Question at position 1 You have just been hired as a senior financial manager of the XYZ Inc. by the eccentric CEO, Elon Tusk. Elon is considering the following potential projects (all cash flows happen at the end of the year). Assume the cost of capital for XYZ Inc. is 14%. [table]
Year | Project A | Project B | Project C
0 | -200,000 | -480,000 | -680,000 1 | 150,000 | 280,000 | -100,000 2 | 80,000 | 280,000 | 350,000 3 | 90,000 | 280,000 | 350,000 4 | 100,000 | 280,000 | 750,000 5 | 110,000 | 280,000 | 650,000
[/table] What is the NPV of Project A?$182,172$160,256$174,566$170,222

Question

Question at position 1 You have just been hired as a senior financial manager of the XYZ Inc. by the eccentric CEO, Elon Tusk. Elon is considering the following potential projects (all cash flows happen at the end of the year). Assume the cost of capital for XYZ Inc. is 14%. [table]
Year | Project A | Project B | Project C
0 | -200,000 | -480,000 | -680,000 1 | 150,000 | 280,000 | -100,000 2 | 80,000 | 280,000 | 350,000 3 | 90,000 | 280,000 | 350,000 4 | 100,000 | 280,000 | 750,000 5 | 110,000 | 280,000 | 650,000
[/table] What is the NPV of Project A?$182,172$160,256$174,566$170,222

BlackTom AI · Accepted Answer

First, restating the problem to ensure clarity: we need the NPV of Project A using a cost of capital of 14%. The cash flows are at year end with: Year 0 = -200,000; Year 1 = 150,000; Year 2 = 80,000; Year 3 = 90,000; Year 4 = 100,000; Year 5 = 110,000.

Compute the discounted cash flows using 14% as the discount rate: CF1 discounted = 150,000 / 1.14 ≈ 131,579; CF2 discounted = 80,000 / 1.14^2 ≈ 80,000 / 1.2996 ≈ 61,548; CF3 discounted = 90,000 / 1.14^3 ≈ 90,000 / 1.481544 ≈ 60,718; CF4 discounted = 100,000 / 1.14^4 ≈ 100,000 / 1.68896016 ≈ 59,236; CF5 discounted = 110,000 / 1.14^5 ≈ 110,000 / 1.92541458 ≈ 57,121.

Now sum the discounted inflows: 131,579 + 61,548 + 60,718 + 59,236 + 57,121 ≈ 370,202.
Subtract the initial investment to obtain NPV: 370,202 − 200,000 ≈ 170,202.

Option-by-option analysis:
- Option A: $182,172
  The value here would imply a total present value of inflows around 382,172 when adding the initial -200,000, or a different combination of discounted cash flows than our calculation. The given discounted inflows sum to about 370,202, which is notably lower than 382,172, suggesting this option overstates the NPV and would require higher discounted inflows or a lower initial outflow in the calculation.
- Option B: $160,256
  This would occur if the sum of discounted inflows were around 360,256 after discounting and subtracting 200,000, or if nearby rounding produced a smaller total. It is lower than the computed ~170,200, indicating underestimation of the present values of future cash receipts.
- Option C: $174,566
  This option implies a sum of discounted inflows around 374,566 after accounting for the initial 200,000 outlay. Since our more exact calculation yields about 370,200, this is a modest overstatement by roughly 4,300, which could arise from slightly different rounding in intermediate steps. It is in the same general ballpark as the precise figure but appears a bit high relative to the standard discounting with 14%.
- Option D: $170,222
  This value is very close to the detailed calculation result of NPV ≈ 170,202. The slight difference could come from rounding at intermediate steps or the use of slightly different rounding conventions for each discounted cash flow. This option aligns most tightly with the core computation of present values at 14% for the given cash flows.

Conceptual notes: NPV is the sum of present values of all cash flows, including the initial investment treated as a negative cash flow at time zero. For projects with multiple years of cash inflows, each inflow must be discounted back to the present using (1 + r)^t where r is the cost of capital and t is the year. The accuracy of the final NPV depends on consistent rounding throughout the calculations; small rounding differences can shift results by a few dollars.

If you want, I can show the exact arithmetic with full precision or recalculate using a different rounding convention to illustrate how the final value can drift slightly depending on the method used.

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