Question

​(Payback ​period, NPV,​ PI, and IRR calculations​) You are considering a project with an initial cash outlay of ​$90,000 and expected free cash flows of ​$22,000 at the end of each year for 7 years. The required rate of return for this project is 9 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​?

Answer 1

(a)-Project's payback period

Project's payback period = Initial Investment cost / Annual cash inflow

= $90,000 / $22,000 per year

= 4.09 Years

(b)-Project's Net Present Value (NPV)

Year	Annual Cash Flow ($)	Present Value factor at 9%	Present Value of Cash Flow ($)
1	22,000	0.917431	20,183.49
2	22,000	0.841680	18,516.96
3	22,000	0.772183	16,988.04
4	22,000	0.708425	15,585.35
5	22,000	0.649931	14,298.49
6	22,000	0.596267	13,117.88
7	22,000	0.547034	12,034.75
TOTAL			110,724.96

Net Present Value = Present value of annual cash inflows – Initial investment cost

= $110,724.96 - $90,000

= $20,724.96

(c)-Project's Profitability Index (PI)

Project's Profitability Index (PI) = Present value of annual cash inflows / Initial investment cost

= $110,724.96 / $90,000

= 1.23

(d)-Project's Internal Rate of Return (IRR)

The Present Value factor for determining IRR = Net Initial Investment / Net Annual Cash Inflow

= $90,000 / $22,000

= 4.09091

From the Present Value Annuity Factor Table (PVAIF Table), the discount rate (IRR) corresponding to the factor of 4.09091 for 7 Years is 15.56%

“Hence, the Internal Rate of Return (IRR) for the Project will be 15.56%”

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.