Question

Your firm is subject to capital rationing and can only invest $60,000. You've estimated the following cash flows (in $) for two projects:

Year	Project A	Project B
0	-54,000	-54,000
1	10,000	30,000
2	20,000	20,000
3	30,000	10,000
4	40,000	0

The required return for both projects is 8%.

What is the payback period for project A?

What is the payback period for project B?

Which project seems better according to the payback method?

Project A or Project B

What is the NPV for project A?

What is the NPV for project B?

Which project seems better according to the NPV method?

Project A or Project B

Compare the answers to parts 3 and 6. If both projects are mutually exclusive, which one should you accept?

Project A or Project B

Answer 1

1) Payback period of Project A

Statement showing cummulative cash flow

Year	Cash flow	Cummulative cash flow
1	10000	10000
2	20000	30000
3	30000	60000
4	40000	100000

Using interpolation method we can find Payback period

Year	Cummulative cash flow
2	30000
3	60000
1	30000
?	24000

=24000/30000

=0.8

Thus payback period = 2+0.8 = 2.8 years

2) Payback period of Project B

Statement showing cummulative cash flow

Year	Cash flow	Cummulative cash flow
1	30000	30000
2	20000	50000
3	10000	60000

Using interpolation method we can find Payback period

Year	Cummulative cash flow
2	50000
3	60000
1	10000
?	4000

=4000/10000

=0.4

Thus payback period = 2+0.4 = 2.4 years

3) According to payback method , project B should be selected as it has lower payback period

4) Statement shoiwng NPV of project A

Year	Cash flow	PVIF @ 8%	PV
	A	B	C = A x B
1	10000	0.9259	9259
2	20000	0.8573	17147
3	30000	0.7938	23815
4	40000	0.7350	29401
Sum of PV of cash inflow	79622
Less: Initial Investment	54000
NPV	25622

Thus NPV of project A = $25622

5) Statement showing NPV of project B

Year	Cash flow	PVIF @ 8%	PV
	A	B	C = A x B
1	30000	0.9259	27778
2	20000	0.8573	17147
3	10000	0.7938	7938
4	0	0.7350	0
Sum of PV of cash inflow	52863
Less: Initial Investment	54000
NPV	-1137

Thus NPV of project B = -1137 $

6) Since NPV of project A is positive, Project A should be selected. Project B should not be selected as it's NPV is negative

7) As per payback method project B should be selected and as per NPV method project A should be selected

There are certian disadvantages of payback period

1) It ignores time value of money

2) It does not consider size of cash flow as well as timming of cash flow

Here project A should be selected since it has positive NPV , as NPV method consider both above points