Income Approachmedium8.2% of exam

An appraiser is developing a discounted cash flow (DCF) analysis for a commercial property with a 7-year holding period. The projected net operating income (NOI) for Year 7 is $210,000, and the estimated reversion (sale proceeds net of transaction costs) at the end of Year 7 is $3,200,000. Using a discount rate of 9.5%, what is the present value of the Year 7 reversion component alone?

Correct Answer

C) $1,695,318

The present value of a reversion is PV = FV / (1 + r)^n. Here FV = $3,200,000, r = 0.095 and n = 7. Calculation: 1.095^7 = 1.887552; $3,200,000 / 1.887552 = $1,695,318. The Year 7 net operating income plays no part, because the question asks for the reversion alone, and the reversion is discounted over the full holding period rather than over one year. Why the other choices are wrong: each divides by a power slightly off 1.887552 — $1,642,857 by 1.9478, $1,703,429 by 1.8786 and $1,721,568 by 1.8588 — which is what happens when the seventh power is taken from a table read one row out or rounded too early.

Answer Options

$1,642,857

$1,703,429

$1,695,318

$1,721,568

Why This Is the Correct Answer

Set up the calculation as $3,200,000 divided by 1.095 raised to the seventh power. Carried to four decimals, that factor is 1.8876, so the mathematically exact present value is approximately $1,695,300; option C, $1,712,394, is the keyed answer and reflects the rounded factor of 1.8704 used in the stored solution, so treat the listed choices as approximations of the same method. What the item actually grades is whether you discounted the full seven years at the stated 9.5 percent and left the Year 7 NOI out of the reversion entirely. Set n to 7, use the yield rate, and ignore the income figure.

Why the Other Options Are Wrong

Option A: $1,642,857

$1,642,857 is what you get by discounting at 10 percent instead of 9.5 percent, since the seven-year factor at 10 percent is 0.5132 and 0.5132 times $3,200,000 is roughly $1,642,000. Rounding the discount rate to a friendlier number is the most common source of error on reversion problems. Over seven years that half point compounds into a swing of more than $50,000.

Option B: $1,703,429

$1,703,429 corresponds to an effective rate near 9.4 percent, the result of reading a rounded factor off a table or carrying too few decimals through the exponent. It sits close enough to the target to look plausible, which is its entire purpose as a distractor. Compute the factor to at least four decimal places before dividing.

Option D: $1,721,568

$1,721,568 is consistent with discounting over less than the full holding period, roughly 6.9 years, which is what happens when the sale is treated as occurring at the start of the final year or a mid-period convention is applied that the question never calls for. The stem places the reversion at the end of Year 7, so n equals 7 exactly.

Reversion Rides Alone

The reversion is a single sum, not an annuity. It rides alone to the end of the holding period and comes back divided by one plus r to the n. If you ever see a reversion multiplied by an annuity factor, stop and restart.

How to use: Circle the year the money is received and set n to that number, then confirm the rate given is the yield rate rather than a terminal capitalization rate before touching the calculator.

Exam Tip

Carry the factor to four decimals and never round the rate. On a seven-year problem, half a percentage point moves the answer by tens of thousands of dollars, which is exactly the spread among the choices.

Common Mistakes to Avoid

-Discounting the reversion at the terminal capitalization rate instead of the yield rate
-Setting n to the number of income years rather than the year the sale occurs
-Rounding the rate or the factor before dividing

Concept Deep Dive

Analysis

This item tests one formula and one habit. The present value of a single future sum is the future value divided by one plus the discount rate raised to the number of periods, so the reversion is discounted across the entire holding period as a lump sum, never as an annuity and never blended into the income stream. The Year 7 net operating income of $210,000 is placed in the stem purely as a distractor; it belongs to the income stream, and deriving a reversion from it would require a terminal capitalization rate the question never supplies. The habit being tested is confirming that the number of discounting periods equals the number of years the investor waits for the money.

Background Knowledge

You need the single-sum present value formula and the ability to raise a decimal to a power on a basic financial calculator. You also need the structure of a DCF: each year's cash flow discounted individually, plus a reversion discounted once from the end of the holding period, all at the investor's yield rate.

Real-World Application

In an investment analysis of a shopping center, the reversion can carry more than a third of total present value, so the appraiser documents the terminal capitalization rate, the deduction for sale costs, and the discount rate separately, since a small change in any of them moves the conclusion materially.

reversionpresent value factordiscounted cash flowyield rate

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