "Suite 200", with 10000 SF in the Office type, available from 1/01 but we don't expect it to Begin Leasing until 1/02 (to reflect the 12 months anticipated vacancy in the sluggish current market). There is 1 lease, with annual creation frequency. In this way we tell ARGUS



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to lease out the entire Suite 200 all at once, after one year. (Alternatively, ARGUS will gradually lease out the vacant space at the rate you indicate.). Enter 5 years in the term expiration item, and a Base Rent of 14 dollars with no rent changes or retail in the lease. The $5.00 anticipated expense stop is reflected in the Reimbursements item, and the 5 months anticipated free rent is in the Rent Abatements item. Enter Yes in the Lease Cost item and fill in the details to tell ARGUS that the tenant improvement allowance will be 10 dollars and the leasing commission will be 6 percent. Enter OfficeMkt in the Market Leasing assumption, and expose the space to the Market upon lease expiration. In a more complicated building you could identify other vacant spaces, or groups of spaces (for example, if there were several different vacant offices, or if you wanted to treat some space as leasing up quickly while other space leases up slowly). Back at the Main Menu, we need to keep the leasing cost assumption constant to be consistent with our Part I example (we assumed there, perhaps unrealistically but simply, that the TIs would always be $10 or $3). To do this, we need to go once again to the Inflation Rates under Property menu and edit the Leasing Costs inflation to have 0 in all years. Now we have completed all of our cash flow related inputs for the example building we considered in Part I. We need only to tell ARGUS what discount rate to apply in order to get ARGUS to calculate the present value of the example property. To do this, go to the Yield popdown from the Main Menu and get into the Present Value Discounting Menu. As investors are often not sure exactly what discount rate is correct, ARGUS allows a sensitivity analysis to be easily conducted using different rates. However, in theory, only one rate can be correct (in the sense of reflecting the true market opportunity cost of capital as of a given point in time). Recall that the discount rate is derived essentially from the capital markets, as the riskfree interest rate (from long-term Government Bonds) plus a risk premium (reflecting how the markets currently perceive real estate risk, and the relative riskiness of this particular type of property, and the particular circumstances of the subject property). The discount rate is a total return (confusingly also called the "overall yield rate", labelled YO, according to appraisal lore). We selected a 12.00% rate in the example in Part I, reflecting a 6% current Long-Term Government Bond yield plus a 6.00% risk premium. If you only want to use a single discount rate, you enter that rate for both the Low and High rates in the Present Value Discounting Menu. As indicated below, we are valuing the property itself, rather than a levered equity interest in the property, so we leave the second part of the input menu blank. Now you are ready to have ARGUS calculate the cash flow projection and perform the valuation. From the Main Menu select the Reports popdown and select the Property Level reports. Check the "Schedule of Cash Flow from Operations", the "Prospectrive Present Value Summary", and the "Property Summary Report”, at the annual frequency. Press the view button to see the results. They should match those from the answer to HW#2, reproduced in Part I of this assignment. If your results do not match, try to figure out where the mistake is (but don’t waste too much time). If your results match, ARGUS should not be a "black box" to you. You should understand what ARGUS is doing to arrive at its output numbers. That, and to familiarize you with lease-by-lease software, was the



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purpose of this assignment. To print results, press the print button. (Notice that the “Export...” button there allows you to export ARGUS output to an excel spreadsheet.) Notice on the Present Value output that ARGUS tells what proportion of the present value comes from discounting the operating cash flows versus what proportion comes from discounting the reversion cash flow (Resale Proceeds). This is an important item to consider. In general, reversion cash flows are more risky than operating cash flows (future sale prices are hard to predict with accuracy). Therefore, it is considered desirable when employing the multi-year discounted cash flow ("Yield Capitalization") method of valuation used here for no more than about half of the total present value to come from the discounted resale proceeds. In this case over 75% of the present value comes from the reversion, which is probably unacceptable. The remedy would be to extend the analysis horizon to 10 years from 5 years, to push the reversion year farther back in time and give it a smaller discounted present value. This is the main reason why an analysis horizon of 10 years is typically used. The idea in multi-year discounted cash flow (DCF) valuation is to force the analyst to go through the exercise of trying to explicitly forecast the rental market and the building cash flows for the foreseeable future, to prevent "lazy" valuations that might overlook important influences on value. Written Assignment—Examining alternative input assumptions In this part of this assignment you will generate some new ARGUS analysis to hand in on the due date of this assignment. One of the great features of software packages like ARGUS is that it is very easy to quickly examine the cash flow and valuation impacts of alternative input assumptions. This is useful because the analyst is rarely completely sure about the exact value of many of the input assumptions he or she is using in the valuation. To examine alternative input assumptions in ARGUS, you create new versions using the Make a Copy option in the File menu. Do this by naming the new file "NAME2" (using the first 4 letters of your last name). When you have completed the new inputs, print the results from the REPORTS Menu. (The same three reports noted above.) Questions to answer & reports to turn in… The question I would like you to examine at this point is, what is the effect if the rent growth "spike" occurs 5 years from now rather than 4 years from now as we assumed previously? This would seem to be a small change in our input assumptions. The analyst could easily be wrong by a year regarding when the market perceives or expects the rent spike will occur. [Remember, for purposes of estimating the current market value of the property, it does not matter per se when (or even if) the rent spike actually will occur, or when the analyst



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thinks it will occur -- what matters is what the market (i.e., the typical investor who might buy the subject property) currently "thinks" or expects, regarding when the rent spike will occur.] You should turn in the changed versions of the three output reports noted previously in Part II (Cash Flow Schedule, Prospective Present Value, and Property Summary). On the first of these, circle the changes caused by the changed input assumption. On the second output report, write the percentage change in property present value caused by the changed assumption. Finally, from the REPORTS Menu, select Market Leasing Assumptions and press the print button. Turn in this print of your Market Leasing Assumptions Menu with your new (Case #2) inputs, and hand in this input printout together with your output. (Alternatively you can print and hand in the "Inflation Rates" inputs from the "Input Assumptions" report.)



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Calculator steps for Chapter 8 Study Questions Answers (text pp.851-852, questions on pp.175-179) NOTE: Not all steps need to be repeated in every problem. Calculator registers retain prior values until changed, and default settings even after calculator is turned off. Ch.8 Practice Problem #2. Calculator steps below.

HP-10B HP-12C

CLEAR ALL CLX

1 P/YR 1 n

1 N 11 i

11 I/YR 14000 FV

0 PMT PV gives 12612.61

14000 FV

PV gives 12612.61

Ch.8 Practice Problem #4. Calculator steps below.

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CLEAR ALL CLX

1 P/YR 2 n

2 N 11 i

11 I/YR 14000 FV

0 PMT PV gives 11362.71

14000 FV

PV gives 11362.71


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CLEAR ALL CLX

1 P/YR 2 n

2 N 11 i

Prentice-Hall Geltner-Miller Real Estate Text, Chapter 8, Page 1



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11 I/YR 25000 PV 25000 PV FV gives 30802.5 0 PMT FV gives 30802.5




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12 P/YR 11 g i

12 N 1 g n 11 I/YR 14000 FV 0 PMT PV gives 12547.96 14000 FV PV gives 12547.96 Ch.8 Practice Problem #10. Calculator steps below.

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12 P/YR 11 g i

24 N 2 g n 11 I/YR 25000 PV 0 PMT FV gives 31120.71 25000 PV FV gives 31120.71 Ch.8 Practice Problem #12. Calculator steps below.

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12 P/YR 6.5 g i

6.5 I/YR 1 g n EFF% gives 6.70 100 CHS PV FV gives 106.70 RCL PV + gives 6.70 Ch.8 Practice Problem #14. Calculator steps below.

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2 P/YR 6.5 ENTER 2 ÷ i

6.5 I/YR 2 n EFF% gives 6.61 100 CHS PV




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FV gives 106.61 RCL PV + gives 6.61




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2 P/YR 6 ENTER 2 ÷ i

6 I/YR 2 n EFF% gives 6.09 100 CHS PV 12 P/YR FV gives 106.09 NOM% gives 5.93 12 n i 12 X gives 5.93 Ch.8 Practice Problem #18. Calculator steps below.

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12 P/YR 6 g i

6 I/YR 1 g n EFF% gives 6.17 100 CHS PV 2 P/YR FV 106.17 NOM% gives 6.08 2 n i 2 X gives 6.08 Ch.8 Practice Problem #22. Calculator steps below.

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1 P/YR 7 n

7 N 40000 CHS PV 40000 +/- PV 100000 FV 0 PMT I gives 13.99 100000 FV I/YR gives 13.99 Ch.8 Practice Problem #24. Calculator steps below.

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12 P/YR 7 g n




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84 N 40000 CHS PV 40000 +/- PV 100000 FV 0 PMT I gives 1.10 ENTER 100000 FV 12 X gives 13.16 I/YR gives 13.16 Ch.8 Practice Problem #28. Calculator steps below.

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1 P/YR 8 i

8 I/YR 20000 CHS PV 20000 +/- PV 0 PMT 0 PMT 40000 FV 40000 FV n gives 10.00 N gives 9.01 Note: HP-12c rounds up

to next whole period. Not as accurate.




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12 P/YR 8 g i

8 I/YR 20000 CHS PV 20000 +/- PV 40000 FV 0 PMT n gives 105 40000 FV 12 ÷ gives 8.75 N gives 104.32 ÷12 gives 8.69 Ch.8 Practice Problem #34. Calculator steps below.

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1 P/YR 8 n

8 N 7.5 i 7.5 I/YR 20000 PMT 20000 PMT 0 FV 0 FV PV gives -117146.07 PV gives -117146.07




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12 P/YR 7.5 g i

7.5 I/YR 1 g n EFF% gives 7.76 100 CHS PV 1 P/YR FV 8 N RCL PV + gives 7.76 7.76 I/YR 7.76 i 20000 PMT 20000 PMT 0 FV 8 n PV gives -115,972.41 PV gives -115,972.41 Ch.8 Practice Problem #38. Calculator steps below.

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12 P/YR 8 g n

96 N 7.5 g i 7.5 I/YR 1666.67 PMT 1666.67 PMT 0 FV 0 FV PV gives -120043.61 PV gives -120043.61 Ch.8 Practice Problem #40. Calculator steps below.

HP-10B HP-12C

CLEAR ALL CLX

12 P/YR 8 g n

96 N 7.5 g i 7.5 I/YR 1666.67 PMT 1666.67 PMT 90000 FV 90000 FV PV gives -169528.98 PV gives -169528.98




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HP-10B HP-12C

CLEAR ALL CLX

12 P/YR 30 g n

360 N 9 g i 9 I/YR 125000 PV 125000 PV 0 FV 0 FV PMT gives -1005.78 PMT gives -1005.78




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HP-10B HP-12C

CLEAR ALL CLX

12 P/YR 8.75 g i

8.75 I/YR 100000 PV 100000 PV 750 CHS PMT 750 +/- PMT 0 FV 0 FV n gives 494 N gives 493.24 Note: rounds up, not

exact answer Ch.8 Practice Problem #46. Calculator steps below.

HP-10B HP-12C

CLEAR ALL CLX

12 P/YR g BEG

BEG/END (set to BEGIN) 7 g n 84 N 9 g i 9 I/YR 2500 PMT 2500 PMT 0 FV 0 FV PV gives -156550.30 PV gives -156550.30 g END BEG/END (toggle off BEG)


HP-10B HP-12C

CLEAR ALL CLX

12 P/YR 3 g n

36 N 5 g i 5 I/Y 0 PV 0 PV 4250000 FV 4250000 FV PMT gives -109667.98 PMT gives –109667.98




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HP-10B

CLEAR ALL, BEG/END=END CLX

1 P/YR 5 n

5 N 10 i 10 I/Y 20 PMT 20 PMT PV gives -75.82 PV gives -75.82 1.10 ENTER 1.05 ÷ 1 - 1.10/1.05-1=.0476X100= 100 X gives 4.76 4.7619 I/Y I BEG/END = BEG G BEG PMT gives 16.61 PMT gives 16.61 X 1.1 = 18.27 1.1 X

CLEAR ALL, BEG/END=END Gives 18.27




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HP-10B

CLEAR ALL, BEG/END=END CLX

0.12 – 0.01 = 0.11 7.5 ENTER

1/x 0.12 ENTER 0.01 - X 7.5 ÷ Gives 68.18 Gives 68.18

Ch.8 Practice Problem #54(a). Calculator steps below.

HP-10B HP-12C

CLEAR ALL CLX

1 P/YR 400000 CHS g CF0

400000 +/- CFj 35000 g CFj

35000 CFj 37000 g CFj 37000 CFj 45000 g CFj 45000 CFj 46000 g CFj 46000 CFj 40000 ENTER 450000 + 40000+450000=490000 CFj Gives 490000 g CFj 12 I/YR 12 i NPV gives 49.28 f NPV gives 49.28 Ch.8 Practice Problem #54(b). Calculator steps below.

HP-10B HP-12C

CLEAR ALL CLX

1 P/YR 375000 CHS g CF0

375000 +/- CFj 35000 g CFj

35000 CFj 37000 g CFj 37000 CFj 45000 g CFj 45000 CFj 46000 g CFj 46000 CFj 40000 ENTER 450000 + 40000+450000=490000 CFj Gives 490000 g CFj IRR gives 13.73% f IRR gives 13.73%




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Ch.8 Practice Problem #56. $46,325,963 Cap Rate = 8.09%




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The construction loan collapses a series of costs (cash outflowsThe construction loan collapses a series of costs (cash outflows) ) incurred during the construction process into a incurred during the construction process into a single valuesingle value as of as of a single (future) a single (future) point in timepoint in time (the projected completion date of (the projected completion date of the construction phase).the construction phase).

