1. Chapter 18: Risk Analysis

2. Introduction to Risk Analysis  Risk is the probability that events will not occur as expected.  Actual return may differ from the expected return.  Risk is important for several reasons:  Investor’s expected return depends on risk.  Risk must be considered when selecting comparable sales.  Discount rates must reflect level of risk.

3. Types of Risk  Space Market Risk  Risk due to changes in the market for real estate space.  Can result from changes in the supply or demand for space.  Capital Market Risk  Risk that changes in the market for capital will affect value.  Caused by changes in mortgage interest rates or equity yield rates.  Affects investors even if they do not use debt financing.

4. Types of Risk  Financial Risk  Results from the use of debt financing (leverage).  Leverage can increase expected return.  Leverage always increases financial risk.  Liquidity Risk  The difficulty of converting an investment into cash at a price close to market value within a reasonable time.  Real estate has a relatively high degree of liquidity risk:  Not publicly traded  Relatively few buyers for a particular property at a given point in time

5. Types of Risk  Inflation Risk  Risk that unexpected inflation will cause future income from operations and reversion to lose purchasing power.  Historically real estate has not had much inflation risk.  Inflation tends to increase replacement cost  Market rents can increase with inflation  Lease provisions like CPI adjustments and expense pass-throughs help protect owner against unexpected inflation  Real estate may have more inflation risk in a weak market

6. Types of Risk  Environmental Risk  Risk that environmental factors will affect ability to develop or lease space, e.g., asbestos or toxic waste  Often difficult to measure and the cost to cure the problem can exceed the value of the property.  Legislative Risk  Risk do to changes in laws and regulations  Examples  Federal income tax laws  Environmental regulations  Changes in zoning  Changes in land-use regulations  Building codes

7. Types of Risk  Management Risk  Risk resulting from poor management.  Properties requiring specialized management such as convention hotels and regional malls have greater management risk.

8. Sensitivity Analysis  Measures how changes in one of the assumptions affects the performance of the property.  Scenarios are alternative assumptions about how the property might perform.  Considers interactions between assumptions.  Pessimistic, most likely and optimistic scenarios are typically considered.

9. Expected Return  Returns may be for calculated for different scenarios  The expected return is found by weighing each return by its probability of occurrence

10. Expected Return ScenarioOverall YieldProbability Pessimistic50.3 Most likely100.4 Optimistic200.3 Expected Return = 0.05(0.30) + 0.10(0.40) + 0.20(0.30) = 0.1150 or 11.50%

11. Variance and Standard Deviation  Variance is a measure of the uncertainty or risk associated with an investment.  Measures the tendency of individual returns to vary from the expected return.  The standard deviation is the square root of the variance.

12. Variance

13. Variance and Standard Deviation  Variance = 0.30(.05-.1150) 2 +0.40(0.10-0.1150) 2 +0.30(0.20-0.1150) 2 Variance=0.003525 or 0.3535%  Standard deviation is equal to the square root of the variance. Standard deviation = (0.003525) 1/2 = 0.05937 or 5.937%

14. Ranking Investments  The expected return and standard deviation can be used to compare investment alternatives.  An investment with a higher expected return is not better if it also has greater variance.

15. Ranking Investments Expected ReturnStandard Deviation Property A9%4% Property B9%2% Property C10%4%

16. Ranking Investments  Sharpe Ratio = (Portfolio return – Risk-free rate)/Portfolio standard deviation  Property A = 9%/4% = 2.25  Property B = 9%/2% = 4.50  Property C = 10%/4% = 2.50

17. Expected Present Value  Present values can be calculated for different scenarios.  The expected present value is found by weighing each present value by its probability of occurrence.  This helps convey the degree of uncertainty in the value estimates.

18. Expected Present Value Example PessimisticMost LikelyOptimistic Increase in NOI02%4% Resale in year 5$1,000,000$1,200,000$1,400,000 Probability20%50%30% A property is projected to have a NOI of $100,000 in year 1.

