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The indicated value of the property is $362,727 ($39,900 / 0.11), which rounds to $363,000.6.You have been asked to estimate the market value of an apartment complex that is producing annual net operating income of $44,500. Four highly similar and competitive apartment properties within two blocks of the subject property have sold in the past three months. All four offer essentially the same amenities and services as the subject. All were open-market transactions with similar terms of sale. All were financed with 30-year fixed-rate mortgages using 70 percent debt and 30 percent equity. The sale prices and estimated first-year net operating incomes were as follows:Comparable 1: Sale price $500,000; NOI $55,000Comparable 2: Sale price $420,000; NOI $50,400Comparable 3: Sale price $475,000; NOI $53,400Comparable 4: Sale price $600,000; NOI $69,000What is the indicated value of the subject property using direct capitalization?5
Solution:The abstracted going-in capitalization rates from the four properties are listed below:Comparable 1: 0.110Comparable 2: 0.120Comparable 3: 0.112Comparable 4: 0.115Simple Ave. 0.114The simple average of the four comparable cap rates is 0.114. Thus, the indicated value of the subject property is $390, 351, ($44,500 / 0.114), which rounds to $390,000.7.You are estimating the value of a small office building. Suppose the estimated NOI for the first year of operations is $100,000.a. If you expect that NOI will remain constant at $100,000 over the next 50 years and that the office building will have no value at the end of 50 years, what is the present value of the building assuming a 12.2% discount rate? If you pay this amount, what is the indicated initial cap rate? 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%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%.). 6
Therefore, using a cap rate of 9.2%, the indicated value of the building is $100,000/0.092, or $1,086,957.