Actual construction expenditures (Actual construction expenditures (““drawsdraws”” on the construction on the construction loan) are added to the accumulating loan) are added to the accumulating balancebalance due on the loan, due on the loan, and interest is charged and compounded (adding to the balance) and interest is charged and compounded (adding to the balance) on all funds drawn out from the loan commitment, from the on all funds drawn out from the loan commitment, from the time each draw is made.time each draw is made.

Thus, interest Thus, interest compounds forwardcompounds forward, and the borrower owes no , and the borrower owes no payments until the loan is due at the end of construction, when payments until the loan is due at the end of construction, when all principle and interest is due.all principle and interest is due.

Bottom line: Borrower (developer) faces no cash outflows for Bottom line: Borrower (developer) faces no cash outflows for construction until the end of the process, when the entire cost construction until the end of the process, when the entire cost is is paid (including the paid (including the ““cost of capitalcost of capital””).).



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The “Canonical” Formula- Graphical Representation

TT KV −

Construction Lease-Up Stabilized

Time 0 Time T

00 KV −

To Time T•Cash flows from the stabilized building (s) are discounted at Stabilized OCC to value main part of VT (or use direct capitalization with projected cap rate).•Cash flows from the lease-up period are compounded at Speculative OCC (Stabilized OCC + 50 to 200bps for lease-up risk) to value rest of VT•Cash flows from the construction period are compounded at Construction OCC to form KT

•VT is discounted at Speculative OCC to arrive at V0•KT is discounted at Construction OCC to arrive at K0

To Time 0



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The “Canonical” Formula- Graphical Representation

TT KV −

Development Phase Stabilized

00 KV −Canonical OCC

T

TTC KV

KVrE1

00

][1 ⎟⎟⎠

⎞⎜⎜⎝

⎛−−

=+

( )[ ] [ ]ttT

C

TT KPVVPVKVrEKV

−=−=+−

00][1



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The “Canonical” Formula- NPV Rule

• V0 – K0 < Land Cost– Don’t undertake the project

• V0 – K0 > Land Cost– Undertake the project



[ ] [ ] [ ] 00 KVKPVVPVKVPV TTTT −=−=−



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Three considerations are important and unique about applying theThree considerations are important and unique about applying the NPV rule NPV rule to evaluating investment in development projects as compared to to evaluating investment in development projects as compared to investments in stabilized operating properties:investments in stabilized operating properties:

1.1. ““TimeTime--toto--BuildBuild””:: Investment cash outflow occurs Investment cash outflow occurs over timeover time, not all at , not all at once up front, due to the once up front, due to the construction phaseconstruction phase..

2.2. Construction loans:Construction loans: Debt financing for the construction phase is Debt financing for the construction phase is almost almost universaluniversal (even when the project will ultimately be financed entirely (even when the project will ultimately be financed entirely by equity).by equity).

3.3. Phased risk regimes:Phased risk regimes: Investment risk is very different (greater) Investment risk is very different (greater) between the construction phase (the between the construction phase (the development investmentdevelopment investment per se) per se) and the stabilized operational phase. (Sometimes an intermediateand the stabilized operational phase. (Sometimes an intermediatephase, phase, ““leaselease--upup””, is also distinguishable.), is also distinguishable.)

We need to account for these differences in the methodology of hWe need to account for these differences in the methodology of how we ow we applyapply the NPV Rule to development investments. . .the NPV Rule to development investments. . .



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The Operating Budget The Operating Budget (Recall the items from Chapter 11)(Recall the items from Chapter 11)::•• Forecast Potential Gross Income (PGI, based on rent analysis)Forecast Potential Gross Income (PGI, based on rent analysis)

•• Less Vacancy AllowanceLess Vacancy Allowance

•• = Effective Gross Income (EGI)= Effective Gross Income (EGI)

•• Less forecast operating expenses (& capital reserve)Less forecast operating expenses (& capital reserve)

•• = Net Operating Income (NOI)= Net Operating Income (NOI)

The most important aspect is normally the rent analysis, which iThe most important aspect is normally the rent analysis, which is based s based (more or less formally) on a (more or less formally) on a market analysismarket analysis of the space market which the of the space market which the building will serve. building will serve. (See Chapter 6, or Wheaton(See Chapter 6, or Wheaton’’s 11.433 course.)s 11.433 course.)

The bottom line:The bottom line:NOI forecast, combined with NOI forecast, combined with cap ratecap rate analysis (of the asset market):analysis (of the asset market):

NOI / cap rate = Projected Completed Building Value = NOI / cap rate = Projected Completed Building Value = ““BenefitBenefit”” of the of the development project.development project.



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SFFA SFFA ““Back DoorBack Door”” Procedure: Procedure: Start with rents & building, and end with supportable developmenStart with rents & building, and end with supportable development costst costs……

Total Total LeaseableLeaseable Square Feet (based on the building efficiency ratio Square Feet (based on the building efficiency ratio times the gross area)times the gross area)X Expected Average Rent Per Square FootX Expected Average Rent Per Square Foot= Projected Potential Gross Income (PGI)= Projected Potential Gross Income (PGI)-- Vacancy AllowanceVacancy Allowance= Expected Effective Gross Income= Expected Effective Gross Income-- Projected Operating ExpensesProjected Operating Expenses= Expected Net Operating Income= Expected Net Operating Income÷÷ Debt Service Coverage RatioDebt Service Coverage Ratio÷÷ Annualized Mortgage ConstantAnnualized Mortgage Constant÷÷ Maximum Loan to Value RatioMaximum Loan to Value Ratio= Maximum Supportable Total Project Costs= Maximum Supportable Total Project Costs(Question: Can it be built for this including all costs?)(Question: Can it be built for this including all costs?)-- Expected Construction Costs (Other than Site)Expected Construction Costs (Other than Site)= Maximum Supportable Site Acquisition Cost= Maximum Supportable Site Acquisition Cost

Question: Can the site be acquired for this or less? Question: Can the site be acquired for this or less?