19. Expected Present Value Example 1.Using a discount rate of 10%, find the PV of the property under each scenario. ScenarioYear 1Year 2Year 3Year 4Year 5Resale Pessimistic$100,000 $1,000,000 Most Likely$100,000$102,000$104,040$106,121$108,243$1,200,000 Optimistic$100,000$104,000$108,160$112,486$116,986$1,400,000 Pessimistic PV@10% = $1,000,000 Most Likely PV@10% = $1,138,171 Optimistic PV@10% = $1,276,880

20. Expected Present Value Example 2.What is the expected present value? Expected PV = 0.20($1,000,000) + 0.50($1,138,171) + 0.30($1,276,880) Expected PV = $1,152,150

21. Expected Present Value Example 3.Compute the Variance and Standard Deviation. Variance = 0.20(1,000,000-1,152,150) 2 + 0.50(1,138,171- 1,152,150) 2 + 0.30(1,276,880-1,152,150) 2 Variance = $9,394,902,591 Standard Deviation = ($9,394,902,591) 1/2 Standard Deviation = $96,927

22. Expected Present Value Example 4.What range of value estimates can you predict within 2 standard deviations of the mean? $1,152,150 + (2 x $96,927) = $1,346,004 $1,152,150 – (2 x $96,927) = $958,296

23. Partitioning the IRR  A method of calculating the relative contribution of different components of cash flow  Cash flow can be broken down as follows: 1.NOI  Income from existing leases  Income from expected lease renewals 2.Reversion  Cash flow from recapture of original investment (i.e. purchase price)  Cash flow from expected price appreciation

24. Partitioning the IRR  Partitioning uses the IRR as a discount rate  The present value of each component of the cash flow stream is calculated  The total of these present values must equal the purchase price  A project with a greater proportion of its return from reversion is usually considered more risky.

25. Example of Partitioning the IRR  An investor considers purchasing one of the following properties. Each can be purchased for $500,000 and would have NOI and expected sales price after 5 years as follows. Property Purchase PriceNOISales Price A$500,000$50,000$500,000 B $10,000$744,204 Calculate the IRR and partition the IRR for each property.

26. Example of Partitioning the IRR PropertyYear 0Years 1-5Year 5IRR A-500,00050,000500,00010% B-500,00010,000744,20410% Partitioning the IRR Using a 10% Discount Rate: PropertyPV of NOI% PV of Sale Price%Total PV% A$189,53938$310,46162$500,000100 B$37,9088$462,09292$500,000100

27. Discounting the NOI and Reversion at Different Rates  NOI is often considered less risky than cash flow from reversion  Thus, the reversion can be discounted at a higher rate than the NOI

28. Discounting the NOI and Reversion at Different Rates  A property is leased for 5 years with a net lease at $90,000 per year. It is expected to sell for $1,200,000 in 5 years when the lease expires. The discount rate for the leased portion of the cash flow is 9%, and the discount rate for the reversion is 12%. What is the indicated value?  PV of $90,000 for 5 years @ 9% = $350,069  PV of $1,200,000 at the end of 5 years @ 12% = $680,912  Indicated value = $350,069 + $680,912 = $1,030,981

29. Discounting the NOI and Reversion at Different Rates  Assuming the property is purchased for $1,030,981, what is the IRR? CF0=-1,030,981 C01=90,000, F01=4 C02=90,000+1,200,000=1,290,000, F02=1 IRR=11.34%

30. Effect of Leverage on Financial Risk  As the loan to value ratio increases the lenders equity yield will increase if leverage is positive.  As the loan to value ratio increases the standard deviation (risk) also increases.

31. Effect of Leverage on Financial Risk  Consider a property with a purchase price of $100,000 with debt financing at a rate of 10% over 30 years. Scenario NOI per yearResaleProbability Pessimistic$10,000$90,0000.3 Most Likely$12,000$100,0000.6 Optimistic$14,000$110,0000.1

32. Effect of Leverage on Financial Risk  Calculate the yield at loan-to-value ratios of 0%, 30%, 60%, and 90%. Loan/Value (%) Pessimistic Return (%) Most Likely Return (%) Optimistic Return (%) Expected Return (%) Standard Deviation (%) 08.311215.4711.242.17 307.5712.8617.711.763.09 605.6614.9723.0212.985.34 90-12.5428.7254.3818.9121.92