An investment provides $11,000 at the end of year 1 and $121,000 including all terminal proceeds at the end of year 2. There are no other cash flows. At a 10% annual discount rate, what present value results?
Correct Answer
B) $110,000
11000÷1.10+121000÷1.10^2 = 110000. Common errors: discounting both cash flows for only one year gives $120,000; adding the cash flows without discounting gives $132,000; discounting both cash flows for two years gives $109,091.
Why This Is the Correct Answer
Option B is correct because $11,000 ÷ 1.10 = $10,000 and $121,000 ÷ 1.21 = $100,000, so present value is $110,000. Each amount is discounted for its own timing.
Why the Other Options Are Wrong
Option A: $109,091
Option A, $109,091, discounts both cash flows for two years: $132,000 ÷ 1.21. The year-1 amount should be discounted one year only, giving $10,000 + $100,000 = $110,000.
Option C: $120,000
Option C, $120,000, discounts both cash flows for only one year: $132,000 ÷ 1.10. The year-2 amount needs two years of discounting, giving $110,000.
Option D: $132,000
Option D, $132,000, adds the cash flows ($11,000 + $121,000) without discounting. Future dollars are worth less today; discounting gives $110,000.
One year, one division
Divide by 1.10 once for each year you wait: once for year 1, twice for year 2.
How to use: Use this count to set the exponent for each cash flow.
Exam Tip
Present value should be less than the simple sum of future cash flows at a positive discount rate.
Common Mistakes to Avoid
- -Using the same discount period for all cash flows
- -Adding future cash flows without discounting
- -Leaving the reversion out of the final year
Concept Deep Dive
Analysis
This question tests discounting cash flows that occur at different times. Each cash flow is divided by (1 + i) raised to the number of years until it is received: $11,000 for one year and $121,000 for two years at 10%.
Background Knowledge
The present value of a future amount is the amount divided by (1 + i) to the nth power. A DCF analysis sums the present values of periodic income and the reversion, each discounted for its own timing.
Real-World Application
An appraiser models a two-year hold on a small property with $11,000 of income in year 1 and $121,000 of income plus sale proceeds in year 2. At a 10% discount rate, the present value is $110,000.
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