Question

The profitability index (PI)is a capital budgeting tool that provides another way to compare a project’s benefits and costs. It is computed as a ratio of the discounted value of the net cash flows expected to be generated by a project over its life (the project’s expected benefits) to its net cost (NINV). A project’s PI value can be interpreted to indicate a project’s discounted return generated by each dollar of net investment required to generate those returns.

Consider the case of Purple Whale Foodstuffs:

Purple Whale Foodstuffs is considering investing $400,000 in a project that is expected to generate the following net cash flows:

Year	Cash Flow
Year 1	$275,000
Year 2	$475,000
Year 3	$475,000
Year 4	$475,000

Purple Whaleuses a WACC of 7% when evaluating proposed capital budgeting projects. Based on these cash flows, determine this project’s PI (rounded to four decimal places):

3.5550

3.0218

3.9105

3.7328

Purple Whale’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 (REJECT OR ACCEPT)  the project.

By comparison, the net present value (NPV) of this project is___________. On the basis of this evaluation criterion, Purple Whale should (NOT INVEST OR INVEST) in the project because the project (WILL OR WILL NOT) increase the firm’s value.

When a project has a PI greater than 1.00, it will exhibit an NPV( GREATER THAN O, EQUAL TO 0, OR LESS THAN 0); when it has a PI of 1.00, it will have an NPV equal to $0. Projects with PIs (LESS THAN, GREATER THAN, EQUAL TO)1.00 will exhibit negative NPVs.

Answer 1

- Calculating the Net Present Value(NPV) of the project:-

Year	Cash Flow of Project ($)	PV Factor @7%	Present Value of Project ($)
0	(400,000.00)	1.00000	(400,000.000)
1	275,000.00	0.93458	257,009.346
2	475,000.00	0.87344	414,883.396
3	475,000.00	0.81630	387,741.492
4	475,000.00	0.76290	362,375.226
		NPV	1,022,009.46

Profitability Index(PI) = 1+(NPV/Initial Investment)

PI = 1+ ($1022,009.46/$400,000)

PI = 3.5550

So, this project’s PI is 3.5550

Option 1

- The net present value (NPV) of this project is $1022,009.46

- On the basis of this evaluation criterion, Purple Whale should (INVEST) in the project because the project (WILL ) increase the firm’s value.

When a project has a PI greater than 1.00, it will exhibit an NPV( GREATER THAN O); when it has a PI of 1.00, it will have an NPV equal to $0. Projects with PIs (LESS THAN)1.00 will exhibit negative NPVs.

Note- PV Factor@7% can be taken from PVAF Table or calculated using this formula which is = 1/(1+0.07)^n

where, n = Respective year.

For example, PV Factor@7% of 2nd year = 1/(1+0.07)^2 = 1/1.1449 = 0.87344

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