An investment will pay $50,000 at the end of each year for ten years. The present value of an annuity factor is approximately 6.418. What is the present value of the payments?
Correct Answer
C) $320,900
50000×6.418 = 320900. Common errors: adding the ten payments without discounting gives $500,000; dividing the undiscounted total by the factor gives $77,906; discounting the factor result one extra year gives $294,404.
Why This Is the Correct Answer
Option C is correct because PV = $50,000 × 6.418 = $320,900. The annuity factor converts the series of ten level year-end payments into a single present value.
Why the Other Options Are Wrong
Option A: $77,906
Option A, $77,906, comes from dividing the undiscounted total by the factor: $50,000 × 10 ÷ 6.418 = $77,906. The factor is multiplied by the single payment, giving $50,000 × 6.418 = $320,900.
Option B: $294,404
Option B, $294,404, results from discounting the factor result one extra year at the roughly 9% rate consistent with the 6.418 factor: $50,000 × 6.418 ÷ 1.09 = $294,404. The factor already reflects year-end timing, so PV is $50,000 × 6.418 = $320,900.
Option D: $500,000
Option D, $500,000, is the ten payments added with no discounting: $50,000 × 10 = $500,000. Applying the annuity factor gives $50,000 × 6.418 = $320,900.
Payment times factor
For a level annuity, one payment times the PV annuity factor equals the present value of all payments.
How to use: Use this when a question supplies an annuity factor for equal periodic payments.
Exam Tip
The present value of an annuity should be less than the simple sum of payments; if not, you skipped the discounting.
Common Mistakes to Avoid
- -Adding payments without discounting
- -Dividing by the annuity factor
- -Discounting the annuity result an extra period
Concept Deep Dive
Analysis
This question tests using a present value of an annuity factor for level year-end payments. Multiply the $50,000 payment by the stated factor of 6.418. The factor already accounts for discounting all ten payments, so no further adjustment is needed.
Background Knowledge
The present value of an ordinary annuity factor is the sum of the present value of one dollar factors for each period. Multiplying a level periodic payment by this factor gives the present value of the entire series. The factor assumes payments at the end of each period.
Real-World Application
An appraiser values a leased fee interest in a ground lease with ten years of level annual rent remaining. The appraiser multiplies the annual rent by the PV annuity factor at the market yield rate to value the income stream.
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