End-of-year 1 cash flow is $80,000 and end-of-year 2 cash flow including all terminal proceeds is $1,080,000. No other cash flows apply. At an 8% annual discount rate, what present value results?
Correct Answer
B) $1,000,000
80000÷1.08+1080000÷1.08^2 = 1000000. Common errors: discounting both cash flows for only one year gives $1,074,074; adding the cash flows without discounting gives $1,160,000; discounting both cash flows for two years gives $994,513.
Why This Is the Correct Answer
Option B is correct because $80,000 ÷ 1.08 = $74,074.07 and $1,080,000 ÷ 1.08² = $925,925.93, which sum to $1,000,000. Each cash flow is discounted from the year it is received. Both are discounted at the 8% rate.
Why the Other Options Are Wrong
Option A: $994,513
Option A, $994,513, discounts both cash flows for two years: ($80,000 + $1,080,000) ÷ 1.08². The year 1 cash flow should be discounted only one year, giving a total of $1,000,000.
Option C: $1,074,074
Option C, $1,074,074, discounts both cash flows for only one year: ($80,000 + $1,080,000) ÷ 1.08. The year 2 amount must be discounted two years, giving $1,000,000.
Option D: $1,160,000
Option D, $1,160,000, adds the two cash flows without discounting: $80,000 + $1,080,000. Future amounts must be converted to present value, which gives $1,000,000.
Exponent equals the year
Divide each cash flow by (1 + rate) raised to the year it arrives: year 1 to the first power, year 2 to the second.
How to use: Use this to set up each term in a multi-year present value.
Exam Tip
Write each cash flow with its own discount factor before adding; using one factor for all cash flows is a common trap.
Common Mistakes to Avoid
- -Discounting all cash flows for the same number of periods
- -Adding cash flows without discounting
- -Forgetting to include terminal proceeds in the final year
Concept Deep Dive
Analysis
This question tests discounting individual cash flows for the correct number of periods. The year 1 amount is discounted one year and the year 2 amount, including terminal proceeds, two years. The distractors use the same period for both or skip discounting.
Background Knowledge
The present value of a single amount is the amount divided by (1 + i) raised to the number of periods. In a DCF, the operating cash flows and net sale price are each discounted by the appropriate factor for their timing.
Real-World Application
An appraiser valuing a property expected to be sold after two years discounts year 1 net income one period and year 2 income plus resale proceeds two periods. The sum is the present value indication.
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