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?

Multiple Choice

• Accept both projects

• Accept either one, but not both

• Accept Project A and reject Project B

• Reject both projects

• Reject Project A and accept Project B

  Correct

Explanation

NPV_A = −$87,000 + $32,600/1.092 + $35,900/1.092² + $43,400/1.092³
NPV_A = $6,288.17

NPV_B = −$85,000 + $14,700/1.127 + $21,200/1.127² + $89,800/1.127³
NPV_B = $7,468.93

Since the projects are mutually exclusive, accept the project with the larger positive NPV.

Answer 1

Net Present Value (NPV) of PROJECT-A

Year	Annual cash inflow ($)	Present Value factor at 9.20%	Present Value of Annual cash inflow ($)
1	32,600	0.915751	29,853.48
2	35,900	0.838600	30,105.73
3	43,400	0.767948	33,328.96
TOTAL			93,288.17

Net Present Value = Present Value of annual cash inflows - Initial Investment

= $93,288.17 - $87,000

= $6,288.17

Net Present Value (NPV) of PROJECT-B

Year	Annual cash inflow ($)	Present Value factor at 12.70%	Present Value of Annual cash inflow ($)
1	14,700	0.887311	13,043.48
2	21,200	0.787322	16,691.22
3	89,800	0.698599	62,734.23
TOTAL			92,468.93

Net Present Value = Present Value of annual cash inflows - Initial Investment

= $92,468.93 - $85,000

= $7,468.93

DECISION

Evaluation of Investment proposal using NPV Decision Rule

If the Projects are mutually exclusive, then the Project with the higher Net Present Value should be selected. Here, the Project-B has the higher NPV of $7,468.93 as compared to the NPV of Project-A. Therefore, the firm should “Reject Project A and accept Project B”.

NOTE

The formula for calculating the Present Value Inflow Factor (PVIF) is [1 / (1 + r)ⁿ], where “r” is the Discount Rate/Cost of capital and “n” is the number of years.