In a discounted cash flow analysis, what is the present value of $100,000 received in 3 years with a discount rate of 10%?
Correct Answer
A) $75,131
Why this is correct: The present value formula is PV = FV / (1 + r)^n, where FV is future value, r is the discount rate, and n is the number of periods. Here, FV = $100,000, r = 0.10, n = 3. Calculation: PV = $100,000 / (1.10)^3. First, calculate 1.10^3 = 1.10 * 1.10 * 1.10 = 1.331. Then, PV = $100,000 / 1.331 = $75,131. Why the other choices are wrong: $133,100 is $100,000 * 1.331 (future value, not present). $110,000 is a simple 10% of $100,000 added. $90,909 is the present value for one year ($100,000/1.10), not three. Exam tip: For PV, you always divide by (1+r)^n. The result must be less than the future amount.
Why This Is the Correct Answer
Option A ($75,131) correctly applies the present value formula: PV = FV ÷ (1 + r)^n. Substituting the values: PV = $100,000 ÷ (1 + 0.10)^3 = $100,000 ÷ (1.10)^3 = $100,000 ÷ 1.331 = $75,131. This calculation properly discounts the future value back three years at the 10% discount rate. The result shows that $75,131 invested today at 10% annual return would grow to exactly $100,000 in three years.
Why the Other Options Are Wrong
Option B: $133,100
Option B ($133,100) represents the future value of $100,000 compounded forward at 10% for three years ($100,000 × 1.10^3), which is the reverse calculation. This shows confusion between present value and future value calculations.
Option C: $110,000
Option C ($110,000) appears to add 10% to the future value instead of discounting it, which is the opposite of what present value calculation requires. This represents a fundamental misunderstanding of the time value of money concept.
Option D: $90,909
Option D ($90,909) represents the present value of $100,000 discounted for only one year at 10% ($100,000 ÷ 1.10 = $90,909). This is a common error where the time period is miscalculated, using n=1 instead of n=3 in the formula.
PV-FV Direction Rule
Remember 'PV is LESS, FV is MORE' - Present Value is always less than Future Value when discount rates are positive. Use the acronym 'DIVIDE' for Present Value calculations: Discount rates require you to DIVIDE future values.
How to use: When you see a present value question, immediately think 'DIVIDE' and remember the result should be smaller than the future value. If your answer is larger than the future value, you've made a calculation error.
Exam Tip
Always double-check that your present value result is less than the future value amount given in the question - if it's not, you've likely confused the formula or made a calculation error.
Common Mistakes to Avoid
- -Confusing present value and future value formulas
- -Using wrong time period (n=1 instead of n=3)
- -Adding the discount rate instead of using it as a divisor
Concept Deep Dive
Analysis
This question tests understanding of present value calculations in discounted cash flow (DCF) analysis, a fundamental concept in real estate valuation. Present value represents what a future sum of money is worth today, accounting for the time value of money and opportunity cost. The discount rate reflects the required rate of return or cost of capital, representing the risk and opportunity cost of the investment. DCF analysis is essential for income-producing properties and investment analysis, allowing appraisers to convert future cash flows into current dollar terms for comparison and valuation purposes.
Background Knowledge
Present value is a core time value of money concept that converts future cash flows to today's dollars using a discount rate. The discount rate represents the required rate of return, reflecting risk, inflation, and opportunity cost of capital.
Real-World Application
Appraisers use present value calculations when valuing income-producing properties using the DCF approach, discounting projected future net operating income and reversion values back to present value to determine current market value.
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