Typical approach for Typical approach for ““Use looking for a SiteUse looking for a Site””..www.bsscommunitycollege.in www.bssnewgeneration.in www.bsslifeskillscollege.in


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Example:Example:•• Office building 35,000 SF (GLA), 29,750 SF (NRA) Office building 35,000 SF (GLA), 29,750 SF (NRA) (85% (85% ““Efficiency RatioEfficiency Ratio””))..•• $12/SF (/yr) realistic rent (based on market analysis, pre$12/SF (/yr) realistic rent (based on market analysis, pre--existing tenant wants space).existing tenant wants space).•• Assume 8% vacancy (typical in market, due to extra space not prAssume 8% vacancy (typical in market, due to extra space not pree--leased).leased).•• Preliminary design construction cost budget (hard + soft) = $2,Preliminary design construction cost budget (hard + soft) = $2,140,000.140,000.•• Projected operating expenses (not passed through) = $63,000.Projected operating expenses (not passed through) = $63,000.•• Permanent mortgage on completion available at 9% (20Permanent mortgage on completion available at 9% (20--yr yr amortamort), 120% DCR.), 120% DCR.•• Site has been found for $500,000: Site has been found for $500,000: Is it feasible?Is it feasible?




So, the project seems feasible.So, the project seems feasible.

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛+

−=240

1209.1

1112/09.

18433

But again, something seems left outBut again, something seems left out…… Project may be feasible, Project may be feasible, butbut……www.bsscommunitycollege.in www.bssnewgeneration.in www.bsslifeskillscollege.in


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SFFA SFFA ““Front DoorFront Door”” Procedure: Procedure: Start with costs & end with rent required for feasibilityStart with costs & end with rent required for feasibility……

Site Acquisition Costs + Construction CostsSite Acquisition Costs + Construction Costs= Total Expected Development Cost= Total Expected Development CostX Loan to Value RatioX Loan to Value Ratio= Permanent Mortgage= Permanent MortgageX Annualized Mortgage ConstantX Annualized Mortgage Constant= Cash Required for Debt Service= Cash Required for Debt ServiceX Lender Required Debt Service Coverage RatioX Lender Required Debt Service Coverage Ratio= Required Net Operating Income or NOI= Required Net Operating Income or NOI+ Estimated Operating Expenses (Not passed through to tenants)+ Estimated Operating Expenses (Not passed through to tenants)= Required Effective Gross Income= Required Effective Gross Income÷÷ Expected Occupancy RateExpected Occupancy Rate= Required Gross Revenue= Required Gross Revenue÷÷ LeasableLeasable Square FeetSquare Feet= Rent Required Per Square Foot= Rent Required Per Square Foot

Question: Is this average required rent per square foot achievabQuestion: Is this average required rent per square foot achievable?le?

Typical approach for Typical approach for ““Site looking for a UseSite looking for a Use””..www.bsscommunitycollege.in www.bssnewgeneration.in www.bsslifeskillscollege.in


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Example:Example:•• Class B office building rehab project: 30,000 SF (of which 27,2Class B office building rehab project: 30,000 SF (of which 27,200 NRSF).00 NRSF).•• Acquisition cost = $660,000; Acquisition cost = $660,000; •• Rehab construction budget: $400,000 hard costs + $180,000 soft Rehab construction budget: $400,000 hard costs + $180,000 soft costs.costs.•• Estimated operating costs (to landlord) = $113,000/yr.Estimated operating costs (to landlord) = $113,000/yr.•• Projected stabilized occupancy = 95%.Projected stabilized occupancy = 95%.•• Permanent loan available on completion @ 11.5% (20Permanent loan available on completion @ 11.5% (20--yr yr amortamort) with 120% DSCR.) with 120% DSCR.•• Estimated feasible rents on completion = $10/SF.Estimated feasible rents on completion = $10/SF.

Site and shell costs:Site and shell costs: $ 660,000$ 660,000+ Rehab costs:+ Rehab costs: 580,000580,000= Total costs:= Total costs: $1,240,000$1,240,000X Lender required LTVX Lender required LTV x 80%x 80%= Permanent mortgage amount: $ 992,000= Permanent mortgage amount: $ 992,000X Annualized mortgage constant: x 0.127972X Annualized mortgage constant: x 0.127972= Cash required for debt svc:= Cash required for debt svc: $ 126,948$ 126,948X Lender required DCR:X Lender required DCR: x 1.20x 1.20= Required NOI:= Required NOI: $ 152,338$ 152,338+ + EstdEstd. . OperOper. Exp. (Landlord):. Exp. (Landlord): 113,000113,000= Required EGI:= Required EGI: $ 265,338$ 265,338÷÷ Projected occupancy (1Projected occupancy (1--vac):vac): ÷÷ 0.950.95= Required PGI:= Required PGI: $ 279,303$ 279,303÷÷ Rentable area:Rentable area: ÷÷ 27200 SF27200 SF---------------------------- ------------------= Required rent/SF:= Required rent/SF: $10.27 /SF $10.27 /SF

What major What major issue is left issue is left out here?out here?

Lender will Lender will base base mortgmortg on on MktMkt Val, not Val, not constrconstr cost.cost.

Use Use mktmkt cap cap rate info to rate info to est. bldg val.est. bldg val.



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11.431J/15.426J Real Estate Finance & Investments I, Fall 2006, Practice Final Exam There are five parts to this exam, plus an extra-credit question. The entire exam is designed to be finished in 2 hours, but you may take up to 3 hours. No open books or notes are permitted, but some possibly useful formulas are given at the end. Your name:_________________ ____________________________________ ID#_____________________ Part I: Multiple Choice (36 points, 3 points each). Select the single best alternative answer, based on what was taught in the course. Clearly indicate your selection by circling the letter. If it is not clear to the TA which your choice is, you will receive no credit. Read the question carefully before answering. 1. A property has a McDonalds restaurant on it, which can earn $50,000 per year. In any other use (including another brand of restaurant), the most it can earn is $40,000 per year. Assuming a discount rate of 10% and constant cash flow in perpetuity, what is the "investment value" of this property to McDonalds, and what is its "market value"?

a) Both investment value and market value are $400,000. b) Both investment value and market value are $500,000. c) Investment value is $400,000 and market value is $500,000. d) Investment value is $500,000 and market value is $400,000.

2. Suppose the riskfree rate of return is 3%, and the expected total return on the property free & clear is 7%, and you have a target total expected return of 11%. Assuming you can borrow at the riskfree rate, what Loan/Value ratio must you obtain for this real estate investment to meet your target expected return?

a) 0% b) 25% c) 50% d) 75% e) 80%

3. An investor believes that a certain property is worth $10,000,000. The seller refuses to sell it for that amount, but has offered to provide a 5-year interest-only loan for $5,000,000 at 4% interest (annual payments at the ends of the years, first payment due in one year). Market interest rates on such a loan are currently 6.5%. How much should the investor be willing to pay for the property from an investment value perspective (taking the loan deal) if the investor faces a 30% marginal income tax rate? (Ch15)

a) $10,000,000 b) $10,383,588 c) $10,403,023 d) $10,519,460 e) Insufficient information to answer the question.

