Project A has a required return on 9.2 percent and cash flows of −$87,000, $32,600, $35,900, and $43,400 for Years 0 to 3, respectively. Project B has a required return of 12.7 percent and cash flows of −$85,000, $14,700, $21,200, and $89,800 for Years 0 to 3, respectively. Which project(s) should you accept based on net present value if the projects are mutually exclusive?单项选择题
A
A. Accept Project A and reject Project B
B
B. Reject Project A and accept Project B
C
C. Accept both projects
D
D. Reject both projects

Question

Project A has a required return on 9.2 percent and cash flows of −$87,000, $32,600, $35,900, and $43,400 for Years 0 to 3, respectively. Project B has a required return of 12.7 percent and cash flows of −$85,000, $14,700, $21,200, and $89,800 for Years 0 to 3, respectively. Which project(s) should you accept based on net present value if the projects are mutually exclusive?单项选择题

A

A. Accept Project A and reject Project B

B

B. Reject Project A and accept Project B

C

C. Accept both projects

D

D. Reject both projects

BlackTom AI · Accepted Answer

Net present value (NPV) discounts each future cash flow at the project’s required return and sums them with the initial outlay to decide accept/reject. For mutually exclusive projects you accept the one with the higher NPV (if positive).

1) Relevant concepts
- NPV = Σ [CFt / (1 + r)^t] − Initial investment.
- Use each project’s own required return to discount its cash flows.
- If projects are mutually exclusive, choose the project with the larger NPV (if NPVs are positive).

2) Step-by-step calculations

Project A (r = 9.2%):
- Year 0: CF0 = −87,000 (no discounting).
- Year 1 PV: 32,600 / (1.092) = 32,600 × 0.9157509 ≈ 29,853.48
- Year 2 PV: 35,900 / (1.092^2). 1.092^2 = 1.192464 → reciprocal ≈ 0.838493 → PV ≈ 35,900 × 0.838493 ≈ 30,101.60
- Year 3 PV: 43,400 / (1.092^3). 1.092^3 ≈ 1.301855 → reciprocal ≈ 0.767845 → PV ≈ 43,400 × 0.767845 ≈ 33,325.09
- Sum of discounted inflows ≈ 29,853.48 + 30,101.60 + 33,325.09 = 93,280.17
- NPV_A = 93,280.17 − 87,000 = 6,280.17 (positive)

Project B (r = 12.7%):
- Year 0: CF0 = −85,000.
- Year 1 PV: 14,700 / 1.127 ≈ 14,700 × 0.887210 ≈ 13,041.79
- Year 2 PV: 21,200 / (1.127^2). 1.127^2 = 1.270129 → reciprocal ≈ 0.787651 → PV ≈ 21,200 × 0.787651 ≈ 16,697.95
- Year 3 PV: 89,800 / (1.127^3). 1.127^3 ≈ 1.431435 → reciprocal ≈ 0.698793 → PV ≈ 89,800 × 0.698793 ≈ 62,751.60
- Sum of discounted inflows ≈ 13,041.79 + 16,697.95 + 62,751.60 = 92,491.34
- NPV_B = 92,491.34 − 85,000 = 7,491.34 (positive)

3) Why the correct answer is correct
Both NPVs are positive, so each project individually adds value. Because the projects are mutually exclusive you must choose the one with the higher NPV. NPV_B (≈ $7,491) > NPV_A (≈ $6,280), so Project B is the better choice.

4) Why other options are incorrect
- A (Accept A, reject B): Incorrect because B has a larger NPV.
- C (Accept both): Incorrect because projects are mutually exclusive; you cannot accept both.
- D (Reject both): Incorrect because both NPVs are positive, so both add value individually.