An investment property is expected to generate $50,000 annually for 10 years, with a discount rate of 8%. What is the approximate present value of this income stream?
Correct Answer
A) $335,500
Why this is correct: This calculates the present value of an ordinary annuity. The formula is PV = Annual Payment * Present Value of Annuity Factor. For 8% over 10 years, the factor is approximately 6.7101 (from tables or formula: (1 - (1 + 0.08)^-10) / 0.08). PV = 50,000 * 6.7101 = 335,505, approximately $335,500. Why the other choices are wrong: $463,200 might use a factor for a lower discount rate or a perpetuity calculation. $500,000 is simply the sum of the payments (50,000 * 10), ignoring time value of money. $400,000 is an incorrect approximation. Exam tip: For PV of annuity questions, know that the factor is always less than the number of years when the discount rate is positive. Here, 6.71 < 10.
Why This Is the Correct Answer
Option B is correct because it properly applies the present value of annuity formula: PV = PMT × [(1 - (1 + r)^-n) / r]. With $50,000 annual payment, 8% discount rate, and 10 years, the present value factor is 6.7101, resulting in $50,000 × 6.7101 = $335,505, which rounds to $335,500. This calculation properly accounts for the time value of money by discounting each future payment back to present value.
Why the Other Options Are Wrong
Option B: $463,200
$463,200 appears to use an incorrect discount rate or calculation method, possibly confusing present value with future value calculations or using wrong annuity factors.
Option C: $500,000
$500,000 represents the simple sum of all payments ($50,000 × 10 years) without any discounting, completely ignoring the time value of money principle.
Option D: $400,000
$400,000 suggests an arbitrary calculation that doesn't follow proper present value methodology, possibly representing an incorrect averaging or estimation approach.
PAF-DIM Method
PAF-DIM: Payment × Annuity Factor = Discounted Income Money. Remember that the annuity factor for common rates: 8% for 10 years ≈ 6.7, 10% for 10 years ≈ 6.1, 12% for 10 years ≈ 5.7.
How to use: When you see an annuity problem, immediately identify: P (Payment amount), A (Annuity factor from tables), F (multiply these together), then D-I-M reminds you this gives Discounted Income Money (present value).
Exam Tip
Memorize key present value annuity factors for common discount rates (8%, 10%, 12%) and time periods (5, 10, 15, 20 years) to quickly eliminate wrong answers without full calculations.
Common Mistakes to Avoid
- -Adding up all payments without discounting (ignoring time value)
- -Using future value formula instead of present value
- -Confusing discount rate with capitalization rate in calculations
Concept Deep Dive
Analysis
This question tests the fundamental concept of present value of an annuity, which is crucial for income approach valuations in real estate appraisal. The present value calculation discounts future cash flows back to today's dollars using a specified discount rate, accounting for the time value of money. This concept is essential for analyzing investment properties where income streams need to be converted to current value for comparison and valuation purposes. The calculation requires understanding both the mathematical formula and the practical application of discount rates in real estate investment analysis.
Background Knowledge
Present value of annuity calculations are fundamental to the income approach in real estate appraisal, requiring knowledge of financial mathematics and time value of money principles. Appraisers must understand how to discount future income streams using appropriate discount rates to determine current market value.
Real-World Application
Appraisers use this calculation when valuing rental properties, analyzing lease agreements, or determining the present worth of future rental income streams for investment property valuations in the income approach.
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