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

BlackTom AI · Accepted Answer

The problem asks for the NPV of Project A with cash flows given at the end of each year, using a cost of capital of 14%. We will first lay out the cash flows and the discounting process, then evaluate each option.

Project A cash flows:
- Initial outlay (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 net present value is calculated as:
NPV = -200,000 + 150,000/(1.14)^1 + 80,000/(1.14)^2 + 90,000/(1.14)^3 + 100,000/(1.14)^4 + 110,000/(1.14)^5

Compute each discounted cash flow:
- Year 1 PV = 150,000 / 1.14 ≈ 131,579
- Year 2 PV = 80,000 / (1.14)^2 ≈ 61,538
- Year 3 PV = 90,000 / (1.14)^3 ≈ 60,676
- Year 4 PV = 100,000 / (1.14)^4 ≈ 59,150
- Year 5 PV = 110,000 / (1.14)^5 ≈ 57,049

Sum of PVs ≈ 131,579 + 61,538 + 60,676 + 59,150 + 57,049 ≈ 369,992

NPV ≈ -200,000 + 369,992 ≈ 169,992

Now, assess the given answer choices:
- Option A: $182,172. This figure is higher than the computed NPV; the error could come from overestimating one or more discounted cash flows or using a lower discount rate, but with the provided cash flows and 14% rate, the PVs computed above do not reach this level. The discrepancy indicates this is not the correct NPV.
- Option B: $174,566. This is also higher than our computed value. It suggests slightly larger present values than calculated or rounding differences, but the core issue remains that it overstates the NPV relative to the precise discounting at 14%.
- Option C: $170,222. This is very close to the NPV we calculated (~169,992). Small differences can arise from rounding intermediate PVs differently or using slightly different rounding conventions for each PV, but this option aligns best with the discounting results at 14%.
- Option D: $160,256. This is noticeably lower than the computed figure, implying larger discounting or smaller cash flows than the given numbers. It does not match the result from applying 14% to the cash flows.

In typical financial calculations, small rounding variations can shift the NPV by a few dollars to a few hundred dollars, but the option closest to the precise NPV using 14% is the one around 170k. The step-by-step discounting shows that the sum of discounted inflows is just under 370k, which when offset by the 200k initial outlay yields an NPV in the low 170k range. The option that sits closest to this result is the one labeled approximately 170k, acknowledging minor rounding differences across tools or calculators.

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