4. Consider a 20-year (monthly-payment), 8%, $80,000 mortgage with 2 points prepaid interest up front. What is the yield to maturity?

a) 8.00% b) 8.12% c) 8.20% d) 8.27%

5. Consider an 8.5% loan amortizing at a 25-year rate with monthly payments. What is the maximum amount that can be loaned on a property whose net operating income (NOI) is $500,000 per year, if the underwriting criteria specify a debt service coverage ratio (DCR) no less than 125%?

a) $2,789,406 b) $3,409,091 c) $3,844,614 d) $4,000,000 e) $4,139,619

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6. For the same property as above, suppose the underwriting criteria is a maximum loan/value ratio (LTV) of 75%, and we estimate property value by direct capitalization using a rate of 11% on the stated NOI. By this criterion what is the maximum loan amount?

a) $2,789,406 b) $3,409,091 c) $3,844,614 d) $4,000,000 e) $4,139,619

7. Suppose a construction project anticipates end-of-month draws of $400,000, $300,000, and $600,000 consecutively. What will be the balance owed at the end of the third month if the interest on the loan is 7% per annum (nominal annual rate, compounded monthly), and no payments of either principal or interest are required during the construction period?

a) $1,306,430. b) $1,314,051. c) $1,378,960. d) Cannot be computed with the information given.

8. Consider the investment evaluation of a real estate development in which the property to be built is projected to reach stabilized occupancy at the end of Year 2 (two years from the time the investment decision must be made and construction will begin). The project is speculative in that there are no leases signed as of Time Zero (the present, when the investment decision must be made). The property level opportunity cost of capital is considered to be 9% for stabilized investments, and 10% for assets not yet stabilized (lease-up investments). Which of the following is true?

a) Property level before-tax cash flows beyond Year 2 should be discounted back to the end of Year 2 at 9%, and the projected stabilized asset value as of the end of Year 2 should be discounted two years to Time Zero at 10%.

b) Property level before-tax cash flows beyond Year 2 should be discounted back to the end of Year 2 at 10%, and the projected stabilized asset value as of the end of Year 2 should be discounted two years to Time Zero at 9%.

c) Property level before-tax cash flows beyond Year 2 should be discounted all the way back to Time Zero at the 10% rate.

d) Property level before-tax cash flows beyond Year 2 should be discounted all the way back to Time Zero at the 9% rate.

9. The opportunity cost of capital (discount rate) applicable on an unlevered basis to assets that are not yet leased up (“speculative built properties”) is best described as:

a) Usually about 50 to 200 basis-points above the OCC for the same property with stabilized occupancy, based in part on analysis of the “interlease” discount rate implied in the property market.

b) Usually about 300 to 500 basis-points above the OCC for the same property with stabilized occupancy, based in part on analysis of the “interlease” discount rate implied in the property market.

c) Usually about 50 to 200 basis-points below the OCC for the same property with stabilized occupancy, based on the typical upward slope of the yield curve in the bond market, because lease-up is near term.

d) Usually about 300 to 500 basis-points below the OCC for the same property with stabilized occupancy, based on the typical upward slope of the yield curve in the bond market, because lease-up is near term.

10. All of the following are typical types of real options found in development projects or developable land ownership, except:

a) The wait option b) The phasing option c) The switch option d) The refinance option

11. All of the following must be known (or assumed) in order to rigorously derive the real option value of a land parcel or development option, except:

a) The current value of the underlying asset (the built property value, V0 ) b) The opportunity cost of capital (OCC) of the underlying asset ( rV ) c) The volatility of the underlying asset (σ) d) The payout rate (or current income yield rate) of the underlying asset ( yV )

12. The replicating portfolio of a development option (land) consists of:

a) A long position in an asset like the stabilized building to be built and a short position (borrowing) in a riskless bond. b) A short position in an asset like the stabilized building to be built and a long position (lending) in a riskless bond. c) Long positions in both the stabilized building and a bond. d) Short positions in both the stabilized building and a bond.

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Part II: Definitions (12 points, 4 points each). Provide a complete definition of each term or phrase in the space below each. Answer in a single, clear sentence. (You may provide a single example or formula to clarify your answer if necessary.) Only define the subject term; do not add extraneous material in your answer. Write legibly; no credit will be given for writing we cannot decipher. 1. Phased risk regimes (in development projects): 2. Back-door feasibility analysis: 3. Promote (hurdle and preferred return):

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Part III: Short Answer Questions (20 points, 10 points each question): Choose 2 out of the 3 questions below, and answer each question in the space provided below that question. Please be sure it is clear to us which question you DON’T want to be graded. If the TA cannot figure it out, we will grade only the first four. 1. What are the major line items in the operating budget of a development project, and why might it make sense for such a budget to consider only a single year’s operation of the building? 2. Why is it that construction loans are almost always used to finance all or most of the construction costs in a development investment, even when the investor has plenty of cash that could be used to pay for construction? 3. Is it appropriate, and if so, why is it appropriate, to apply a riskless or nearly riskless OCC to construction cost cash flows in the typical development project?

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Part IV: Longer Problems (20 points, 10 points each) Choose 2 out of the following three questions and answer in the space provided on the page. Indicate clearly which questions we should grade or we will grade the first two. 1. Based on the following information, develop a front door “Simple Financial Feasibility Analysis” (SFFA) for this project estimating the required minimum market gross rent per SF that will support development.

• 40,000 NRSF office building project. • Acquisition & construction cost = $1,500,000; • Estimated operating costs (to landlord) = $100,000/yr. • Projected stabilized occupancy = 95%. • Permanent loan available on completion @ 9% (interest-only loan) with 130% debt service coverage requirement on

the net operating income, and 75% maximum loan-to-value ratio. Show your work.

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2. A lender and a developer combine to undertake a development with an expected 4-year holding period, and the following projected net cash flows (in thousands), including both land purchase and construction at time 0. Year 0 1 2 3 4 Project net cash flows ($10,000) $1,000 $1,000 $1,000 $11,000

Construction is instantaneous at time 0, and the lender will provide $8,000,000 to cover all construction costs at that time zero after the developer has purchased the land for $2,000,000 (assume both occur simultaneously at time 0). The loan is a “mini-perm” loan for four years at a 6% interest rate, with the loan’s principal balance to be retired starting in year 1 based on priority access to all available project cash flow. Set up the projected capital accounts for the lender and the developer with their projected cash flows each year, and compute the projected IRR for: (a) The underlying project as a whole; (b) The lender; and (c) The developer. Please use the following template to help you organize and present your answer. (You may use the back of the page for computations.) Period 0 1 2 3 4 IRR Project net cash flows ($10,000) $1,000 $1,000 $1,000 $11,000 Lender: Credit Line Ceiling Available Beginning Balance Draw Interest Earned Repayments to Lender Ending Loan Balance Lender CF Project CFs after loan CFs Developer: Beginning Balance Draw Repayments Ending Balance Developer CF Project CFs after Loan & Dvlpr CFs

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Part V. Required Problem (20 points) In the following situation: Today (time 0) Next Year (Yr.1) Probability 100% 50% 50% Value of Developed Property $1000 $700 $1300 Development Cost (exclu land) $800 $800 $800 Suppose no further value after next year, construction is instantaneous, the riskfree interest rate is 4%, the expected return (OCC) on unlevered investments in developed property is 7.5%, what is the value today of the land? And should development be undertaken now or should you wait.

