A commercial investor is valuing a 10-year lease on 5,000 square feet at $30 per square foot in year one, with rent rising 3% each year. Rent is paid annually at the end of each year. Using a 7% discount rate, what is the present value of the lease payments, to the nearest dollar?
Correct Answer
A) $1,188,079
Year-one rent is 5,000 × $30 = $150,000, growing 3% a year. The present value of a growing annuity paid at year-end is $150,000 × [1 − (1.03/1.07)^10] ÷ (0.07 − 0.03) = $150,000 × 7.92053 = $1,188,079. Ignoring growth gives $1,053,537, treating payments as made at the start of each year gives $1,271,245, and adding the rents without discounting gives $1,719,582.
Why This Is the Correct Answer
Using the growing-annuity formula with a $150,000 first payment, 3% growth, 7% discount rate and 10 end-of-year payments gives $150,000 × 7.92053 = $1,188,079.
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