Question

You are asked to choose between two mutually exclusive projects. The market rate of return is 14%. For both projects cash streams begin today (period zero) if you undertake them. For the first project the cash stream is (for years 0 through 3 ): −$750,$310,$430,$330 For the second project, cash stream is: −$2100,$1200,$760,$850

a) If these are independent projects and you do not have a budget constraint, which project(s) would you accept using Profitability Index criteria?
b) If projects are mutually exclusive, which project would you pick if any, using the Profitability Index criteria?
c) Now, assume that there is a third project: C. You do not know the cash flow of Project C. However, you know that the PI of the incremental cash flow of C over A is 0.76 . If you had to choose between project A and C, which one would you choose? Also, can you tell, for sure, that Project C, by itself, better or worse than the market?

Answer 1

a) If both projects are accepted, b) in the case of mutually exclusive projects, the second project would be chosen. c) We would choose project C over A based on the PI of the incremental cash flow.

Step-by-step explanation:

a) To determine the Profitability Index (PI) for each project, we divide the present value of the expected cash flows by the initial investment. For the first project, the present value of cash flows is $310 + $430 + $330 = $1,070 and the initial investment is -$750. Therefore, the PI for the first project is 1,070 / 750 = 1.43. For the second project, the present value of cash flows is $1,200 + $760 + $850 = $2,810 and the initial investment is -$2,100. Therefore, the PI for the second project is 2,810 / 2,100 = 1.34. Since both projects have a PI greater than 1, both projects would be accepted.

b) If the projects are mutually exclusive, meaning only one can be chosen, we would compare the PI values and choose the project with the higher PI. In this case, the second project has a higher PI of 1.34 compared to the first project's PI of 1.43. So, if projects are mutually exclusive, we would choose the second project.

c) To compare project A and project C, we need to determine the PI of the incremental cash flow of project C over A. Let's assume the incremental cash flow of C over A is X. The PI of X is given as 0.76. This means that X / initial investment of project A = 0.76. Since X is greater than 0, the incremental cash flow of project C over A is positive. Therefore, we would choose project C over A.

As for whether project C is better or worse than the market, the information provided does not allow us to determine that. We only know the PI of the incremental cash flow of C over A, not the individual PI of project C. Therefore, we cannot compare project C to the market without additional information.