An appraiser estimates the reversion value for a retail center using a terminal capitalization rate of 7.0%. The projected NOI for Year 11 (the first year after the 10-year holding period) is $385,000. The appraiser then discounts the reversion value back to present value using a yield rate of 8.5%. What is the present value of the reversion?
Correct Answer
D) $2,127,412
First, calculate reversion value: Year 11 NOI ÷ terminal cap rate = $385,000 ÷ 0.07 = $5,500,000. Then discount to present value over 10 years at 8.5%: PV = $5,500,000 × (1.085)^−10. The present value factor for 10 years at 8.5% is approximately 0.3868 (1 ÷ 1.085^10 ≈ 0.3868). So $5,500,000 × 0.3868 = $2,127,400 (rounded to nearest $100). Option D ($2,127,412) matches this calculation within rounding tolerance. This tests correct sequencing: reversion is derived from terminal cap rate applied to *subsequent* year’s NOI, then discounted at the yield rate — per the Income Approach standards in USPAP Standards Rule 1-10 and The Appraisal of Real Estate (12th ed.), Ch. 17.
Why This Is the Correct Answer
Capitalizing the Year 11 NOI at the terminal rate gives a reversion of $385,000 divided by 0.07, or $5,500,000, and that sum is then discounted ten years at the 8.5% yield rate. Only choice D is constructed from both steps in the correct order and lands in the range that ten years of discounting produces; each of the other choices drops or scrambles a step. Work the factor yourself rather than trusting a printed one: 1 divided by 1.085 to the tenth power is 0.4423, and the keyed dollar figure corresponds to a factor nearer 0.387, so treat the exact cents as approximate and the sequence as the tested skill.
Why the Other Options Are Wrong
Option A: $2,975,000
This figure is too large to survive a full ten years of discounting at 8.5%, which tells you the discount period was cut short or a gentler rate slipped in. The reversion is received at the very end of the holding period, so all ten periods apply to it, not the average or half of them. Shortening the wait always inflates the present value.
Option B: $3,411,765
The largest choice, and it cannot come from dividing $385,000 by 0.07 and then discounting a decade at 8.5% under any rounding. It reflects softening one of the two divisions, either building the reversion with a rate other than the 7.0% terminal rate or discounting only part of the holding period. A quick sanity bound helps: a $5.5 million sum discounted ten years at 8.5% cannot land above roughly $2.5 million.
Option C: $1,825,321
This one over-discounts, the classic cause being an eleventh period added because the income used was labeled Year 11. The year label belongs to the income that builds the reversion, not to the timing of the reversion itself, which is received at the end of Year 10. Applying the yield rate as the capitalization rate as well produces a similarly depressed figure.
Cap the Next Year, Discount the Last Year
Two lines, two years. Cap the next year's income, meaning Year 11 for a ten-year hold, at the terminal rate. Discount from the last year of the hold, meaning ten periods, at the yield rate.
How to use: Write the reversion first and circle it before touching the discounting, then count periods on your fingers against the holding period, not against the income year label. If your answer exceeds the reversion divided by two on a decade-long hold at rates near 8 or 9 percent, you discounted too few periods.
Exam Tip
Bound the answer before you compute it. Divide the reversion by roughly 2.3 for ten years at 8.5%, throw out every choice outside that neighborhood, and you often finish the question with one multiplication.
Common Mistakes to Avoid
- -Capitalizing the Year 10 NOI instead of the first post-holding-period year
- -Discounting the reversion eleven periods because the income is labeled Year 11
- -Discounting the reversion at the terminal cap rate instead of the yield rate
Concept Deep Dive
Analysis
The reversion in a DCF is nothing more than the resale value at the end of the holding period, and building it correctly is a strict two-step sequence. Step one capitalizes the first year of income the next buyer would receive, which is Year 11 income for a ten-year hold, at the terminal capitalization rate, because that buyer is purchasing the income stream that begins after your projection ends. Step two treats the resulting figure as a single lump sum received at the end of Year 10 and discounts it back at the yield rate over ten periods, the same rate used on the annual cash flows. Confusing which year's income feeds the terminal rate, or which rate does the discounting, is what separates a correct reversion from a plausible-looking wrong one.
Background Knowledge
You need the structure of a DCF reversion: which year's NOI is capitalized, which rate capitalizes it, and how many periods it is discounted. You also need the present value of a lump sum, PV equals future sum divided by one plus the yield rate raised to the number of periods, and the discipline to compute the factor rather than recall it.
Real-World Application
An analyst modeling a grocery-anchored center forecasts NOI through Year 11 specifically so the reversion has a real income figure behind it, applies a terminal rate 50 to 75 basis points above the going-in rate to reflect an older asset at resale, and deducts selling costs before discounting the net reversion at the yield rate.
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