An appraiser is valuing the leased fee interest in a property subject to a long-term ground lease. The lease has 25 years remaining with rent of $50,000 annually, and the reversion value is estimated at $2,000,000. Using a 7% discount rate, what is the present value of the reversion? (PV factor for 25 years at 7% = 0.1842)
Correct Answer
C) $368,400
Why this is correct: The present value of a future sum is calculated as Future Value multiplied by the Present Value factor. Here, the future reversion value is $2,000,000. The given PV factor for 25 years at 7% is 0.1842. Calculation: $2,000,000 * 0.1842 = $368,400. Why the other choices are wrong: $2,000,000 is the future value, not the present value. $542,600 and $1,631,600 are incorrect calculations, possibly from misapplying the factor or confusing it with the present value of the income stream. Exam tip: In leasehold problems, separate the income stream (annuity) from the reversion (lump sum). Use PV = FV * PV factor for the reversion.
Why This Is the Correct Answer
Option A correctly applies the present value formula: Future Value × Present Value Factor = $2,000,000 × 0.1842 = $368,400. This calculation properly discounts the future reversion value of $2,000,000 back to present value using the given 7% discount rate over 25 years. The present value factor of 0.1842 represents how much $1 received 25 years from now is worth today at a 7% discount rate. This demonstrates that due to the time value of money, $2,000,000 received in 25 years is only worth $368,400 in today's dollars.
Why the Other Options Are Wrong
PV-FV-Factor Triangle
Draw a triangle with PV at bottom left, FV at bottom right, and Factor at the top. Cover what you're solving for and multiply the other two: PV = FV × Factor, FV = PV ÷ Factor, Factor = PV ÷ FV
How to use: When you see a reversion problem, immediately draw the triangle, identify what you have (FV and Factor), cover PV, and multiply FV × Factor to get your answer
Exam Tip
Always double-check that you're multiplying (not dividing) the future value by the present value factor when calculating present value of a reversion
Common Mistakes to Avoid
- -Using the future value instead of calculating present value
- -Dividing instead of multiplying by the present value factor
- -Confusing present value factors with future value factors
Concept Deep Dive
Analysis
This question tests the fundamental concept of present value calculation in income capitalization approach, specifically for leased fee interests. The appraiser must understand that a leased fee interest consists of two components: the present value of the lease payments and the present value of the reversion (property value at lease expiration). Present value calculations are essential because money received in the future is worth less than money received today due to the time value of money. The discount rate reflects the required rate of return and risk associated with the investment.
Background Knowledge
Present value calculations are fundamental to the income capitalization approach in real estate appraisal. Appraisers must understand that future cash flows and reversions must be discounted to present value using appropriate discount rates that reflect market conditions, risk, and required returns. The present value factor can be calculated using the formula 1/(1+r)^n or obtained from present value tables.
Real-World Application
In practice, appraisers regularly value leased fee interests for investment properties, ground leases, and sale-leaseback arrangements where they must calculate both the present value of lease income and the present value of the property reversion to determine total property value
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