Question

(Payback ​period, NPV,​ PI, and IRR calculations​) You are considering a project with an initial cash outlay of ​$80000 and expected free cash flows of ​$25000 at the end of each year for 6 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

Initial Cash Outlay= $80,000
Cash Flows after Tax(Free Cash flows)= $25,000
Period= 6Years
Required rate of return= 9%

a. Payback period
= Initial Investment / Net Annual Cash Inflow
=$80000/$25000
=3.20 Years

b. NPV
= Present Values of future cash inflows-Present value of cash outflows
The present value of future cash inflows
Annual cash inflow*PVAF(9%,6years)
$25,000*4.486
$112,150
=$112,150-$80,000
=$32,150

c. Profitability index
=Presnet value of cash inflows / Initial Investment
=$112,150/$80,000
=1.40

d. IRR
LR+(NPV at LR)/(NPV at LR-NPV at HR)*(HR-LR)
LR= Lower Rate
HR= Higher Rate

NPV at 10% rate (LR)
= Present Values of future cash inflows-Present value of cash outflows
The present value of future cash inflows
Annual cash inflow*PVAF(10%,6years)
$25,000*4.356
$108,900
=$108,900-$80,000
= $28,900

NPV at 25% rate (HR)
Present Values of future cash inflows-Present value of cash outflows
The present value of future cash inflows
Annual cash inflow*PVAF(25%,6years)
$25,000*2.951
$73,775
=$73,775-$80,000
=($6,225)

10%+($28,900)/($28,900+6225)*(25-15)
10%+12.34%
22.34%