The problem asks us to calculate the Net Present Value (NPV) and Profitability Index (PI) for two projects, Project A and Project B, given their cash flows over 4 years and a firm cost of capital of 9%.

1. Problem Description

The problem asks us to calculate the Net Present Value (NPV) and Profitability Index (PI) for two projects, Project A and Project B, given their cash flows over 4 years and a firm cost of capital of 9%.

2. Solution Steps

First, we calculate the NPV for each project. The formula for NPV is:

$NPV = \sum_{t=0}^{n} \frac{CF_t}{(1+r)^t}$

where $CF_t$ is the cash flow at time t, r is the discount rate (cost of capital), and n is the number of periods.

For Project A:

$NPV_A = \frac{-21000}{(1+0.09)^0} + \frac{8000}{(1+0.09)^1} + \frac{8000}{(1+0.09)^2} + \frac{8000}{(1+0.09)^3} + \frac{8000}{(1+0.09)^4}$

$NPV_A = -21000 + \frac{8000}{1.09} + \frac{8000}{1.09^2} + \frac{8000}{1.09^3} + \frac{8000}{1.09^4}$

$NPV_A = -21000 + 7339.45 + 6733.44 + 6177.47 + 5667.39$

$NPV_A = -21000 + 25917.75$

$NPV_A = 4917.75$

For Project B:

$NPV_B = \frac{-26000}{(1+0.09)^0} + \frac{9000}{(1+0.09)^1} + \frac{9000}{(1+0.09)^2} + \frac{9000}{(1+0.09)^3} + \frac{9000}{(1+0.09)^4}$

$NPV_B = -26000 + \frac{9000}{1.09} + \frac{9000}{1.09^2} + \frac{9000}{1.09^3} + \frac{9000}{1.09^4}$

$NPV_B = -26000 + 8256.88 + 7575.12 + 6949.65 + 6375.83$

$NPV_B = -26000 + 29157.48$

$NPV_B = 3157.48$

Next, we calculate the Profitability Index (PI) for each project. The formula for PI is:

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

For Project A:

$PI_A = \frac{4917.75 + 21000}{21000} = \frac{25917.75}{21000} = 1.23417857$

For Project B:

$PI_B = \frac{3157.48 + 26000}{26000} = \frac{29157.48}{26000} = 1.12144154$

3. Final Answer

NPV of Project A: 4917.75

NPV of Project B: 3157.48

Profitability Index of Project A: 1.234

Profitability Index of Project B: 1.121