Rossdale Flowers has a new greenhouse project with an initial cost of $275,000 that is expected to generate cash flows of $41,900 for 7 years and a cash flow of $57,300 in Year 8. If the required return is 7.5 percent, what is the project's NPV?

Question

BlackTom AI · Accepted Answer

To tackle this NPV problem, I will lay out the cash flows and the required return, then compute the present value of each cash flow.
First, the initial outlay is an outflow of 275,000 at time 0, so it will reduce the project value by 275,000.
Next, for years 1 through 7, the project yields 41,900 each year. This is an ordinary annuity with 7 payments at a 7.5% discount rate. The present value factor for an ordinary annuity is (1 - (1 + i)^-n) / i, where i = 0.075 and n = 7.
Calculating (1 + i)^-n: (1.075)^-7 ≈ 0.6028, so (1 - 0.6028) ≈ 0.3972. Divide by i: 0.3972 / 0.075 ≈ 5.296. Multiply by the annual cash flow: 41,900 × 5.296 ≈ 221,900 (roughly 221,886 in this estimate). This is the present value of the 7 yearly cash inflows.
For year 8, the cash flow is 57,300. Its present value is 57,300 / (1.075)^8. Estimating (1.075)^8 ≈ 1.783, so the discount factor is about 0.561, giving a present value of roughly 57,300 × 0.561 ≈ 32,200.
Add the PVs of all inflows: approximately 221,900 + 32,200 ≈ 254,100. Subtract the initial outlay: 254,100 − 275,000 ≈ −20,900. This rough calculation aligns with the more precise value around −20,944.
Thus, the NPV is negative, indicating the project would not meet the 7.5% return threshold. Specifically, using precise figures yields approximately −$20,944.17.
If you compare this result to any alternative choices, you would see that any option claiming a nonnegative NPV would be incorrect, and the magnitude here reflects more accurate PV computations of the 7-year annuity plus the single Year 8 cash flow discounted at 7.5%.

Rossdale Flowers has a new greenhouse project with an initial cost of $275,000 that is expected to generate cash flows of $41,900 for 7 years and a cash flow of $57,300 in Year 8. If the required return is 7.5 percent, what is the project's NPV?单项选择题

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