fundamentals of project financial and investment analysis

Real Estate Financial and Investment Analysis 1

FUNDAMENTALS OF PROJECT FINANCIAL AND INVESTMENT ANALYSIS

This presentation will lay the groundwork for the remainder of the course, reviewing basic principles of finance as they relate to real estate project financial-investment analysis and evaluation.

There will be four sessions:

I. Structuring a real estate feasibility analysis

II. Evaluating the risk/return tradeoff for real estate projects

III. Developing techniques of financial analysis

IV. Examining problems and pitfalls of financial investment analysis.


I. STRUCTURING A REAL ESTATEFEASIBILITY ANALYSIS

This introductory session will address the concept of feasibility and real estate investment analysis; development of the first-year pro forma; and the usefulness of the CAP rate.


Yes, Virginia there are only three things that matter in real estate...

LOCATION! LOCATION! LOCATION!

L

REGIONAL FACTORS

&

MACROECONOMIC

CIRCUMSTANCES

x L x

NEIGHBORHOOD

ELEMENTS

L

SITE-SPECIFIC

FEATURES


OUTLINE OF A FEASIBILITY STUDY

1. Site Analysis

• Survey of site to determine net useable land area

• Zoning of site and related constraints

• Availability of utilities to site

• Subsurface soil conditions

• Preliminary title report, CC & Rs

2. Initial Concept

• Establish target land development concept in terms of developer’s goals, permitted zoning, and developer’s financial resources



3. Demand Analysis

• Evaluate the economic base that supports the community in which project is located:

– Population projections

– Employment projections

– Income Projections

• Study the demand forces that pertain to your specific project type

• Analyze the competitive market within which you must operate

4. Supply Analysis

• Determine market area related to project

• Analyze the present and future inventory of product that you will be competing with in relation to your delivery date

• Determine product mix in relation to competitive rents, pricing, and amenities



5. Specific Development Scheme

• With architects and engineers, developer relates concept to market conditions, with a specific development scheme, land use plan

6. Cost Estimates

• Based on a specific plan, developer then estimate all hard and soft costs based on the “bid date” of the project



7. Financial Structure

• Reviews profitability for go/no go decisions

• Review mortgage loan ratios, terms of borrowing, equity position, tax considerations

• Determine phasing, if any, and absorption rates

8. Rate of Return Analysis

• Review risk factors related to project

• Review length of investment period

• Determine rate of return “on” and “of” the investment


WILSHIRE BOULEVARD OFFICE BUILDING

Building Synopsis

• Gross building area 205,000 sq. ft.

• Net leasable area 176,000 sq. ft. (86%)

• Parking structure 427 cars



Direct Costs

• Office building: 205,000 sq. ft. at $43/sq. ft.

• Parking structure

– Above grade: 22,420 sq. ft. at $24/sq. ft.

– Below grade: 125,000 sq. ft. at $28/sq. ft.

• Tenant improvements: 176,000 sq. ft. at $11/sq. ft.

• Site development

• Architectural & Engineering

– 6% of hard costs ($14,984,000)

• Contingency

– 5% of $15,883,040

TOTAL

$8,815,000

538,000

3,511,000

1,936,000

84,000

889,040

794,152

$16,667,192



Indirect Costs

• Real estate taxes

– 1% of direct cost plus land; 15 mos./2

• Permits, legal fees, title, escrow, insurance

• Development fee: 3% of hard costs

• Leasing commission: 3% on $22 x 176,000 x 5 years

• Lease-up expense: $4/sq. ft. x 176,000 sq. ft. for 6 mos.

• Consulting fee

TOTAL

$123,000

150,000

500,015

580,800

352,000

150,000

$1,855,815



TOTAL DIRECT AND INDIRECT COSTS

Financing cost: 16% for 15 mos./2 on total costs

& financing cost ($20,581,119)

Land

TOTAL COST INCLUDING FINANCING

$18,523,007

2,058,112

3,000,000

$23,581,119



FULL-YEAR OPERATING PRO FORMA

Gross rental income - $22/sq. ft. on 176,000 sq.ft. $3,872,000Parking income - 40/car for 427 cars +204,960Less 5% vacancy and collection problems -203,848

Effective Gross Income $3,873,112

Building operating expense - $4 x 176,000 sq. ft. -704,000Parking garage operating -30,000

