Question

9. Profitability index Estimating the cash flow generated by $1 invested in a project The profitability index (PI) is a capital budgeting tool that is defined as the present value of a project’s cash inflows divided by the absolute value of its initial cash outflow. Consider this case: Happy Dog Soap Company is considering investing $2,750,000 in a project that is expected to generate the following net cash flows: Year Cash Flow Year 1 $275,000 Year 2 $500,000 Year 3 $475,000 Year 4 $475,000 Happy Dog Soap Company uses a WACC of 8% when evaluating proposed capital budgeting projects. Based on these cash flows, determine this project’s PI (rounded to four decimal places): 0.4869 0.5125 0.5638 0.4613 Happy Dog Soap Company’s decision to accept or reject this project is independent of its decisions on other projects. Based on the project’s PI, the firm should (ACCEPT or REJECT) the project? By comparison, the NPV of this project is (-$1,340,491, -$1,608,589, or -$1,072,343)?. On the basis of this evaluation criterion, Happy Dog Soap Company should INVEST or NOT INVEST in the project because the project WILL or WILL NOT increase the firm’s value.

Answer 1

Initial investment or Present value of Cash outflow=	2750000
Calculation of Present value of Cash inflows
Year	Cash flows	PVF@8%	PV = CF*PVF
1	275,000	0.9259259259	$254,629.63
2	500,000	0.8573388203	$428,669.41
3	475,000	0.793832241	$377,070.31
4	475,000	0.7350298528	$349,139.18
PV of cash inflows			$1,409,508.53

Profitability Index = PV of cash inflows/PV of cash outflow

1409508.53/2750000

0.5125

So PI of project is 0.5125

Project is Mutual exclusive. But Pi is less than 1(i.e. 0.5125) Any project having PI below 1 will not be accepted. As this would be having negative NPV and ultimatly firm value will decrease

NPV =PV of cash inflows - PV of cash outflow

1409508.53-2750000

-$1,340,491.47

NPV is -$1,340,491.47.

So Happy Dog Soap Company should NOT INVEST in the project because the project WILL NOT increase the firm’s value.

Note :PVF formula =( 1/(1+i)^n)

for year 1 = 1/(1+8%)^1

for year 2 = 1/(1+8%)^2 and so on.

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