**1i.**Two investments have the following pattern of expected returns:

Investment A requires an outlay of $110,000 and Investment B requires an outlay of $120,000.

**a.**What is the BTIRR on each investment?

**b.**If the BTIRR were partitioned based on what proportions of the BTIRR would be represented by each?

**c.**What do these proportions mean?

**1ii.** What is meant by partitioning the internal rate of return? Why is this procedure meaningful?

**2i.** Mike Riskless is considering two projects. He has estimated the IRR for each under three possible scenarios and assigned probabilities of occurrence to each scenario.

Riskless is aware that the pattern of returns for Investment II looks very attractive relative to Investment I; however, he believes that Investment II could be more risky than Investment I. He would like to know how he can compare the two investments considering both the risk and return on each. What do you suggest?

**2ii.** What is a risk premium? Why does such a premium exist between interest rates on mortgages and rates of return earned on equity invested in real estate?

**3i.** An investor has projected three possible scenarios for a project as follows:

Pessimistic—NOI will be $200,000 the first year, and then decrease 2 percent per year over a five-year holding period. The property will sell for $1.8 million after five years.

Most likely—NOI will be level at $200,000 per year for the next five years (level NOI) and the property will sell for $2 million.

Optimistic—NOI will be $200,000 the first year and increase 3 percent per year over a five-year holding period. The property will then sell for $2.2 million.

The asking price for the property is $2 million. The investor thinks there is about a 30 percent probability for the pessimistic scenario, a 40 percent probability for the most likely scenario, and a 30 percent probability for the optimistic scenario.

**a.**Compute the IRR for each scenario.

**b.**Compute the expected IRR.

**c.**Compute the variance and standard deviation of the IRRs.

**d.**Would this project be better than one with a 12 percent expected return and a standard deviation of 4 percent?

**3ii.** What are some of the types of risk that should be considered when analyzing real estate and other categories of investment?

**4i.** Use the same information as in problem 3. Now assume a loan for $1.5 million is obtained at a 10 percent interest rate and a 15-year term.

** a.**Calculate the expected IRR on equity and the standard deviation of the return on equity.

**b.**Contrast the results from (a) with those from problem 3. Has the loan increased the risk? Explain.

**4ii.** What is the difference between business risk and financial risk?

**5i.** A developer plans to start construction of a building in one year if at that point rent levels make construction feasible. At that time the building will cost $1,000,000 to construct. During the first year after construction would take place, there is a 60 percent chance that NOI will be $150,000 and a 40 percent chance that the NOI will be $75,000. In either case, NOI would be expected to increase at 2 percent per year after the first year. How much should the developer be willing to pay for the land if he wants a 12 percent rate of return?

**5ii.** Why is the variance (or standard deviation) used as a measure of risk? What are the advantages and disadvantages of this risk measure?

**6i.** ARGUS Problem. Refer to the Worthington Distribution Center example in the chapter. Using ARGUS, suppose that the renewal probability for the market leasing assumption that applies to the computer distributing company is only 50 percent and that there would be 12 months vacant if it did not renew. How does this affect the property value?

**6ii.** What is meant by a ‘ real option’ ?

**7i.** ARGUS Problem. Refer to the Westgate Shopping Center example. Use ARGUS to replicate the assumptions for the “pessimistic scenario” discussed in the chapter. What inputs did you have to change in order to get the same answer (rounded) as the book?

**7ii.** What is meant by the term ‘overage’ for retail space ?

**8.**How does the use of scenarios differ from sensitivity analysis?

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