Net Effective Income or Net Operating Income (NOI) $3,139,112

Debt service on $20,581,927 Loan for 30 yrs. at 10.5% -2,259,252

Net Spendable Income (Net cash flow before taxes and after debt service)

$879,860

Economic value of building capped at 9% $34,879,022


BASIC ACCOUNTING FOR INCOME PROPERTIES

GROSS POSSIBLE INCOME (GPI)

- VACANCY AND BAD DEBT FACTOR

EFFECTIVE GROSS INCOME (EGI)

- OPERATING EXPENSES

NET OPERATING INCOME (NOI) OR NET EFFECTIVE INCOME

- DEBT SERVICE

CASH FLOW BEFORE TAXES (CFBT)

- NET TAXES*

NET SPENDABLE INCOME (NSI)

* CFBT + Principal Paydowns - Depreciation = TAXABLE INCOME


THE CAP RATE CONCEPT

N ˆ O Ik

=MV, where

MV is the estimate of fair market value,

N ˆ O I is the estimate of the first normal year's net operating income, andk is the capitalization rate; 1/ k is a first year's price (value) to earnings ratio.


GRAPHIC INTERPRETATION OF CAP RATE

MV=(1/k)NOI

MV

NOI


WHAT THE CAP RATE MUST TAKE INTO ACCOUNT

1. Riskless Rate of Return

• real return

• inflationary adjustment

2. Liquidity

3. Management Return

4. Parcel Specificity Risk


HOW TO CHOOSE THE CORRECT CAP RATE

How do you know what the correct capitalization rate is? Only by knowing intimately every feature of the property you are considering, along with the basic factors touched upon above:

• Investor demand for and the existing supply of the particular type of property

• Stability and security of future income

• Capitalization rates of price earning ratios of alternate, non-real estate investments with comparable risk.


DETERMINING RISK AND DEMAND

The investor can determine risk and demand as it affects the CAP rate by carefully examining the property’s features:

1. Exact Location

In the main business district, for example, even a few feet may make one location better than another. Access to mass transportation becomes increasingly important as the costs of private transportation and/or regulations become increasingly higher.

2. Age of the Building

The older the building, the less future income can be derived from it in its present state.

3. Size of the Land Parcel


DETERMINING RISK AND DEMAND

4. Quality of the Tenancies

For example, other things being equal, a long-term lease represents more stable value than a short-term lease (e.g., hotel/motel room rentals are far less secure than apartment building leases).

5. Existing Financing on the Property Even between properties of otherwise equal investment value, better financing on one may give it an apparently lower CAP rate.

6. Operating Costs

Pay particular attention to higher energy costs for heating and air conditioning. In any comparison of buildings for investment purposes, the type of construction (glass walls, for example) can have an important bearing on those costs. Labor costs and the likelihood of continued increases also need to be considered.


EXCEL SPREAD SHEET AND CHART INSERTS

PP 16 - 22


II. EVALUATING THE RISK-RETURN TRADEOFF FOR A REAL ESTATE PROJECT

Now we will address the generation of the discounted cash flow, and take a first cut at financial ratio analysis.


