Question

​Payback, NPV, and IRR   Rieger International is attempting to evaluate the feasibility of investing ​$102,000 in a piece of equipment that has a 55​-year life. The firm has estimated the cash inflows associated with the proposal as shown in the following​ table The firm has a 11​% cost of capital.

Year (t) Cash inflows (CF)

1 $30k

2 $25k

3 $40k

4 $35k

5 $20k

a.  Calculate the payback period for the proposed investment.

b.  Calculate the net present value​ (NPV) for the proposed investment.

c.  Calculate the internal rate of return ​(IRR)​, rounded to the nearest whole​ percent, for the proposed investment.

d.  Evaluate the acceptability of the proposed investment using NPV and IRR. What recommendation would you make relative to implementation of the​ project?

Answer 1

(a) Payback period

Years	CF	Cummulative CF
0	-102000	-102000
1	30000	-72000
2	25000	-47000
3	40000	-7000
4	35000	28000
5	20000	48000

Payback period = 3 years + 7000 / 35000 = 3.2 Years

(b) Calculation of NPV

Years	CF	DF	PV
0	-102000	1	-102000
1	30000	0.900901	27027.03
2	25000	0.811622	20290.56
3	40000	0.731191	29247.66
4	35000	0.658731	23055.58
5	20000	0.593451	11869.03
		NPV	9489.85

(c) Calculation of IRR

When we try with a discount rate of 15%

Years	CF	DF	PV
0	-102000	1	-102000
1	30000	0.869565	26086.96
2	25000	0.756144	18903.59
3	40000	0.657516	26300.65
4	35000	0.571753	20011.36
5	20000	0.497177	9943.535
		NPV	-753.904

When we try at 14% discount rate

Years	CF	DF	PV
0	-102000	1	-102000
1	30000	0.877193	26315.79
2	25000	0.769468	19236.69
3	40000	0.674972	26998.86
4	35000	0.59208	20722.81
5	20000	0.519369	10387.37
		NPV	1661.521

The nearest whole percent = 15% when NPV is nearest to zero.

Hence IRR = 15%

(d) NPV of the project is positive and IRR is more than the cost of capital. Thus the project if financially feasible. So we can recommend to ACCEPT the project.