Question

​Payback, NPV, and IRR: Rieger International is evaluating the feasibility of investing

​$96,000 in a piece of equipment that has a 5​-year life. The firm has estimated the cash inflows associated with the proposal as shown in the following​ table: The firm has a 8% cost of capital.

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?

year cash inflows

1 35,000
2 30,000
3 30,000
4 35,000
5 30,000

Answer 1

A) Payback period is the period in which we get back the invested amount

1st year = 35,000 (Cumulative = 35,000)

2nd year = 30,000 (Cumulative = 65,000)

3rd year = 30,000 (Cumulative = 95,000)

4th year = 35,000 {35,000 : 1 year :: 1,000 : (1/35)} = 0.0285

Payback period = 3.0285 Years

B) NPV = Present value of cash inflows - Present value of cash outflow

= {(35,000/(1+8%)1) + (30,000/(1+8%)2) + ..... + (30,000/(1+8%)5)} - 96,000

= $128,086 - $96,000 = $32,086

C) IRR gives the internal rate of return by equating:

Present value of cash inflow = Present value of cash outflow {and replacing rate of return (8%) by IRR}

96,000 = 35,000/(1+IRR)1 + 30,000/(1+IRR)2 + ... + 30,000/(1+IRR)5

Solving this, we get IRR = 20%

D) As the project has positive NPV and IRR (20%) greater than cost of capital (8%), the project should be accepted.