Harry's Inc. is considering a project that has the following cash flow and WACC data. What is the project's NPV? Note that if a project's projected NPV is negative, it should be rejected.

WACC:

6.75%

Year

0

1

2

3

4

5

Cash flows

-$1,000

$300

$300

$300

$300

$300

Question

Harry's Inc. is considering a project that has the following cash flow and WACC data. What is the project's NPV? Note that if a project's projected NPV is negative, it should be rejected.

WACC:

6.75%

Year

0

1

2

3

4

5

Cash flows

-$1,000

$300

BlackTom AI · Accepted Answer

NPV is the present value of the future cash inflows minus the initial outlay, discounted at the WACC of 6.75%.

1) Relevant knowledge points
- NPV formula for multiple cash flows: NPV = Σ (Ct / (1+r)^t) – C0.
- For a level cash flow each year, the present value can be computed using the annuity formula: PV = C * [1 − (1+r)^−n] / r.

2) Step-by-step reasoning
We have C0 = −1000, annual inflows Ct = 300 for t = 1 to 5, r = 0.0675, n = 5. Use the annuity formula to get the PV at t = 0 of the five $300 receipts, then subtract the initial outlay.

3) Intermediate calculations
Compute (1+r)^5:
(1.0675)^2 = 1.13955625
(1.0675)^3 ≈ 1.216476296875
(1.0675)^4 ≈ 1.2985884469140625
(1.0675)^5 ≈ 1.3862431670807617

Then (1+r)^−5 = 1 / 1.3862431670807617 ≈ 0.72137416.

Annuity PV factor = [1 − (1+r)^−n] / r = [1 − 0.72137416] / 0.0675 = 0.27862584 / 0.0675 ≈ 4.12779.

PV of inflows = 300 * 4.12779 ≈ 1,238.337.

NPV = PV of inflows − initial outlay = 1,238.337 − 1,000 = 238.337 ≈ 238.34.

4) Why the correct answer is correct
The calculation discounts each $300 cash inflow back to present value at the correct required return (6.75%) and sums them; subtracting the initial −$1,000 yields a positive NPV of about $238.34. That positive NPV indicates the project adds value and should be accepted.

5) Why other answers would be incorrect
Common mistakes include failing to discount the inflows (which would give $500 total inflows), using the wrong discount rate, or using wrong exponentiation; any such error will produce a different PV and thus an incorrect NPV. Since the correct discounting yields +238.34, negative NPVs or other positive values differing from this result are incorrect.

6) Conclusion
The project’s NPV is approximately $238.34, matching the provided answer.

Harry's Inc. is considering a project that has the following cash flow and WACC data. What is the project's NPV? Note that if a project's projected NPV is negative, it should be rejected. WACC: 6.75% Year 0 1 2 3 4 5 Cash flows -$1,000 $300 $300 $300 $300 $300单项选择题

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