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Part VI: Extra-credit question. Earn up to 5 points extra credit. It can help you but not hurt you. Describe the call option model of land value. What is the “underlying asset” in this model? What is the “exercise price”? What is the typical maturity of the land development option? Formulas that may (or may not) be useful in this exam . . . a + da + d2a + . . . + dn-1a = a(1-dn)/(1-d). PMT/(1+r) + PMT/(1+r)2 + . . .+ PMT/(1+r)n = (PMT/r)[1 – 1/(1+r)n]. CF + CF/(1+r) + CF/(1+r)2 + . . .+ CF/(1+r)n-1 = (1+r)(CF/r)[1 – 1/(1+r)n]. CF/(1+r) + (1+g)CF/(1+r)2 + (1+g)2CF/(1+r)3 + . . . (forever) = CF/(r-g). EAY = (1+CEY/2)2-1; MEY=((1+EAY)(1/12)-1)*12. PMT = PV*(i/m)/(1 – 1/(1 + i/m)N); i=IntRate/Yr, m=Pmts/Yr. N=(Cu-Cd)/(Vu-Vd) B=(NVd-Cd)/(1+rf).

( )( ) ( )fVVrrE

downup rCCCECdownup

fV +−−= −− 1][ %%

][100

( )( ) ( )( ) ( )

( )

1][1][1

][1][1][1

−⎥⎦

⎤⎢⎣

⎡

+−+++−

=T

TT

VTT

D

TD

TVTT

C LrEVrErErELVrE

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PRACTICE ONLY 11.431J/15.426J Real Estate Finance & Investments, Fall 2003, Practice Midterm Exam There are two parts to this quiz, plus an extra-credit question. The entire quiz is designed to be easily finished in 75 minutes. No open books or notes are permitted. (Some mathematical formulas are given on the last page.) Your name:_________________________________________ ID#_____________________ Part I: Multiple Choice (80% of grade, 26 equal-weighted questions). Select the best alternative answer, based on what was taught in the course. Clearly indicate your selection by circling it. If it is not clear to the TA which your choice is, you will receive no credit. Read the question carefully before answering. 1. Total development costs (including sufficient profit for the developers) are $200/SF. Cap rates in the asset market are 10%. What is the “replacement cost rent” in this market? (a) $20.00/SF. (b) $16.00/SF. (c) $12.50/SF. (d) $10.00/SF. 2. All of the following are fundamental causal determinants of cap rates in the property asset market, except: (a) The opportunity cost of capital (as determined in the capital market). (b) The expected growth in property rents (as determined in the space market). (c) The risk perceived for the property (as determined in the space and capital market). (d) The net income divided by the property price. 3. Which of the following is an example of “negative feedback” in the real estate system? (a) Since the stock of built space cannot readily shrink, rents will fall when demand falls. (b) Lenders make money by issuing loans, so they tend to keep the capital flowing to developers even during down markets. (c) Real estate markets exhibit inertia, so market participants rationally extrapolate past rent trends into the future. (d) Growth in space usage demand stimulates increased rents or improved prospects for future rents, which increases the present value of real estate assets, which improves the profitability of new development projects. 4. Which of the following is true about typical real estate investment (unlevered, at the direct property level) and inflation risk? (a) Real estate investment appreciation returns do not generally keep pace with inflation in the long run, but real estate investment provides a hedge against inflation risk in that unexpected changes in inflation tend to be positively correlated with changes in property value in the short to medium term. (b) Real estate investment appreciation returns generally at least equal the inflation rate in the long run, but real estate does not provide a good hedge against inflation risk in that unexpected changes in inflation do not tend to be positively correlated with changes in property value in the short to medium term. (c) Real estate investment appreciation returns generally at least equal the inflation rate in the long run, and real estate investment provides a hedge against inflation risk in that unexpected changes in inflation tend to be positively correlated with changes in property value in the short to medium term. (d) Real estate investment appreciation returns do not generally keep pace with inflation in the long run, and real estate does not provide a good hedge against inflation risk in that unexpected changes in inflation do not tend to be positively correlated with changes in property value in the short to medium term. 5. In which of the following situations would it be most appropriate to measure an investment manager's performance using the IRR rather than the time-weighted average periodic return? (a) Client hires manager to place capital as soon as possible. (b) Client requires a large proportion of its invested capital to be liquid at all times for withdrawal on demand. (c) Client gives manager a line of capital with discretion over when to acquire and dispose of illiquid assets. (d) All of the above.

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6. The expected return on an investment in a property is inversely related to the price you pay for the property fundamentally because: (a) The future cash flows the property can generate are independent the price you pay for the property today. (b) The return must include a risk premium. (c) Inflation must be subtracted out. (d) The investor faces a budget constraint. (e) None of the above. 7. The table below shows two 10-year cash flow projections (in $ millions, including reversion) for the same property. The upper row is the projection that will be presented by the broker trying to sell the building, the bottom row is the realistic expectations. Suppose that it would be relatively easy for any potential buyers to ascertain that the most likely current market value for the property is about $10 million. What is the most likely amount of “disappointment” in the ex post annual rate of total return earned by an investor who buys this property believing the broker’s cash flow projection? Year 1 2 3 4 5 6 7 8 9 10Presented $1.0000 $1.0300 $1.0609 $1.0927 $1.1255 $1.1593 $1.1941 $1.2299 $1.2668 $14.7439Realistic $1.0000 $1.0000 $1.0000 $1.0000 $1.0000 $1.0000 $1.0000 $1.0000 $1.0000 $11.0000(a) 0.00% (b) 1.00% (c) 3.00% (d) 26.68% (e) Cannot be determined from the information given. 8. The table below shows the projected cash flows (including reversion) for Property A and Property B. If both properties sell at fair market value for a cap rate (initial and terminal cash yields) of 8%, then which statement below correctly describes the relative investment risk in the two properties?

