Question

Project A has cash flows of −$92,000, $49,400, $27,200, $24,500, and $30,690 for Years 0 to 4, respectively. Project B has an initial cost of $50,000 and an annual cash inflow of $20,500 for four years. The required rate of return is 18 percent. These are mutually exclusive projects. Which project(s) should be accepted or rejected?

Answer 1

Mutually exclusive projects are a set of projects out of which only one project can be selected.
We need to calculate the NPV for both the projects and the project with higher NPV should be selected.

NPV=-Initial cost + Present value of future cash flows

Project A:

Present value of future cash flows when the required return is 18% is calculated as:
Present value=49400/(1+18%)^1+27200/(1+18%)^2+24500/(1+18%)^3+30690/(1+18%)^4
=49400/1.18+27200/1.3924+24500/1.643032+30690/1.93877776
=41864.40678+19534.61649+14911.45638+15829.56058
=92140.04
NPV=-92000+92140.04
=$140.04

Project B:

Present value of future cash flows when the required return is 18% is calculated as:
Present value=20500/(1+18%)^1+20500/(1+18%)^2+20500/(1+18%)^3+20500/(1+18%)^4
=20500/1.18+20500/1.3924+20500/1.643032+20500/1.93877776
=17372.88136+14722.78081+12476.93289+10573.67194
=55146.267
NPV=-50000+55146.267=5146.267

Now, as the NPV of project B is greater than project A, project B should be accepted.