Question

Consider the following projects: Cash Flows ($) Project C0 C1 D –10,900 21,800 E –20,900 36,575 Assume that the projects are mutually exclusive and that the opportunity cost of capital is 8%. a. Calculate the profitability index for each project. (Do not round intermediate calculations. Round your answers to 2 decimal places.) Project Profitability Index D E b-1. Calculate the profitability-index using the incremental cash flows. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Profitability-index b-2. Which project should you choose? Project D Project E

Answer 1

The profitability index of Project D is 1.85 and of Project E is 1.62. Using incremental cash flows, the profitability-index is 1.37, indicating that Project D is the better choice.

Step-by-step explanation:

To calculate the profitability index for each project, we can use the formula: Profitability Index (PI) = (Present Value of Future Cash Flows) / (Initial Investment).

Given an opportunity cost of capital of 8%, we first calculate the present value of future cash flows for projects D and E. We can do this using the formula PV = C1 / (1 + r), where C1 is the cash flow in period 1, and r is the rate.

For Project D:

PV = 21,800 / (1 + 0.08) = 21,800 / 1.08 = $20,185.19

PI = 20,185.19 / 10,900 = 1.85

For Project E:

PV = 36,575 / (1 + 0.08) = 36,575 / 1.08 = $33,873.15

PI = 33,873.15 / 20,900 = 1.62

To calculate the profitability-index using the incremental cash flows, we need to find the difference in cash flows between Project E and Project D:

Incremental Cash Flow (C1) = 36,575 - 21,800 = 14,775

Incremental Investment (C0) = 20,900 - 10,900 = 10,000

PV of Incremental Cash Flow = 14,775 / 1.08 = $13,676.85

Incremental PI = 13,676.85 / 10,000 = 1.37

Based on the incremental profitability index, we should choose Project D, as its PI is higher than Project E's PI when we compare the incremental investment and cash flows.