A tenant receives a fixed $22,000 net rent benefit at each year-end for 40 years. There is no terminal or other cash flow. At a 6% annual discount rate, what is the present value to the nearest dollar?
Correct Answer
B) $331,019
PV = $22,000 × [1 − 1.06^(−40)] ÷ 0.06 = $22,000 × 15.0463 = $331,018.53, or $331,019 to the nearest dollar. The benefit is an ordinary annuity received at each year-end, and no reversion is added. Common errors: adding the 40 payments without discounting gives $880,000; capitalizing the benefit as a perpetuity gives $366,667; discounting the total of all payments as a single year-40 amount gives $85,556.
Why This Is the Correct Answer
PV = $22,000 × [1 − 1.06^(−40)] ÷ 0.06 = $22,000 × 15.0463 = $331,018.53, or $331,019 to the nearest dollar. The benefit is an ordinary annuity received at each year-end, and no reversion is added. Common errors: adding the 40 payments without discounting gives $880,000; capitalizing the benefit as a perpetuity gives $366,667; discounting the total of all payments as a single year-40 amount gives $85,556.
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Previous Question
An appraiser previously capitalized a property's annual NOI of $80,000 at a 6.4% overall rate. NOI remains the same, but the overall rate is now 8.0%. What is the new indicated value?
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A property has annual effective gross income of $520,000 and an operating expense ratio of 28% of EGI. Market data indicate an overall capitalization rate of 7.5%. What value is indicated by direct capitalization, to the nearest dollar?