A site will be redeveloped in three years. Meanwhile a parking use nets $20,000 a year, and the land is expected to be worth $500,000 when the change occurs. Ignoring removal costs, what is today’s value at a 10% discount rate (3-year annuity factor 2.4869; reversion factor 0.7513)?
Correct Answer
D) $425,388
Transitional value is the present worth of the interim net benefits plus the present worth of the future value: $20,000 × 2.4869 = $49,738, and $500,000 × 0.7513 = $375,650. The total is $425,388.
Why This Is the Correct Answer
Option D is correct because transitional value is the sum of the present worth of interim benefits and the present worth of the future value. The interim income is $20,000 × 2.4869 = $49,738, and the reversion is $500,000 × 0.7513 = $375,650. The total is $425,388.
Why the Other Options Are Wrong
Option A: $560,000
Option A, $560,000, adds $500,000 plus 3 × $20,000 with no discounting. Both parts must be discounted, giving $49,738 + $375,650 = $425,388.
Option B: $375,650
Option B, $375,650, is only the discounted reversion ($500,000 × 0.7513). It leaves out the present value of the parking income, $49,738, so the total should be $425,388.
Option C: $549,738
Option C, $549,738, adds the discounted interim income ($49,738) to the undiscounted $500,000 reversion. The reversion must be discounted to $375,650, giving $425,388.
Income now plus land later
Discount the interim income with the annuity factor and the future land value with the reversion factor, then add them.
How to use: Use this two-part setup for any interim use or transitional property question.
Exam Tip
Make sure every future dollar is discounted; answers that leave out discounting on either part are traps.
Common Mistakes to Avoid
- -Adding undiscounted income and reversion
- -Leaving out the interim income
- -Discounting the income but not the reversion
Concept Deep Dive
Analysis
This question tests the valuation of transitional land with an interim use. Value equals the present worth of interim net income plus the present worth of the future land value. Both parts must be discounted with the given factors.
Background Knowledge
A property in transition may have an interim use until its highest and best use becomes feasible. Its present value combines the discounted net income from the interim use and the discounted value expected when the change occurs, less any costs of the transition where applicable.
Real-World Application
An appraiser values a downtown lot used as surface parking until a planned office project can start in three years. The appraiser discounts the parking income and the expected land value at the time of development to estimate its value today.
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