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

To determine the NPV of Project A, start by listing the cash flows and the discount rate: initial investment at t=0 is -200,000, and the subsequent end-of-year cash inflows are 150,000 (t=1), 80,000 (t=2), 90,000 (t=3), 100,000 (t=4), and 110,000 (t=5). The given cost of capital is 14%, so each cash flow must be discounted by (1 + 0.14)^t.

Year 1: PV = 150,000 / 1.14 ≈ 131,579. This is because 1.14 times 131,579 ≈ 150,000.

Year 2: PV = 80,000 / (1.14)^2. Since 1.14^2 = 1.2996, PV ≈ 80,000 / 1.2996 ≈ 61,635. This reflects the time value of money, reducing the future cash flow to present terms.

Year 3: PV = 90,000 / (1.14)^3. With 1.14^3 ≈ 1.481544, PV ≈ 90,000 / 1.481544 ≈ 60,707. This continues the pattern of discounting each future amount.

Year 4: PV = 100,000 / (1.14)^4. Since 1.14^4 ≈ 1.68896, PV ≈ 100,000 / 1.68896 ≈ 59,230. The year-4 inflow is quite valuable but still discounted substantially.

Year 5: PV = 110,000 / (1.14)^5. With 1.14^5 ≈ 1.92541, PV ≈ 110,000 / 1.92541 ≈ 57,090. The fifth-year cash flow, though large, is heavily discounted.

Summing the present values of all inflows: 131,579 + 61,635 + 60,707 + 59,230 + 57,090 ≈ 370,241. The NPV is this sum minus the initial investment: NPV ≈ -200,000 + 370,241 = 170,241.

Now compare with the provided options. The closest value is around 170,222, which aligns with the calculated figure considering rounding in the intermediate steps. The other options would require substantially different PV components:
- A noticeably higher figure (around 182,172 or 174,566) would imply larger discounted inflows or smaller discounting than the given 14% over the five years, which is inconsistent with the computed PVs above.
- A figure around 160,256 would require smaller discounted inflows or a larger initial outlay relative to these cash flows, which is not supported by the data.
Thus, the NPV is best represented by the option ~$170,222, matching our calculation and rounding considerations.

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