Ten fixed payments of $50,000 are received at each year-end. No terminal or other cash flow exists. At an 8% annual discount rate, what present value results, rounded to the nearest dollar?
Correct Answer
B) $335,504
50000×(1−1.08^(−10))÷0.08 = 335504.07. Common errors: adding the ten payments without discounting gives $500,000; capitalizing the payments as a perpetuity gives $625,000; discounting the total of all payments as a single year-10 amount gives $231,597.
Why This Is the Correct Answer
Option B is correct because $50,000 × (1 − 1.08^−10) ÷ 0.08 = $50,000 × 6.7101 ≈ $335,504. Each year-end payment is discounted for its own number of periods, and the annuity factor sums those present values.
Why the Other Options Are Wrong
Option A: $231,597
Option A, $231,597, comes from discounting the total of all payments as a single year-10 amount ($500,000 ÷ 1.08^10). Payments arrive each year, so earlier ones are discounted less; the correct value is $335,504.
Option C: $500,000
Option C, $500,000, simply adds the ten payments ($50,000 × 10) without discounting. Money received in the future is worth less today, so the present value is $335,504.
Option D: $625,000
Option D, $625,000, capitalizes the payments as a perpetuity ($50,000 ÷ 0.08). The income lasts only ten years, so the finite annuity factor applies, giving $335,504.
Finite stream, finite factor
A perpetuity divides by the rate; a ten-year stream is worth less because payments stop. Its value falls between the undiscounted sum and the lump-sum discount.
How to use: Use this range check to eliminate the perpetuity, undiscounted and lump-sum answers.
Exam Tip
The present value of a finite level annuity should be less than both the undiscounted total and the perpetuity value.
Common Mistakes to Avoid
- -Treating a finite income stream as a perpetuity
- -Summing payments without discounting
- -Discounting all payments as one amount at the final year
Concept Deep Dive
Analysis
This question tests the present value of a finite ordinary annuity. Ten equal year-end payments of $50,000 are discounted at 8%, using the annuity factor (1 − 1.08^−10) ÷ 0.08. Distractors ignore discounting, treat the income as perpetual, or discount the total as one lump sum.
Background Knowledge
The present value of $1 is $1 divided by (1 + i) raised to the number of periods. The present value of an ordinary annuity sums the present values of equal payments received at the end of each period. A perpetuity formula (payment ÷ rate) applies only when income continues indefinitely.
Real-World Application
An appraiser values the contract rent stream under a lease in which the tenant pays $50,000 net at each year-end for ten years. Discounting those ten payments at an 8% market yield gives a present value of about $335,504; the reversion would be valued and added separately in a full leased fee analysis.
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