DISCOUNTED CASH FLOW MODELS

I. DCF Model-Basic Data Requirements

A. Investment outlays

• land costs

• building costs

• depreciation method

• useful life

B. Operational characteristics

• rental income

• vacancy and collection factors

• operating expenses

• changes over time




C. Financing• amount of equity• amount of debt• amortization schedules• interest rates• required rate of return

D. Reversion• holding period• terminal value• debt retirement plans• reversion period expenses




E. Taxation elements

• ordinary income

• capital gains

• recapture provisions

• minimum tax, preference items


II. DCF MODEL: INPUTS AND OUTPUTS

Basic DataRequirements

of Model

Basic DataRequirements

of Model

Annual CashFlows during

Holding Period

Annual CashFlows during

Holding Period

Reversion CashFlow at End ofHolding Period

Reversion CashFlow at End ofHolding Period

Implicit Assumptions - CAP Rates - Price/Rent Ratios - Expense Ratios

Implicit Assumptions - CAP Rates - Price/Rent Ratios - Expense Ratios

Riskiness - Leverage - Coverage - Break-even Points

Riskiness - Leverage - Coverage - Break-even Points

CASH FLOW ANALYSISCASH FLOW ANALYSIS

Rate of Return- IRR/NPV

Rate of Return- IRR/NPV


RISK DICHOTOMY FOR REAL ESTATE

RiskRisk

Debt/EquityDebt/Equity

Business RiskBusiness Risk

AssetsAssets

Financial RiskFinancial Risk


III. PROBLEMS INHERENT IN REAL ESTATE INVESTMENT ANALYSIS FOR INCOME

PROPERTIES: UNDERLYING RISK ANALYSIS

A. Stabilized pro forma net operating income

B. Projected changes in operating expenses and revenue base

C. Projected selling price or refinancing value

D. Estimated holding period

E. Reinvestment opportunities

F. Tax effects and financing effects


A HIDDEN ISSUE IN MANY ANALYSIS:EXPECTED DISTRIBUTION OF RETURNS FOR INVESTMENTS

_R Ri

ESTIMATED RATE OF RETURN

= Expected mean rate of returnRi = The ith investment expeced rate of return

IMPORTANT ISSUES TO CONSIDER

Is distribution stable?Does the mean shift over time?Does the shape change over time?How is the distribution affected by tax changes, changes in

inflation, general economic conditions, and so forth?

R


SPREAD SHEET ANALYSIS - 1986 TAX LAWS

EXCEL SPREAD SHEET AND CHART INSERTS


OFFICE BUILDING MARKET ANALYSIS

1. KEY ELEMENT: Non manufacturing employment growth is the underlying demand generation for office space.

2. Analysis of the office buildings, though related more or less to all sub-markets, must stratify the market into appropriate subsections (see Figure 1).

Figure 1

Downtown Suburbs

High-rise Mid-rise Office Parks Other

Multiple Multiple Office use only Office useSingle Single Mixed use Mised use

Further subclassification is possible for each submarket based on age,amenities, and locations.


EXPLAINING OFFICE MARKET INSTABILITY

1. High financial leverage typical of office building finance makes new construction highly sensitive to changes in mortgage money rates and terms.

2. Tax shelter resulting from depreciation and interest deduction from taxable income provides a strong inducement to builders and investors to construct office buildings during periods of prosperity.

3. Office building construction often reflects non-market considerations, such as corporate prestige and image.


EXPLAINING OFFICE MARKET INSTABILITY

4. The elasticity of supplies of existing office space facilitates the postponement of new demand under conditions of uncertainty, high money rates, or recession.

5. The eternal optimism of developers, the naivete of lenders, and the lack of sophisticated market analysis techniques prolong periods of over- and under-construction.

6. The long planning and construction period required often results in continued high construction volume long after weakness becomes apparent in the demand for office space.


OFFICE SPACE MARKET ANALYSIS

D - S =

Demand Supply Normal expanded demandto allow for vacancy

(G + U + )Net real growth from

net employmentOffice space for

upgrading tenantsNew space removed

- ( + )Space added Space overhang

previous years

Where, = vacany rate(normal)G = tenants coming from community employment growthU = demand from present tenants for upgrading

= office space removed from inventory= office space added by new construction or rehabilitation= vacant space carryover from previous years

11- Vn

Or

On Ov

Vn

OrOnOv



Demand for office space results from

• Expansion of space requirements by existing tenants

• New tenants moving from other cities

• New business firms in the community

Increases in supply of office space may result from

• Existing tenants going out of business, reducing space, or moving to other cities

• Addition of new office space being added (including remodeling)

• Vacant office space available from previous years



Then:

This indicates than an additional 1.4 million square feet of space could be builtand absorbed.

D- S= 11- Vn

(G+U+Or)- (Ou+Ov)

= 11- 0.05

(1,000,000+750,000+0)- (200,000+250,000)

=1,392,105 square feet

Example 1: Consider a community with following characteristics

• 5 percent office-space vacancy target, Vn

• Net real growth G of 1 million square feet of space

• Upgrade demand U for 760,000 square feet

• No space removed Or from inventory

• 200,000 square feet of space added Ou to the market

• 250,000 square feet of over hang Ov



Example 2: Using the above data and not knowing the amount of space added Ou to the market, the absorption rate can be determined by first setting the market in equilibrium:

Then,

Thus,

D- S=0

Ou= 11- Vn

(G+U+Or )- (Ou+Ov)

