The problem provides the initial investments and cash flows for two mutually exclusive projects, Project A and Project B. We are given the firm's cost of capital as 0.1. We are asked to calculate the profitability index for both projects.

1. Problem Description

The problem provides the initial investments and cash flows for two mutually exclusive projects, Project A and Project B. We are given the firm's cost of capital as 0.

1. We are asked to calculate the profitability index for both projects.

2. Solution Steps

The profitability index (PI) is calculated as the present value of future cash flows divided by the initial investment.

Formula:

$PI = \frac{PV \text{ of future cash flows}}{\text{Initial Investment}}$

First, we need to calculate the present value (PV) of the future cash flows for each project using the given cost of capital (discount rate) of 10% or 0.

1.

For Project A:

Year 1: $8000 / (1 + 0.1)^1 = 8000 / 1.1 = 7272.73$

Year 2: $8000 / (1 + 0.1)^2 = 8000 / 1.21 = 6611.57$

Year 3: $8000 / (1 + 0.1)^3 = 8000 / 1.331 = 6010.52$

Year 4: $8000 / (1 + 0.1)^4 = 8000 / 1.4641 = 5464.11$

Total PV of future cash flows for Project A = $7272.73 + 6611.57 + 6010.52 + 5464.11 = 25358.93$

PI for Project A = $25358.93 / 22000 = 1.152678636 \approx 1.15$

For Project B:

Year 1: $9000 / (1 + 0.1)^1 = 9000 / 1.1 = 8181.82$

Year 2: $9000 / (1 + 0.1)^2 = 9000 / 1.21 = 7438.02$

Year 3: $9000 / (1 + 0.1)^3 = 9000 / 1.331 = 6761.83$

Year 4: $9000 / (1 + 0.1)^4 = 9000 / 1.4641 = 6147.12$

Total PV of future cash flows for Project B = $8181.82 + 7438.02 + 6761.83 + 6147.12 = 28528.79$

PI for Project B = $28528.79 / 28000 = 1.018885357 \approx 1.02$

3. Final Answer

Profitability Index of Project A: 1.15

Profitability Index of Project B: 1.02