Question

An investor is considering a capital expenditure for new production facilities. The relevant cash flows are listed below:

Initial Investment = $185,000

​

Year Cashflow

1 $75,000

2 63,000

3 69,000

4 82,000

​a. ​Calculate the firm’s net present value and profitability index. Assume a cost of capital of 12%.

b.​ Calculate the project's internal rate of return (interpolate your results to two decimal points). Is this an acceptable project? Why or why not?

Answer 1

Net Present Value(NPV) is the difference between the present value of cash inflows and the present value of cash outflows. It is used in evaluating capital budgeting decisions. Projects with NPV greater than 0 are investable.

The profitability index(PI) describes an index that represents the relationship between cost and benefit of a project.

PI = Present value of future cash flows / Initial investment

We accept the project if PI > 1.

The Internal rate of return(IRR) is a measure of an investment’s expected future rate of return. If IRR > cost of capital, we accept the project. IRR is the rate at which NPV is equal to 0.

We can calculate NPV and IRR in excel,

Year	Cash Flows	PV @ 12%(Discounting factor)	Discounted cash flows
0	-185000	1.000	-185000
1	75000	0.893	66964
2	63000	0.797	50223
3	69000	0.712	49113
4	82000	0.636	52112
		NPV	33,412.82
		Present value of future cash flows	218,412.82
		IRR	20.20%

PI = Present value of future cash flows / Initial investment

PI = 218,412.82 / 185,000 = 1.18

a) Hence firms NPV is $33,412.82 and PI is 1.18. As NPV > 0 and PI > 1, the project is investable.

b) The IRR is 20.20%. As it is greater than cost of capital(12%), we accept the project.

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