= 11- 0.05

(1,000,000+750,000+0)- 250,000

=1,592,105 square feet


ANALYZING OFFICE BUILDING INVESTMENTS:SPECIFIC BUILDINGS

1. Building-site specific

• Street identity and prestige

• Efficiency ratio for net rentable space

• Percent of full floor users

• Tenant improvements

• Tenant mix

• Tenant turnover and leasing conditions

• Parking

2. Locational features

• Downtown

• Airport

• Regional shopping centers

• Freeways/heavily traveled main roads


ANALYZING OFFICE BUILDING INVESTMENTS:SPECIFIC BUILDINGS

3. Market elements

• Amount and quality of competing space (correct strata)

• Current rentals

• Vacancies (and reasons for vacancies)

• Absorption rates

• Market capture potential

4. Key to office building investment analysis

• Purchase price of the property

• Financing terms

• Lease terms

• Present and future levels of operating income and expenses

• Future selling price

• Applicable depreciation rules

• Income and capital gains tax rates


PROFITABILITY RATIOS(Calculated for each year of project)

1. NOIMV

• measures overall economic total property value (cost) return of captial asset• does not take into account taxes, financing or time value of money

2. CFBTI0

• measures impact of leverage(before taxes) on equity investor return• does not take into account tax benefits or time value of money

3. CFATI0

• measures equity investor returns annually after taxes and financing• does not take into account time value of money

One might also calculate profitability ratios which include loan amortizationbuild-up and/or equity build-ups from parcel appreciation.

Note: I0 = Initial investmentMV = Property Value


RISK RATIOS

1. NOIDS

• measures liquidity of project• measures occupancy rate and rent rates needed to meet debt service (coverage ratio)

2. Loan BalanceProperty Value

• measures leverage of project over time and riskiness as seen by lender• measures potential for refinancing (loan-value ratio)

3. DS - OEGPI

• measures total operating expenses (including debt service) as portion of gross possible income• measures occupancy rate needed to remain "liquid" (break-even point)

Other variants of these ratios can be used to analyze specific cash flow riskeffects.

Note: DS = Periodic Debt ServiceOE = Operating ExpenseGPI = Gross Possible Income


ASSUMPTION RATIOS

1. NOIMV

• measures overall capitalization rate over time• used to see if project's "numbers" are consistent with market CAP rates for comparable properties

2. MVGPI

• another measure of market comparability (gross rent multiplier)

3. OE OEGPI or GEI

• measures operating expense characteristics of project which can be compared with comparable properties

Again, variants of these ratios can be used to check comparability ofspecific property elements.


PROFITABILITY RATIOS

TIME PERIOD(to be filled in by student)

NOIMV

MVI0

ATCFI0

12345


RISK RATIOS*

TIME PERIOD(to be filled in by student)

NOIDS

DS + OEGPI

12345

*Initial loan-to-value ratio is __________ divided by __________which equals __________.


ASSUMPTION RATIOS

NOI1V0

= =

V0GPI1

= =

OE1GPI1

= =


III. DEVELOPNG THE TECHNIQUES OF FINANCIAL ANALYSIS

This session will focus on two of the most widely used analytic tools:

• Net present value (NPV)

• Internal rate of return (IRR)


FUNDAMENTALS OF INVESTMENT ANALYSIS MESURING RETURNS

I. Time Value of Money: Time and Risk

• A certain dollar today is worth more than a certain dollar tomorrow

• A risky dollar tomorrow is worth less than a more certain dollar tomorrow


I. TIME VALUE OF MONEY: TIME AND RISK

A. Timing: Present Value and Future Value

If $1.00 now could be invested at 10percent for one year, it would produce $1.10 as the total return. In this context, it is said that:

• The present value (PV) of $1.10 next year is $1.00

• The future value (FV) of $1.00 today is $1.10

• The interest rate is the opportunity cost of funds

Under the same circustances, $1.21 two years from now has a PV of $1.00:

PV =Q

11+r

, where 11+r

= discount factor and r= the discount rate.

