Question

You are considering a project with an initial cash outlay of $85,000 and expected free cash flows of $20,000 at the end of each year for 5 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​?

a. The​ project's payback period is _____years.  ​(Round to two decimal​ places.)

b. The​ project's NPV is $______ .(Round to the nearest​ cent.)

c. The project's PI is ? ​(Round to three decimal​ places.)

d. The​ project's IRR is ______%.

​(Round to two decimal​ places.)

Answer 1

(a)-Project's payback period

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

= $85,000 / $20,000

= 4.25 Years

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

Year	Annual Cash Flow ($)	Present Value factor at 9%	Present Value of Cash Flow ($)
1	20,000	0.917431	18,348.62
2	20,000	0.841680	16,833.60
3	20,000	0.772183	15,443.67
4	20,000	0.708425	14,168.50
5	20,000	0.649931	12,998.63
TOTAL			77,793.03

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

= $77,793.03 - $85,000

= -$7,206.97

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

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

= $77,793.03 / $85,000

= 0.915

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

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

= $85,000 / $20,000

= 4.25000

From the Present Value Annuity Factor Table (PVAIF Table), the discount rate (IRR) corresponding to the factor of 4.25000 for 5 Years is 5.67%

“Hence, the Internal Rate of Return (IRR) for the Project will be 5.67%”

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.