Rossdale Flowers has a new greenhouse project with an initial cost of $365,000 that is expected to generate cash flows of $48,600 for 10 years and a cash flow of $64,000 in Year 11. If the required return is 8.4 percent, what is the project's NPV?

Question

BlackTom AI · Accepted Answer

We start by restating the problem to ensure clarity: Rossdale Flowers invests an initial cost of 365,000 (a cash outflow), and is expected to receive 48,600 per year for years 1 through 10, plus 64,000 in year 11. The discount rate is 8.4%. We are asked to determine the net present value (NPV) of the project.

Option 1: −$18,338.06
- To evaluate this, compute the present value of the cash flows. The first 10 years form an ordinary annuity with payment 48,600. The PV of these 10 payments is 48,600 multiplied by the annuity factor at 8.4% for 10 years, which is [1 − (1.084)^(−10)] / 0.084 ≈ 6.587. Thus PV of years 1–10 ≈ 48,600 × 6.587 ≈ 320,128.
- The 11th year cash flow is 64,000 discounted for 11 years: 64,000 / (1.084)^(11). Using (1.084)^(11) ≈ 2.428, this PV ≈ 64,000 / 2.428 ≈ 26,341.
- Total PV of inflows ≈ 320,128 + 26,341 ≈ 346,469. Subtract the initial outflow of 365,000 gives NPV ≈ 346,469 − 365,000 ≈ −18,531.
- The option −$18,338.06 is very close to this calculated value, accounting for rounding differences in the PV factors. Overall, this option represents a negative NPV in the range suggested by the precise calculation.

Option 2: −$24,679.65
- This would require a larger PV of inflows or a larger initial outflow than calculated. If we recomputed with more extreme rounding or a different PV factor, the result would be further negative than −18k. The discrepancy with the precise calculation (−18.5k region) indicates this option is too negative given the cash flows and rate.

Option 3: $104,852.67
- A positive NPV of this magnitude would imply that the PV of inflows far exceeds the initial investment, which is inconsistent with the cash flow amounts (48,600 for ten years and 64,000 in year 11) at an 8.4% discount rate. The discounted sum would have to exceed 365,000 by more than 104,852, which does not align with the calculated PVs above.

Option 4: $1,675.04
- This is a small positive number. Given the calculated inflows and discounting, the NPV is not near zero; the present value of inflows minus 365,000 yields a clearly negative result in the tens of thousands, not a marginal positive amount.

Option 5: $83,158.48
- This is a sizable positive NPV, which would require either much larger PV of inflows or a smaller initial expenditure. The cash flows and rate provided do not support a positive NPV of this magnitude when computed in the standard present-value manner.

Summary of reasoning across options:
- The central calculation involves two components: the PV of 48,600 per year for 10 years and the PV of 64,000 in year 11, all discounted at 8.4%, minus the initial investment of 365,000.
- The PV of the 10-year annuity is roughly 320,000, and the PV of the year-11 inflow is roughly 26,000, giving total inflows around 346,000. Subtracting 365,000 yields an NPV around −18,000 to −19,000, aligning with option 1 and lying well away from the other options.
- Each other option either overstates the negative NPV (options 2), or incorrectly yields a positive NPV (options 3, 4, 5) given the same cash-flow data and discount rate.

Note: All intermediate values shown are rounded; precise calculator results will yield values very close to those described, with minor variation due to rounding of the annuity factor and the year-11 discounting.

Rossdale Flowers has a new greenhouse project with an initial cost of $365,000 that is expected to generate cash flows of $48,600 for 10 years and a cash flow of $64,000 in Year 11. If the required return is 8.4 percent, what is the project's NPV?单项选择题

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