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Solution: The present value, using a financial calculator, is $817,078. N = 50I = 12.2PV = ?PMT = 100,000FV = 0The initial (going-in) cap rate is $100,000/$817,078 = 12.24%9-4
b. If you expect that NOI will remain constant at $100,000 forever, what is the value of the building assuming a 12.2% discount rate? If you pay this amount, what is the indicated initial cap rate?Solution: The value of the building with NOI remaining constant at $100,000 is calculated using the formula for a perpetuity, which is $100,000/0.122, or $819,672. If you pay $819,672 for the property, the initial (going-in) cap rate is 12.2% ($100,000 / $819,672).c. If you expect the initial $100,000 NOI will grow forever at a 3% annual rate, what is the value of the building assuming a 12.2% discount rate? If you pay this amount, what is the indicated initial cap rate?Solution: The capitalization rate consists of a required IRR on equity and a growth rate. Applying the general constant-growth formula and assuming that the growth rate is 3%, the indicated capitalization rate is equal to 9.2% (12.2% - 3.0%.). Therefore, using a cap rate of 9.2%, the indicated value of the building is $100,000/0.092, or $1,086,957.8.Describe the conditions under which the use of gross income multipliers to value the subject property is appropriate.Solution: The use of gross income multipliers is predicated on two primary assumptions. First, it is assumed that the operating expense percentage of the subject property and the comparable properties are equal. Second, this approach assumes that the subject property and comparable properties are collecting market rents. In practice, gross income multipliers are most appropriate for valuing apartment buildings.9.In what situations or for which types of properties might discounted cash flow analysis be preferred to direct capitalization?Solution: Direct capitalization is dependent on information obtained from sales of properties that are deemed to be comparable to the subject property. Identifying comparable properties is particularly difficult with commercial real estate investments. Discounted cash flow analysis is useful for valuing income-producing properties because the unique expected cash flows for a particular property are evaluated using the appropriate required internal rate of return. DCF is especially useful when valuing multi-tenant office buildings and shopping centers were lease terms can vary widely across even otherwise similar properties.