Living Colour Company has a project available with the following cash flows:

Year Cash Flow
0 −$ 32,030
1 8,540
2 10,330
3 14,890
4 16,370
5 11,480

If the required return for the project is 9.8 percent, what is the project's NPV?

Question

Living Colour Company has a project available with the following cash flows:

Year	Cash Flow
0	−$ 32,030
1	8,540
2	10,330
3	14,890
4	16,370
5	11,480

If the required return for the project is 9.8 percent, what is the project's NPV?

BlackTom AI · Accepted Answer

To evaluate the project’s NPV at a required return of 9.8%, we must discount each cash flow back to present value terms and sum them, including the initial outlay.

Option 1: $6,827.03
This would imply a much smaller sum of discounted inflows relative to the outlay. If the discounted cash flows were this low, the NPV would be far less than the outlay, which is inconsistent with the actual cash flows given and the 9.8% discount rate. Hence this result is too low.

Option 2: $29,580.00
This is substantially larger than the initial investment and the sum of the undiscounted inflows (which total 60,? approximately), even after discounting at 9.8%. A value this high would require either much larger inflows or a much smaller discount rate; neither is the case here. Therefore this option overstates NPV.

Option 3: $14,020.37
Proceeding with the actual discounting: discount rate is 9.8%, so we compute PVs for each year 1–5 and subtract the initial outlay of 32,030. The present values approximate to: Year 1 ≈ 7,778; Year 2 ≈ 8,567; Year 3 ≈ 11,250; Year 4 ≈ 11,270; Year 5 ≈ 7,190. Summing these PVs yields roughly 46,056, and subtracting 32,030 gives an NPV near 14,026. That aligns closely with the option listed as $14,020.37, making it a plausible and correct result.

Option 4: $15,188.73
This is a plausible NPV magnitude, but when computing the discounted values with 9.8%, the sum of the discounted inflows tends to about 46,056, leading to an NPV around 14,026 rather than 15,189. The small difference indicates this option is slightly high given the actual cash flows.

Option 5: $16,023.28
This is even higher than option 4. As shown by the PV calculations, the NPV is more like 14k, not above 16k, so this overstates the value.

Overall, after discounting each yearly cash flow at 9.8%, the net present value is approximately 14,020, which corresponds to option 3. The other options reflect either underestimation or overestimation based on incorrect discounting or arithmetic mistakes.

Living Colour Company has a project available with the following cash flows: Year Cash Flow 0 −$ 32,030 1 8,540 2 10,330 3 14,890 4 16,370 5 11,480 If the required return for the project is 9.8 percent, what is the project's NPV?单项选择题

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