Annual net cash flow projections for two properties ($ millions) Year 1 2 3 4 5 6 7 8 9 10 A $1.0000 $1.0300 $1.0609 $1.0927 $1.1255 $1.1593 $1.1941 $1.2299 $1.2668 $18.10 B $1.0000 $1.0000 $1.0000 $1.0000 $1.0000 $1.0000 $1.0000 $1.0000 $1.0000 $13.50 (a) Property A is more risky. (b) Property B is more risky. (c) Both properties are equally risky. (d) Cannot be determined based on the information given. 9. You are trying to apply a multi-year DCF analysis to evaluate an investment property with some long-term leases in it. You observe that other properties with similar lease structure and risk have been selling at cap rates around 11% (based on NOI with no capital reserve). You believe these other properties typically face capital expenditures on the order of 1% of property value per year in the long run, and that given such expenditures their net cash flows and values would reasonably be expected to grow in the long run at about 3% per year. What discount rate should you apply to your subject property in your DCF valuation? (a) The Treasury bond rate because of the long-term leases. (b) 10% (c) 13% (d) 14% (e) Cannot be determined from the information given. 10. Normally, one would expect what relation between the "going-in" and "going-out" cap rate? (a) The going-in cap rate should be higher than the going out. (b) The going-out cap rate should be at least as high as the going-in rate. (c) There is no particular relation between the two.

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11. Suppose the lease on a certain space will expire at the beginning of 2001. You believe that the probability of the existing tenant renewing is 50 percent. If he renews, you will need to spend only an estimated $5.00/SF to upgrade his space. If he does not renew, it will take $25.00/SF to modernize the space, even then you expect 6 months of vacancy. What expected cash flow forecast should you put in year 2001 of your pro-forma for this space, if you expect triple-net market rents on new leases in 2001 to be $20/SF? (a) $17.50/SF (b) $15.00/SF (c) zero (d) - $10.00/SF (e) Insufficient information provided to answer the question. 12. Suppose you analyze a particular deal and it appears that for an investment of $1,000,000 your client can obtain a positive NPV of over $500,000. Your client is typical of the type of high tax bracket individual investors who commonly purchase and sell this type of property, and indeed typically determine equilibrium prices in the asset market in which these properties are sold. What should you do? (a) Reject the deal out of hand because it costs twice as much as its NPV. (b) Phone your client right away on your cell phone and urge her to pounce on this deal before it "gets away" - the seller must have made a mistake in their offering price! (c) Buy the property with cash, take out an 80% loan-to-value ratio mortgage, and laugh all the way to the bank with $200,000 of arbitrage profits! (d) Sharpen your pencil, double-check your assumptions and analysis, try to find what is unique about your client. (e) Cannot be answered from the information given. 13. Which statement is true ex ante? (a) Leverage normally increases the owner's income return (cash yield) if you pay market value for the property. (b) Leverage normally increases the owner's income return (cash yield) if you pay more than market value for the property. (c) Leverage normally increases the owner's total return (including appreciation) if you pay market value for the property. (d) Leverage normally increases the owner's total return (including appreciation) if you pay more than market value for the property. 14. Assuming riskless debt, if the return risk is ±15% with a 40% Loan/Value Ratio, then with a 80% Loan/Value Ratio the return risk is: (a) ±7.5% (b) ±15% (c) ±30% (d) ±45% (e) Cannot be determined from the information given. 15. All of the following are true about the “property before-tax (PBT) shortcut”, except: (a) The PBT shortcut is useful not only because it simplifies the investment analysis but because it avoids the necessity of estimating after-tax parameters that may be difficult to observe without error. (b) The shortcut is made possible by the existence of a reasonably well functioning market for the type of investment asset in question. (c) The shortcut works for estimating market value always, and for estimating investment value for investors who are typical of the marginal investors in the relevant asset market. (d) At the PBT level the investor’s own subjective opportunity cost of capital can be used as the discount rate in order to estimate that investor’s “investment value” (IV) for the property.

16. After-tax cash flow will exceed before-tax cash flow whenever: (a) Taxable income is negative. (b) Capital expenditures exceed net operating income. (c) The building is fully depreciated. (d) Interest and depreciation expenses are less than net operating income.

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17. A non-residential commercial property which cost $500,000 is considered to have 30 percent of its total value attributable to land. The annual depreciation expense chargeable against taxable income is: (a) $18,182 (b) $15,873 (c) $13,967 (d) $8,974 18. The difference between the net operating income (NOI) and the equity before-tax cash flow (EBTCF) is: (a) Property Tax Expense and capital expenditures. (b) The debt service and capital expenditures. (c) Property taxes and income taxes. (d) Interest expense and depreciation expense. 19. The NOI is $40,000; there are $5,000 in tenant improvement expenditures paid for by the landlord; there is a $200,000 interest-only loan at 8 percent annual interest; the depreciable cost basis of this residential property is $300,000; the owner's tax bracket is 33 percent. What is the Equity After-Tax Cash Flow (EATCF)? (a) $14,680 (b) $27,800 (c) $30,680 (d) $35,000 (e) Cannot be determined from the information given. 20. A seller has offered you a $1,000,000 interest-only 5 year loan at 6% (annual payments), when market interest rates on such loans are 8%. Basing your decision on market values, how much more should you be willing to pay for the property than you otherwise think it is worth, due to the financing offer? (a) Zero, by definition. (b) $26,497 (c) $79,854 (d) $98,412 21. Again considering the same seller loan offer as in the previous question, suppose you face a 35% marginal income tax rate and so does the marginal investor in the debt market. Now basing your decision on investment value, how much more should you be willing to pay for the property than you otherwise think it is worth, due to the financing offer? (a) Zero, by definition. (b) $26,497 (c) $55,973 (d) $86,602 22. Consider a 20-year (monthly-payment), 8%, $80,000 mortgage with 2 points prepaid interest up front. What is the "effective interest rate" or yield over the borrower’s expected holding period if the borrower expects to hold the loan for 12 years? (a) 8.00% (b) 8.25% (c) 8.31% (d) 8.56% 23. In comparing an adjustable rate mortgage (ARM) with a fixed rate mortgage (FRM): (a) Both the borrower and lender bear more interest rate risk with the ARM than with the FRM. (b) Both the borrower and the lender bear less interest rate risk with the ARM than with the FRM. (c) The ARM borrower bears more interest rate risk, but the ARM lender bears less interest rate risk, than with the FRM. (d) The ARM borrower bears less interest rate risk, but the ARM lender bears more interest rate risk, than with the FRM.

