Ten year-end payments of $50,000 each are to be received. The approximate present value of an annuity factor for the period is 6.1446. What is the present value of the payments?
Correct Answer
C) $307,230
50000×6.1446 = 307230. Common errors: adding the ten payments without discounting gives $500,000; dividing the undiscounted total by the factor gives $81,372; discounting the factor result one extra year gives $279,300.
Why This Is the Correct Answer
Option C is correct because $50,000 × 6.1446 = $307,230. The annuity factor converts each of the ten level year-end payments to present value in a single step. The result is less than the $500,000 undiscounted total, as it should be.
Why the Other Options Are Wrong
Option A: $81,372
Option A, $81,372, divides the undiscounted total by the factor: ($50,000 × 10) ÷ 6.1446. The factor is a multiplier applied to one payment, so the present value is $50,000 × 6.1446 = $307,230.
Option B: $279,300
Option B, $279,300, takes the correct result and discounts it one extra year: $50,000 × 6.1446 ÷ 1.10. The factor already reflects year-end timing, so no further discounting is needed and the answer is $307,230.
Option D: $500,000
Option D, $500,000, adds the ten payments ($50,000 × 10) without discounting. Money received in the future is worth less today, so the present value is $50,000 × 6.1446 = $307,230.
One payment times one factor
An annuity factor already bundles all the periods and the discounting, so multiply a single payment by it once.
How to use: Use this whenever a problem supplies a present value of annuity factor for level payments.
Exam Tip
The present value of a level series is less than the simple sum of the payments when the rate is positive. Use that as a quick check.
Common Mistakes to Avoid
- -Adding the payments without discounting
- -Dividing by the annuity factor instead of multiplying
- -Discounting an annuity result again after applying the factor
Concept Deep Dive
Analysis
This question tests applying a given present-value-of-an-annuity factor to a level series of year-end payments. The factor already accounts for both the number of payments and the discounting, so the payment is multiplied by it once. Any further adjustment or simple summation misstates the value.
Background Knowledge
The present value of an annuity factor sums the present value of one dollar for each period of a level payment series. Multiplying the periodic payment by that factor gives the present value of the whole series.
Real-World Application
An appraiser valuing a lease with ten years of level annual rent uses an annuity factor at the market discount rate. Multiplying the annual rent by the factor gives the present value of the rent stream.
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