1.00 = 1.101.1

PV =

Q2

(1+r)2 , thus 1.00 = 1.21(1.1)2


I. TIME VALUE OF MONEY: TIME AND RISK

B. NPV (net present value) and IRR (internal rate of return)

NPV = Discounted cash flow of benefit stream - Discounted cash flow of cost stream

Example:

• If r = 5%, then

• If r = 10%, then

• If r = 15%, then

NPV =

Q1

1+r+

Q2

(1+r)2 ++Q

t(1+r)t

- C0

C0=2.00, Q1=1.10, Q2 =1.21

NPV =1.10

1.05+ 1.21

(1.05)2 - 2.00=0.15

NPV =1.10

1.1+ 1.21

(1.1)2 - 2.00=0

NPV =1.10

1.15+ 1.21

(1.15)2 - 2.00=- 0.13


II. SIMPLE INVESTMENT DECISION RULES

A . N P V R u l e

B . I R R R u l e

N o t e : T h e r e i s n o c o n f l i c t i n N P V a n d I R R r u l e s f o r s i m p l e s t s i t u a t i o n s , w h e r e

Reject 0NPV Accept 0NPV

Reject IRR Accept IRR

rr

tQ

t

C ii)

.0 C and allfor 0 Q i)

0

0

t


Definition: IRR is a discount rate that takes the NPV = 0. Hence 10 percent is IRR of our example.

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0 5 10 15

r

NPV


Example: Two Mutually exclusive investments

Period Option A Option B

0 -2.00 -2.001 +1.10 0.002 +1.21 +2.42

IRR for Option A

IRR for Option B

Discount Rate NPV Option A NPV Option B

0 0.31 0.225 0.15 0.20

10 0.00 0.0015 -0.13 -0.17

0=- 2.00+1.10

(1+r)+

1.21

(1+r)2 => IRR=10%

0=- 2.00+2.42

(1+r)2 => IRR=10%


Reinvestment Assumption

For Option A, if 1.10 at the end of year 1 reinvested at 10% will yield 1.10(1.1)=1.21. Hence, if one can reinvest at the IRR=10%, Option A’s Benefit Stream FV=1.21+1.21-2.42. This is identical to FV of Benefit Stream for Option B.

Conclusion

If IRR, reinvestment, and discount rate are identical, IRR rate and NPV will yield proper and consistent investment decisions.


III. IRR and NPV Conflicts

A. Multiple IRR solutions

B. Mutually exclusive investments with different timing of cash flows

C. Mutually exclusive investments with scale differences

D. Reinvestment rate substantially different from IRR


Class Problem

Consider two alternative income-generating real estate investments, Project Aand Project B, each with an initial outlays (purchase price) of $10,000 in cash. Each project has a life of three years, with anticipated net cash flows aftertaxes as follows in Table 1:

Table 1: Net Cash Flow After Taxes

Year 1 Year 2 Year 3

Project A $5,000 $5,000 $5,000Project B $0 $0 $16,500

For each project, assume that there is no salvage value after Year 3 and thatnet cash flows are received at the end of each year.

1. What is the internal rate of return for each investment? Show the formulayou used. (Table 2 may provide helpful data for those with "slowcalculators.")


Table 2

AlternativeReinvestment

Rates (percent)

Project APresent Value of

Cash FlowDiscount Rates

Indicated in LeftColumn

Project AYear 3 Terminal

Value, UsingReinvestment

Rates Indicated inLeft-Most Column

Project BPresent Value of

Cash Flow,Discount Rate

Indicated in Left-Most Column

6.0 $13,365 $15,920 $13,86010.0 12,435 16,550 12,39118.2 10,900 17,900 10,00020.0 10,520 18,200 9,55323.0 10,000 18,750 8,415


2. Using the internal rate of return criteria, which investment should beundertaken? Does the IRR rule hold true for this problem? Explain fully.

3. Suppose now that there are possible reinvestment opportunities for net cashflows for your investments. Explain where the "terminal value" calculationsfor Project A in Table 2 come from. What are their significance indetermining optimal investment choice? Finally, what are the "terminalvalues" for Project B at the corresponding reinvestment rates?

4. Assuming that each investment has a reinvestment rate for generated cashflows of 20 percent and that investors have an opportunity cost for fundsprovided for investment of 6 percent, which investment project should beselected? Explain fully and show important calculations, formulae, and soforth.


SUGGESTED SOLUTION TO CLASS PROBLEM

IRR

PA = 23.0% and PB = 18.2%

NPV A(r)=0=5000

(1+r)+

5000

(1+r)2+

5000

(1+r)3- 10,000

NPVB(r)=0=16,500

(1+r)3- 10,000

0

5,000

10,000

15,000

20,000

0 10Px

18.2Pb

23Pa

r


1. Choose investment with greatest NPV which differs with interest rate used for discounting PX.

2. NTVA = 5000(1+i)2 + 5000(1+ i)+5000

Terminal Value of Cash Flows, excluding initial cost of $10,000.

