Risk Analysis

Types of Income Property Risk

Property Market Risk o Demand Side o Supply Side

Financial Market Risk o Leverage o Refinancing Risk

Liquidity Risk (Unexpected) Inflation Risk Legal Risk Environmental Risk

Risk Analysis

Measuring Risk

Standard deviation in expected return o Identify possible alternatives (sensitivity analysis) o Attach probabilities to alternative outcomes o Compute expected return o Compute the variance & standard deviation in return

Partitioning the IRR: how much of the return comes from o Operating the property o Selling the property

Modified IRR: selecting an alternative reinvestment rate Introduction to real options in real estate investments

Risk AnalysisWillow Brook

FutureCap Rate Selling Price Prob ATIRR Prob x ATIRR

7.50% $20,455,246 0.10 26.25% 2.625%8.50% $18,048,746 0.15 20.22% 3.033%9.50% $16,148,878 0.40 14.33% 5.732%10.50% $14,610,890 0.20 8.36% 1.672%11.50% $13,340,378 0.10 2.01% 0.201%12.50% $12,273,147 0.05 -5.17% -0.259%

1.0000 13.005%

Risk Analysis

Deviation from DeviationCap Rate Prob ATIRR Expected Squared x Prob

0.075 0.10 26.25% 0.1325 0.0175 0.001750.085 0.15 20.22% 0.0722 0.0052 0.000780.095 0.40 14.33% 0.0133 0.0002 0.000070.105 0.20 8.36% -0.0464 0.0022 0.000430.115 0.10 2.01% -0.1099 0.0121 0.001210.125 0.05 -5.17% -0.1817 0.0330 0.00165

Variance = 0.5897%Std = 7.68%

Risk AnalysisPartition the IRR

What share of the investment return comes from:

Operations? Reversion?

To partition the IRR:

1. Compute the IRR on the expected cash flows (either property, before tax or after tax cash flows).

2. Discount the cash flows from operations (or reversion) at the IRR

rate.

3. The share of the return that comes from operations is:

PV of Operating Cash Flows/Equity

Risk AnalysisPartition the ATIRR for Willow Brook

Year Equity ATCF from ATCF fromOperations Reversion

0 -$3,132,0001 $294,5052 $317,1233 $340,2574 $363,9075 $388,074 $3,892,592

ATIRR = 14.33%

PV of ATCFO @ ATIRR = $1,139,477 Percent of Equity: 36.38%

PV of ATCFR @ ATIRR = $1,992,523 Percent of Equity: 63.62%

Risk Analysis

Modified IRR

The IRR calculation assumes that all cash flows are reinvested at the IRR rate.

Some investors prefer a more conservative reinvestment

assumption.

The Modified IRR is the internal rate of return computed assuming the investment cash flows are reinvested at some fixed rate.

Risk AnalysisModified IRR for Willow Brook

Year ATCF FV @ ATIRR FV @ 6%(= 14.33%)

1 $294,505 $503,192 $371,8062 $317,123 $473,924 $377,6993 $340,257 $444,762 $382,3134 $363,907 $416,055 $385,7415 $4,280,666 $4,280,666 $4,280,666

Total FV = $6,118,598 $5,798,225

IRR = 14.33%

Modified IRR = 13.11%

Risk Analysis

Real Options in Real Estate

What is a real option (as opposed to a financial option)?

The option to delay an investment (or development) The option to expand a project (if subsequent events are favorable)

The option to contract (if subsequent events are unfavorable)

Risk Analysis

Real Options in Real Estate

Example from Brueggeman and Fisher:

Purchase land today and expect to begin development in one year Building costs $800,000 to construct (in year 1 dollars)

End of year 1 market NOI expected to be:

o $130,000 with 50% probability o $ 70,000 with 50% probability

Discount rate = 12%; expected growth rate = 2%

Risk Analysis

Real Options in Real Estate

Conventional land valuation:

o Expected NOI = 0.5 x $130,000 + 0.5 x $70,000 = $100,000

o Property Value1 = $100,000/(0.12 - 0.02)

= $1,000,000

o Land Value1 = Property Value1 - Building Cost1 = $1,000,000 - $800,000 = $200,000 o Land Value0 = $200,000/(1.12) = $178,571

Risk Analysis

Real Options in Real Estate

Real Option Approach (ROA) to land valuation:

o Suppose at the end of year 1, the market NOI for the completed project is likely to be $70,000.

o What is the land worth?

o So the land is worth $_____ and the developer will abandon

(or more likely postpone) his/her construction plans.

o So the land is worth $_____ with probability 0.5.

Risk AnalysisReal Options in Real Estate

Real Option Approach (ROA) to land valuation:

o Now suppose one year passes and the expected market NOI is $130,000.

o Property Value1 =

Building Cost1 = Land Value1 =

o So one year from now the land is worth $ 500,000 with probability 0.5

o Expected land value one year from now is:

0.5 x $0 + 0.5 x $500,000 = $250,000 o Expected land value today = $250,000/(1.12) = $223,214

Risk Analysis

The option is worth

$ 44,643 = $ 223,214 - $ 178,571