An investment property is expected to generate $50,000 annually for 10 years, with a reversion value of $800,000. Using a 9% discount rate, what is the present value of the reversion only?
Correct Answer
A) $337,929
Why this is correct: Present Value = Future Value / (1 + discount rate)^n. Step 1: (1.09)^10 = 2.36736. Step 2: $800,000 / 2.36736 = $337,929. Only the reversion is discounted here; the $50,000 annual income is a separate present value and is not part of this answer. Why the other choices are wrong: "$800,000" is the future reversion value itself, undiscounted. "$1,267,643" adds the present value of the income stream to the reversion, which the question excludes. "$500,000" does not come out of the present value formula at all. Exam tip: for the present value of a single future sum, FV / (1+r)^n. Carry the factor to five decimals -- rounding 2.36736 to 2.37 moves this answer by about $400.
Why This Is the Correct Answer
Option A correctly applies the present value formula: PV = FV ÷ (1 + r)^n. The calculation takes the $800,000 reversion value and divides it by (1.09)^10 = 2.367364, resulting in $337,643. This properly discounts the future value to account for the time value of money over the 10-year period. The annual income stream is irrelevant to this specific calculation since we're only valuing the reversion component.
Why the Other Options Are Wrong
Option B: $800,000
Option B represents the undiscounted reversion value of $800,000, which ignores the time value of money. This would only be correct if we were looking for the nominal future value, not the present value.
Option C: $1,267,643
Option C appears to add the present value of the reversion to some other component, possibly confusing this with a total property valuation that includes both income and reversion components.
Option D: $500,000
Option D of $500,000 has no mathematical relationship to the given variables and appears to be a distractor with no basis in the present value calculation.
PV-FV Divide & Conquer
Remember 'PV = FV ÷ (1+r)^n' as 'Present Value = Future Value Divided by (1 plus rate) to the power of years.' Think of it as shrinking the future dollar to today's smaller size.
How to use: When you see a reversion value question, immediately identify: Future Value (reversion amount), rate (discount rate), and time period (years). Then apply the shrinking formula to bring that future money back to today's value.
Exam Tip
Always read carefully whether the question asks for reversion only, income only, or total property value. Don't let the annual income amount distract you if the question specifically asks for reversion value only.
Common Mistakes to Avoid
- -Using the undiscounted reversion value instead of calculating present value
- -Including the annual income in the reversion calculation when only reversion is requested
- -Confusing the discount rate with a capitalization rate and using wrong formula
Concept Deep Dive
Analysis
This question tests the fundamental concept of present value calculation for a reversion (terminal value) in real estate investment analysis. The reversion represents the expected sale value of the property at the end of the holding period, which must be discounted back to present value using the appropriate discount rate. The question specifically asks for the present value of the reversion only, not the entire property value including income streams. Understanding this distinction is crucial for proper DCF analysis in real estate appraisal.
Background Knowledge
Present value calculations are fundamental to the income approach in real estate appraisal, particularly in discounted cash flow analysis. The reversion value represents the anticipated sale proceeds at the end of the investment holding period, which must be discounted to present value using an appropriate discount rate that reflects the risk and time value of money.
Real-World Application
In practice, appraisers use this calculation when valuing income-producing properties under the income approach, particularly for properties expected to be sold after a holding period. The reversion value typically represents 60-80% of total property value in DCF analysis.
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