Question

You are considering a project with an initial cash outlay of $80,000 and expected free cash flows of $20,000 at the end of each year for 6 years. The required rate of return for this project is 10 percent. a. What is the project’s payback period? b. What is the project’s NPV? c. What is the project’s PI? d. What is the project’s IRR? e. Indicate if the project should be accepted and why

Answer 1

Payback:

Payback period = Initial investment / cash flows

Payback period = 80,000 / 20,000

Payback period = 4 years

NPV:

NPV = Present value of cash inflows - present value of cash outflows

NPV = Annuity * [1 - 1 / (1 + r)ⁿ] / r - Initial investment

NPV = 20,000 * [1 - 1 / (1 + 0.1)⁶] / 0.1 - 80,000

NPV = 20,000 * [1 - 0.564474] / 0.1 - 80,000

NPV = 20,000 * 4.355261 - 80,000

NPV = $7,105.21

PI:

PI = Present value of cash flows / initial investment

Present value of cash flows = Annuity * [1 - 1 / (1 + r)ⁿ] / r

Present value of cash flows = 20,000 * [1 - 1 / (1 + 0.1)⁶] / 0.1

Present value of cash flows = 20,000 * [1 - 0.564474] / 0.1

Present value of cash flows = 20,000 * 4.355261

Present value of cash flows = 87,105.22

PI = 87,105.22 / 80,000

PI = 1.09

IRR:

IRR is the rate of return that makes NPV equal to 0

NPV = 20,000 * [1 - 1 / (1 + R)⁶] / R - 80,000

Using trial and error method, i.e., after trying various values for R, lets try R as 12.98%

NPV = 20,000 * [1 - 1 / (1 + 0.1298)⁶] / 0.1298 - 80,000

NPV = 20,000 * 3.999777 - 80,000

NPV = 0

Therefore, IRR is 12.98%

Projects having positive NPV, IRR greater required rate of return and PI more than 1 should be accepted. Since the projects meet these conditions, project should be accepted.