Question

​(Payback period, 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 5 years. The required rate of return for this project is 8 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)

Year	Cash flow stream	Cumulative cash flow
0	-70000	-70000
1	28000	-42000
2	28000	-14000
3	28000	14000
4	28000	42000
5	28000	70000

Payback period is the time by which undiscounted cashflow cover the intial investment outlay

this is happening between year 2 and 3

therefore by interpolation payback period = 2 + (0-(-14000))/(14000-(-14000))

2.5 Years

b

Project
Discount rate	8.000%
Year	0	1	2	3	4
Cash flow stream	-70000	28000	28000	28000	28000
Discounting factor	1.000	1.080	1.166	1.260	1.360
Discounted cash flows project	-70000.000	25925.926	24005.487	22227.303	20580.836
NPV = Sum of discounted cash flows
NPV Project =	41795.88
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor

c

PI= (NPV+initial inv.)/initial inv.

=(41795.88+70000)/70000

1.6

d

Project
IRR is the rate at which NPV =0
IRR	28.65%
Year	0	1	2	3	4	5
Cash flow stream	-70000.000	28000.000	28000.000	28000.000	28000.000	28000.000
Discounting factor	1.000	1.286	1.655	2.129	2.739	3.524
Discounted cash flows project	-70000.000	21764.597	16917.775	13150.306	10221.825	7945.497
NPV = Sum of discounted cash flows
NPV Project =	0.000
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor