The projected reversion from a property is $2,000,000. The applicable present value factor is approximately 0.1842. What is the present value of the reversion?
Correct Answer
A) $368,400
2000000×0.1842 = 368400. Common errors: reporting the discount instead of the present value gives $1,631,600; dividing by the factor instead of multiplying gives $10,857,763; ignoring the present-value factor gives $2,000,000.
Why This Is the Correct Answer
Option A is correct because $2,000,000 × 0.1842 = $368,400. A present value of one factor is the value today of one received in the future, so multiplying the future reversion by that factor gives its present value.
Why the Other Options Are Wrong
Option B: $1,631,600
Option B, $1,631,600, reports the discount rather than the present value: $2,000,000 × (1 − 0.1842) = $1,631,600. That is the amount removed by discounting; the present value itself is $2,000,000 × 0.1842 = $368,400.
Option C: $2,000,000
Option C, $2,000,000, ignores the present value factor and reports the future amount unchanged. A sum received in the future is worth less today, so it must be multiplied by 0.1842, giving $368,400.
Option D: $10,857,763
Option D, $10,857,763, divides by the factor instead of multiplying: $2,000,000 ÷ 0.1842 = $10,857,763. Dividing by a factor below one makes the result larger than the future amount, which cannot be a present value; the correct figure is $368,400.
Factor Below One Shrinks
A present value factor is less than one, so multiplying by it makes the future amount smaller. If your answer grew, you divided by mistake.
How to use: Use this check to confirm you multiplied rather than divided by a present value factor.
Exam Tip
When a factor is given, use it as stated; the present value of a future sum should be smaller than the sum itself.
Common Mistakes to Avoid
- -Dividing by the present value factor
- -Reporting the discount amount instead of the present value
- -Ignoring the factor and using the future amount
Concept Deep Dive
Analysis
This question tests applying a given present value factor to a future amount. When a present value of one factor is given, the present value equals the future amount multiplied by the factor. The distractors divide by the factor, report the discount, or ignore the factor.
Background Knowledge
The present value of one factor equals 1 ÷ (1 + i)^n and is less than one for any positive discount rate. Appraisers multiply a future reversion by this factor to find its contribution to present value in yield capitalization.
Real-World Application
An appraiser valuing a ground lease estimates the reversion of the land at lease expiration. The appraiser multiplies the forecast reversion value by the present value of one factor for the remaining term and discount rate.
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