Question

A firm is considering two mutually exclusive investment alternatives, both of which cost $5,000. The firm's expected rate of return is 12 percent. The cash flows associated with each investment are:

Year	Investment A	Investment B
1	$ 2000	$ 1000
2	$1500	$ 1500
3	$1500	$ 2000
4	$1000	$3000

For each alternative calculate the payback period, the net present value, and the profitably index. Which alternative (if any) should be selected?

Answer 1

To find payback period

Year	Investment A	Cumulative Cash flows
0	-5000
1	2000	2000
2	1500	3500
3	1500	5000
4	1000	6000

Payback period = 3 years

Year	Investment B	Cumulative Cash flows
0	-5000
1	1000	1000
2	1500	2500
3	2000	4500
4	3000	7500

Payback period = 3 + [ 5000 - 4500 ]   3000

Payback period = 3.17years

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Net present value of investment A = - $ 5000 + $ 2000 1.12¹ + $ 1500 1.12² + $ 1500 1.12³ + $ 10001.12⁴

Net present value of investment A = - $ 315.31

Net present value of investment B = - $ 5000 + $ 1000 1.12¹ + $ 1500 1.12² + $ 2000 1.12³ + $ 30001.12⁴

Net present value of investment B = $481.76

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Profitability index of investment A = Present value of benefits Present value of costs

Profitability index of investment A = $4684.69 $5000

Profitability index of investment A = 0.9367

Profitability index of investment B = $ 5418.76 $ 5000

Profitability index of investment B = 1.08375

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Investment 2 should be selected because it has a positive net present value and a profitability index of greater than 1