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?$170,222$182,172$174,566$160,256

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?$170,222$182,172$174,566$160,256

BlackTom AI · Accepted Answer

We start by restating the problem to ensure clarity: we are evaluating Project A with cash flows as follows (end of year): Year 0 = -200,000; Year 1 = 150,000; Year 2 = 80,000; Year 3 = 90,000; Year 4 = 100,000; Year 5 = 110,000. The cost of capital is 14%, so the NPV is the present value of all future cash flows minus the initial investment: NPV = -200,000 + 150,000/1.14 + 80,000/1.14^2 + 90,000/1.14^3 + 100,000/1.14^4 + 110,000/1.14^5.

Option by option analysis:

Option A: $170,222
- To verify, compute each term precisely and add them up. First year PV: 150,000/1.14 ≈ 131,579. Second year PV: 80,000/1.14^2, with 1.14^2 = 1.2996, gives ≈ 61,555. Third year PV: 90,000/1.14^3, with 1.14^3 ≈ 1.481544, gives ≈ 60,723. Fourth year PV: 100,000/1.14^4, with 1.14^4 ≈ 1.688960, gives ≈ 59,235. Fifth year PV: 110,000/1.14^5, with 1.14^5 ≈ 1.925415, gives ≈ 57,055. Sum of PVs ≈ 131,579 + 61,555 + 60,723 + 59,235 + 57,055 ≈ 370,147. Subtracting initial investment: NPV ≈ 370,147 − 200,000 = 170,147. This is very close to 170,222 when rounding differences are accounted for, so Option A is in the right neighborhood.

Option B: $182,172
- If we compare to the computed total, this value would require a larger sum of PVs by about 12,000. The discrepancy could come from using slightly different discount factors or a rounding approach, but with standard 14% discounting the sum of PVs as shown above yields around 370,000 total PV, driving NPV near 170k, not 182k.

Option C: $174,566
- This option is also higher than the standard computed NPV by a few thousand. The difference would imply a PV sum around 374,566 before subtracting the 200,000 investment, which is not aligned with the 1.14 discount ladder given the cash flows here.

Option D: $160,256
- This would occur if the PVs totaled about 360,256 before subtracting 200,000. Given the cash flows are all positive after Year 0 and the discount rate is 14%, this is lower than the computed benchmark and suggests under-weighting one or more of the later-year cash flows or using a higher rate.

Across these options, the most consistent match to the standard NPV calculation with a 14% cost of capital is the approximate 170k region, which aligns best with Option A when rounding is applied. The other figures require changes to the cash flows, discounting, or rounding that are not consistent with the provided data.

In summary, when applying the 14% discount rate to Project A’s cash flows and summing, the resulting NPV is approximately 170,000, which explains why Option A sits closest to the computed value. If your screen shows a different key answer, it may reflect a rounding method, a transcription error in the cash flows, or a mismatched decimal treatment in the discounting steps.

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