Question

NPV,​ PI, and IRR calculations​) You are considering a project with an initial cash outlay of ​$70,000 and expected free cash flows of ​$28,000 at the end of each year for 6 years. The required rate of return for this project is 7 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

Initial Outlay = $70,000
Annual FCF = $28,000
Period = 6 years
Required Return = 7%

Answer a.

Payback Period = Initial Outlay / Annual FCF
Payback Period = $70,000 / $28,000
Payback Period = 2.50 years

Answer b.

Present Value of Cash Flows = $28,000/1.07 + $28,000/1.07^2 + ... + $28,000/1.07^5 + $28,000/1.07^6
Present Value of Cash Flows = $28,000 * (1 - (1/1.07)^6) / 0.07
Present Value of Cash Flows = $28,000 * 4.76654
Present Value of Cash Flows = $133,463.12

Net Present Value = Present Value of Cash Flows - Initial Outlay
Net Present Value = $133,463.12 - $70,000.00
Net Present Value = $63,463.12

Answer c.

Profitability Index = Present Value of Cash Flows / Initial Outlay
Profitability Index = $133,463.12 / $70,000.00
Profitability Index = 1.91

Answer d.

Let IRR be i%

NPV = -$70,000 + $28,000/(1+i) + $28,000/(1+i)^2 + ... + $28,000/(1+i)^6
0 = -$70,000 + $28,000/(1+i) + $28,000/(1+i)^2 + ... + $28,000/(1+i)^6

Using financial calculator, i = 32.66%

IRR = 32.66%