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24. Consider an 8.5% loan amortizing at a 25-year rate with monthly payments. What is the maximum amount that can be loaned on a property whose net operating income (NOI) is $500,000 per year, if the underwriting criteria specify a debt service coverage ratio (DCR) no less than 125%? (a) $2,789,406 (b) $3,409,091 (c) $3,844,614 (d) $4,000,000 (e) $4,139,619 25. For the same property as above, suppose the underwriting criteria is a maximum loan/value ratio (LTV) of 75%, and we estimate property value by direct capitalization using a rate of 11% on the stated NOI. By this criterion what is the maximum loan amount? (a) $2,789,406 (b) $3,409,091 (c) $3,844,614 (d) $4,000,000 (e) $4,139,619

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Part II (20%): 1 of 2 questions. Answer either one of the questions below, or diversify your portfolio by answering both. If you answer both, we will grade both and assign each question half of the 20% for this part. If you answer only one, that one you answer will get the full 20%. Please be sure it is clear to us which question(s) you want to be graded. If the TA cannot figure it out on her own, she will grade both. 1. Suppose you own a vacant but developable land parcel on the outskirts of the metropolitan area. This land produces no income but owes 2% of its value per year in property taxes. Meanwhile, typical income properties are yielding 9% (that is, they have a current cash yield, or “cap rate”, of 9%). If inflation is expected to be around 3% per year, and you expect your land will appreciate at 10% per year, what should you do with this land parcel? (Be specific and please explain why you should do what you say.) 2. (a) Fully explain and clarify the following statement: “There are two types of tax shields available to investors in property equity: deprecation tax shields (DTS) and interest tax shields (ITS), but only one of these types of tax shields generally adds to the investment value of the investment no matter what the investor’s marginal tax rate.” (b) As part of your answer, quantify the NPV to two different borrowers, from an after-tax investment value perspective, of a perpetual loan of $1,000,000 at 6% interest when the market yield on corporate bonds is 6% and on otherwise identical municipal bonds is 4%, and Borrower A faces a marginal tax rate of 30% while Borrower B faces a marginal tax rate of 35%. (c) Also, compare the NPV to Borrower B to the PV of the that borrower’s interest tax shields (the PV of the borrower’s tax deductions associated with the loan).

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Part III: Extra-credit question. Earn up to 5% extra credit. It can help you but not hurt you. And this time, no diversification. You must pick only one of the questions below to answer. If the TA cannot tell which one you wanted, he will simply grade the first. (Aside: Do you get how valuable diversification is if you are risk-averse?) 1. Consider the following fully-amortizing 5-year ARM (contract interest rate can change once every 60 months) with 15-year maturity, monthly payments. The ARM has initial interest rate 6.5% with 2 points, caps are 2% per jump, 5% lifetime, margin is 300 basis points, index is Treasury Bonds that are currently yielding 6.0%. The loan amount is $100,000. Under the “straight line” assumption about future interest rates (i.e., assuming the market rate on the index remains constant), what is the yield to maturity? (Show your work if you want to possibly get partial credit.) 2. (5 points) Consider a $4,000,000, 7%, 25-year mortgage with monthly payments and a 7-year maturity with balloon. If the market yield is 7.5% (BEY), how many disbursement discount points must the lender charge to avoid doing a negative NPV deal from a market value perspective? Formulas that may (or may not) be useful in this exam . . . a + da + d2a + . . . + dn-1a = a(1-dn)/(1-d). PMT/(1+r) + PMT/(1+r)2 + . . .+ PMT/(1+r)n = (PMT/r)[1 – 1/(1+r)n]. CF + CF/(1+r) + CF/(1+r)2 + . . .+ CF/(1+r)n-1 = (1+r)(CF/r)[1 – 1/(1+r)n]. CF/(1+r) + (1+g)CF/(1+r)2 + (1+g)2CF/(1+r)3 + . . . (forever) = CF/(r-g). EAY = (1+CEY/2)^2-1; MEY=((1+EAY)^(1/12)-1)*12. PMT = PV*(i/m)/(1 – 1/(1 + i/m)^N); i=IntRate/Yr, m=Pmts/Yr.

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11.431J/15.426J Real Estate Finance & Investments, Fall 2006, Midterm Diagnostic Exam Your name:____________________________________ ID#_____________________ Answer all of the questions in the space provided below each one. Think about your answer before you start writing, and organize your thoughts. Please write clearly and legibly. (Make notes or outline on the back if that helps you organize, but those won’t count in the marking.) 1. (15 pts) Explain in your own words what is “the NPV Investment Decision Rule”, and why it makes sense, what it is based on.

2. (20 pts) Define and contrast: “Market Value” (MV), and “Investment Value” (IV). Use a market supply and demand diagram to illustrate the difference between these two values. (Clearly label and define all axes, lines, and points in the chart.) Explain how the DCF computation of MV and IV differ in their use or treatment of investors’ income taxes.

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3. (10 pts) What is the difference between a property’s Net Operating Income (NOI) and its Property Before-Tax Cash Flow (PBTCF)?

4. (20 pts) Suppose a property can be bought for $1,000,000 and it will provide $100,000/year net cash flow forever, and you can borrow a perpetual interest-only mortgage secured by that property at an 8% interest rate, up to an amount of $750,000. (a) Does this present “positive” or “negative leverage”, and (b) why? (c) Will the expected return to the levered equity be less than 8%, exactly 8%, between 8% and 10%, exactly 10%, or greater than 10%? (d) Do you think that the use of leverage in this case will increase the NPV of the investment for the equity investor in the property? (e) Why or why not?

5. (10 pts) Do you think in general (or typically on average) the going-in cap rate is larger or smaller than the going-out or terminal cap rate? Why?



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6. (25 pts) Below is a 10-year projection of a before-tax cash flow stream. Suppose that the market before-tax OCC for cash flows of this type of risk is 10% per annum, and the marginal investor in the market for the type of asset that produces these cash flows faces a 35% income tax rate, but you face a 25% income tax rate. The reversion amount of $10,000 in Year 10 is not subject to any income tax. What is: (a) the market value (MV) of this cash flow stream? (b) the investment value (IV) to you of this cash flow stream? (Show your computations.)

Year 1 2 3 4 5 6 7 8 9 10 $1,000 $1,000 $1,000 $1,000 $1,000 $1,000 $1,000 $1,000 $1,000 $11,000

Formulas that may (or may not) be useful in this exam . . . a + da + d2a + . . . + dn-1a = a(1-dn)/(1-d). = a/(1-d) if n = ∞ and < 1. PMT/(1+r) + PMT/(1+r)2 + . . .+ PMT/(1+r)n = (PMT/r)[1 – 1/(1+r)n]. CF + CF/(1+r) + CF/(1+r)2 + . . .+ CF/(1+r)n-1 = (1+r)(CF/r)[1 – 1/(1+r)n]. CF/(1+r) + (1+g)CF/(1+r)2 + (1+g)2CF/(1+r)3 + . . . (forever) = CF/(r-g). EAY = (1+CEY/2)2-1; MEY=((1+EAY)(1/12)-1)*12. PMT = PV*(i/m)/(1 – 1/(1 + i/m)N); i=IntRate/Yr, m=Pmts/Yr. PV0[V1] = CEQ[V1] / (1 + rf) ; CEQ[V1] = E[V1] – (V1

up – V1down)(E[rV] – rf) / (Vup% – Vdown%) = ((1 + rf) / (1 + E[rV]))E[V1]

E = Mc2



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(selections from chs.1, 2, 7 of text.)

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