NTVB = 16,500

NTV and NPV rules yield same answers! Why?

3. At i = 20% NTVA = 18,000 > 16,500 = NTVB if A is preferred to B; does NPV rule yield same result?


IV. EXAMINING THE PROBLEMS AND PITFALLS OF FINANCIAL ANALYSIS

The day concludes with a presentation on duration and reinvestment issues, how to take uncertainty into account, and a summary of analytic techniques.

Approaches to risk analysis

• Most likely outcome versus best/worst scenarios

• Sensitivity analysis for key parameters

• Probabilistic approaches

Problems with the use of IRR

• Uniqueness

• Assumed reinvestment rate = IRR

• Borrowing/lending rate = market rate = IRR


Three apparently different problems with the discount rate

• Cash flow disparity

• Project scale

• Time horizon difference


Reinvestment rate assumption and typical problems

• Time disparity of cash flows

Year Investment A Investment B

0 (10,000) (10,000)1 0 11,0002 15,625 2,600

IRR 25% 30%


• Scale size differences


0 (35,000) (50,000)1 43,750 61,000

IRR 25% 22%


• Time horizon issue


0 (100) (100)1 0 02 0 03 0 04 0 05 147 06 07 08 09 010 (179)

IRR 8% 6%


Other issues related to the use of IRR include:

• Are the IRR and interest rates independent of one another for most investment decisions?

• How does the optimal holding period affect cash flows?

• How does the analysis change if there are capital budgeting/rationing constraints?


DURATION: AN INTRODUCTION

T h e f o l l o w i n g f o r m u l a c a n b e u s e d t o d e r i v e d u r a t i o n :

W e i g h t e d a v e r a g e t i m e u n t i l c a s h f l o w p a y m e n t . T h ew e i g h t s a r e t h e “ p r e s e n t v a l u e ” o f t h e c a s h f l o w st h e m s e l v e s .

T

ttr)(

tQ

T

ttr)(

tQt

D

1 1

1 1Duration

Value-RateInterest of Elasticity 1

1 :Note

r)Δ(r

PVΔ PV D


This illustration shows how duration can be calculated:

$10,000 loan at 10%, all due in 10 years

Time Periods CF PV@10%

0 -10,000 -10,000 -1.0 0.01-9 0 0 0.0 0.010 29,937 10,000 1.0 1.0

D=10

For "zero coupon" instrument: maturity = duration

Qt(1+r)t •10,000

t •Qt(1+r)t •10,000


For an interest-only instrument, the duration changes:

For Interest Only Instrument


0 -10,000 -10,000 -1.0000 0.00001 1,000 909 0.0909 0.09092 1,000 826 0.0826 0.1652• • • • •• • • • •• • • • •9 1,000 424 0.0424 0.381610 10,000 4,246 0.4246 4.2460

D = 6.7638

Qt(1+r)t •10,000

t •Qt(1+r)t •10,000


For a fully amortized 10%, 10-year loan:


0 -10,000 -10,000 -1.0000 0.00001 1,627 1,479 0.1479 0.14792 1,627 1,344 0.1344 0.2688• • • • •• • • • •• • • • •

10 1,627 627 0.0627 0.6270

D = 4.7240

Qt(1+r)t •10,000

t •Qt(1+r)t •10,000


Duration and overall investment returns are shown below:

(1) (2) (3) (4) (3+4) (2+3+4)Time

PeriodProject

Cash FlowsReinvest at

iLReinvest at

iRTotal

ReinvestTotal

Investment

0 (-1,000) - - - -1,0001 400 -400 - -400 02 560 +420 -980 -560 03 480 - 1,127 1,127 1,607

IRR 20% 5% 15% 11.86% 17.13%


Finally, these charts show the computations for durations and overall return:


0 -1,000 -1,000 -1.000 0.0001 400 333 0.333 0.3332 560 389 0.389 0.7783 480 278 0.278 0.834

D = 1.945 yrs.

Qt(1+r)t •1,000

t •Qt(1+r)t •1,000

Overall Return =IRRA

(DT

)+IRR(D

1- T)

=(.20)(1.9453

)+(.1186)(1.945

1- 3)

=(.20)(.648)+(.1186)(.352)=.1713

fundamentals of project financial and investment analysis

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