Question

11. 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:

Purple Whale Foodstuffs is considering investing $2,750,000 in a project that is expected to generate the following net cash flows:

Year	Cash Flow
Year 1	$350,000
Year 2	$500,000
Year 3	$425,000
Year 4	$400,000

Purple Whale Foodstuffs uses a WACC of 10% when evaluating proposed capital budgeting projects. Based on these cash flows, determine this project’s PI---------- (rounded to four decimal places):

A. 0.5055

B. 0.4573

C. 0.4814

D. 0.5536

Purple Whale Foodstuffs’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_________ the project.(Accept/reject)

By comparison, the NPV of this project is _________ . On the basis of this evaluation criterion, Purple Whale Foodstuffs should_________(invest/not invest) in the project because the project___________(will/will not) increase the firm’s value.

A project with a negative NPV will have a PI that is__________(=0/<0/>0); when it has a PI of 1.0, it will have an NPV ____________(=$0/<$0/>$0) .

Answer 1

Profitability index = Present Value of Future cash flow/ Initial investment

                                =1323919.13/2750000

   = 0.4814

PI of the project is 0.4814

Year	Cash Flow	PV factor @10% (1/(1+r)^n)	Present Value of Future cash flow
1	350000	0.90909091	318181.82
2	500000	0.82644628	413223.14
3	425000	0.7513148	319308.79
4	400000	0.68301346	273205.38
Present Value of Cash Outflow	1323919.13
Present Value of Cash Inflow	2750000
Net Present Value	-1426080.87
Profitability Index	0.4814

                               

Purple Whale Foodstuffs’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________ the project.(Accept/reject)

By comparison, the NPV of this project is _-1426080.87________ . On the basis of this evaluation criterion, Purple Whale Foodstuffs should not invest in the project because the project will not increase the firm’s value.

A project with a negative NPV will have a PI that is__less than 1__(>0)______(=0/<0/>0); when it has a PI of 1.0, it will have an NPV ___>$0_________(=$0/<$0/>$0)