What is the present value of $150,000 to be received in 5 years, assuming a discount rate of 8%?
Correct Answer
B) $102,087
Why this is correct: Present value discounts a future sum to its worth today, using the formula: PV = FV / (1 + r)^n. Here, FV=$150,000, r=8% (0.08), n=5 years. Step-by-step: (1.08)^5 = 1.469328. Then, $150,000 / 1.469328 ≈ $102,087. Why the other choices are wrong: "$150,000" ignores discounting entirely, treating future value as present value. "$220,407" incorrectly calculates future value (compounds): $150,000 × (1.08)^5, instead of discounting. "$138,888" uses simple interest approximation: $150,000 / (1 + 0.08×5) = $150,000 / 1.4, which is not correct for compound discounting. Exam tip: Remember PV = FV / (1+r)^n. The denominator is (1+rate) raised to the power of years. Use your calculator's exponent function for precision.
Why This Is the Correct Answer
Option A ($102,087) correctly applies the present value formula: PV = FV ÷ (1 + r)^n. Substituting the given values: PV = $150,000 ÷ (1 + 0.08)^5 = $150,000 ÷ (1.08)^5. Calculating (1.08)^5 = 1.4693, then $150,000 ÷ 1.4693 = $102,087. This represents the amount that, if invested today at 8% annual return, would grow to exactly $150,000 in 5 years.
Why the Other Options Are Wrong
Option A: $150,000
Option A ($150,000) represents the future value, not the present value. This would be correct if asking what the future amount will be, but ignores the time value of money concept entirely. Using this answer assumes no discounting is needed, which contradicts the fundamental principle that future money is worth less than present money.
Option C: $220,407
Option C ($220,407) appears to be a future value calculation error, possibly using the wrong formula or confusing present value with future value calculations. This amount is significantly higher than both the present and future values, suggesting a fundamental mathematical error in the calculation process.
Option D: $138,888
Option D ($138,888) suggests an incorrect discount rate was used or there was an error in the calculation process. This amount is too high for the present value given the specified 8% discount rate over 5 years, indicating insufficient discounting was applied.
PV-FD Formula Bridge
Remember 'Present Value = Future Divided' - PV equals FV divided by (1 + rate)^years. Think of it as building a bridge from future money back to today by dividing out the growth.
How to use: When you see present value questions, immediately write 'PV = FV ÷ (1 + r)^n' and identify each component: Future Value, discount rate (r), and number of years (n). Always divide, never multiply, when going from future to present.
Exam Tip
Always double-check that you're using the correct formula direction - dividing for present value (going backward in time) versus multiplying for future value (going forward in time). Write out the formula first to avoid confusion.
Common Mistakes to Avoid
- -Confusing present value and future value formulas
- -Using multiplication instead of division when calculating present value
- -Forgetting to raise (1 + rate) to the power of years
Concept Deep Dive
Analysis
This question tests the fundamental concept of present value, which is the current worth of a future sum of money given a specific discount rate. Present value calculations are essential in real estate appraisal for income capitalization approaches, where future income streams must be converted to current value. The concept recognizes that money received in the future is worth less than the same amount received today due to the time value of money and opportunity cost. Understanding present value allows appraisers to compare investment alternatives and determine the current market value of income-producing properties.
Background Knowledge
Present value is a core financial concept stating that money available today is worth more than the same amount in the future due to its earning potential and inflation. The present value formula PV = FV ÷ (1 + r)^n allows conversion of future cash flows to current dollars, essential for income approach valuations in real estate appraisal.
Real-World Application
Appraisers use present value when valuing income-producing properties under the income approach. For example, if a property will generate $150,000 in net operating income 5 years from now, the appraiser must discount this to present value to determine its contribution to current market value.
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