A retail company is considering two mutually exclusive expansion strategies. The company's cost of capital is 9%. We are given the cash flows for Project A and Project B over 5 years. We need to calculate the payback period, net present value (NPV), and profitability index (PI) for both projects.

1. Problem Description

A retail company is considering two mutually exclusive expansion strategies. The company's cost of capital is 9%. We are given the cash flows for Project A and Project B over 5 years. We need to calculate the payback period, net present value (NPV), and profitability index (PI) for both projects.

2. Solution Steps

First, let's calculate the payback period for Project A.

The initial investment is $1,350,

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0. Year 1: $323,000 received. Cumulative: -$1,350,000 + $323,000 = -$1,027,000

Year 2: $323,000 received. Cumulative: -$1,027,000 + $323,000 = -$704,000

Year 3: $323,000 received. Cumulative: -$704,000 + $323,000 = -$381,000

Year 4: $323,000 received. Cumulative: -$381,000 + $323,000 = -$58,000

Year 5: $323,000 received. Cumulative: -$58,000 + $323,000 =$265,000

The payback period is between 4 and 5 years. To find the exact payback period, we calculate the fraction of the year needed to recover the remaining $58,

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0. Payback period = 4 + ($58,000 / $323,000) = 4 + 0.179566 = 4.179566

Now, let's calculate the payback period for Project B.

The initial investment is $1,480,

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0. Year 1: $427,000 received. Cumulative: -$1,480,000 + $427,000 = -$1,053,000

Year 2: $427,000 received. Cumulative: -$1,053,000 + $427,000 = -$626,000

Year 3: $427,000 received. Cumulative: -$626,000 + $427,000 = -$199,000

Year 4: $427,000 received. Cumulative: -$199,000 + $427,000 =$228,000

The payback period is between 3 and 4 years. To find the exact payback period, we calculate the fraction of the year needed to recover the remaining $199,

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0. Payback period = 3 + ($199,000 / $427,000) = 3 + 0.466042 = 3.466042

Next, we will compute the Net Present Value (NPV) for Project A and B.

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:

$NPV_A = -\frac{1350000}{(1.09)^0} + \frac{323000}{(1.09)^1} + \frac{323000}{(1.09)^2} + \frac{323000}{(1.09)^3} + \frac{323000}{(1.09)^4} + \frac{323000}{(1.09)^5}$

$NPV_A = -1350000 + 296330.275 + 271862.637 + 249415.263 + 228821.342 + 209927.836 = -93592.647$

For Project B:

$NPV_B = -\frac{1480000}{(1.09)^0} + \frac{427000}{(1.09)^1} + \frac{427000}{(1.09)^2} + \frac{427000}{(1.09)^3} + \frac{427000}{(1.09)^4} + \frac{427000}{(1.09)^5}$

$NPV_B = -1480000 + 391743.119 + 359397.357 + 329722.346 + 302500.317 + 277523.227 = 180886.366$

Finally, let's calculate the Profitability Index (PI) for Project A and B.

The formula for PI is:

$PI = \frac{Present \ Value \ of \ Future \ Cash \ Flows}{Initial \ Investment}$

For Project A:

$PI_A = \frac{1356407.353}{1350000} = 0.99734$ (sum of present values of future cashflows = 1350000+ NPV_A)

For Project B:

$PI_B = \frac{1660886.366}{1480000} = 1.12222$ (sum of present values of future cashflows = 1480000+ NPV_B)

3. Final Answer

Payback period of project A: 4.18 years

Payback period of project B: 3.47 years

Net present value of project A: -$93,592.65

Net present value of project B: $180,886.37

Profitability index of project A: 0.997

Profitability index of project B: 1.122