Question

You are analyzing two proposed capital investments with the following cash flows:

Year	Project X	Project Y
0	-$20,000	-$20,000
1	13,630	7,720
2	5,860	7,720
3	6,160	7,720

4

2,020

7,720

The cost of capital for both projects is 10 percent.

Calculate the profitability index (PI) for each project. (Do not round discount factors. Round intermediate calculations to 2 decimal places, e.g. 15.25 and final answer to 4 decimal places, e.g. 1.2527.)

1) What is the PI for project X?
2) What is the PI for project Y?

3) If you have unlimited funds you should invest in..?

a) neither project

b) Project Y

c) Project X

d) Both projects

4) If they are mutually exclusive you should invest in...?

a) neither project

b) Project Y

c) Project X

Answer 1

Answer 1 and 2
Calculation of P.V. of cash outflows
	Project X			Project Y
	Cash outflow	P.V.F. @10%	P.V.of cash flows	Cash outflow	P.V.F.	P.V.of cash flows
Year 0	20000	1	20000	20000	1	20000
P.V. of cash outflows			20000			20000
Calculation of P.V. of cash inflows
Year 1	13630	0.9090909091	12390.90909	7720	0.9090909091	7018.181818
Year 1	5860	0.826446281	4842.975207	7720	0.826446281	6380.165289
Year 3	6160	0.7513148009	4628.099174	7720	0.7513148009	5800.150263
Year 4	2020	0.6830134554	1379.68718	7720	0.6830134554	5272.863875
P.V. of cash inflows			23241.67065			24471.36125

Profitability Index = P.V. of cash inflows / P.V. of cash inflows
P.I. of Project X = 23242.67065/20000=		1.162083533
P.I. of project Y = 24471.36125/20000=		1.223568062
So, PI of project X us 1.1621
PI of project Y is 1.2236
Answer 3
To choose an project on basis of PI, PI must be equal to or greater than 1.
As both projects are having PI more than 1. So both Poject X and Project Y should be chosen, as unlimited funds are available
So, answer is (d) both projects
Answer 4
If projects are mutually exclusive, projects having highest PI should be chosen.
Project Y PI is more than Project X 1.2236. So project Y should be chosen.
Answer is (b) project Y.

P.V.F. formula = 1/(1+0.10)^n

n means year 1, 2, 3 and 4

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