# NPV and Profitability Index: Problem and Solution

ABC Corporation plans to invest in project C which have an initial investment of \$500,000. ABC’s cost of capital is 8%. The operating cash inflows to be generated from the project will be as follows:

End of 1st year: \$100,000

End of 2nd year: \$300,000

End of 3rd year: \$250,000

1. What is the profitability index for project C?

2. What is NPV for project C?

3. Taking NPV found in previous step into account, is project acceptable according to NPV technique?

4. Based on Profitability Index (PI), is project C is acceptable?

Solution:

1. First we need to find present values of mixed stream of operating cash inflows. We will use financial calculator to do so.

End of 1st year:

FV: \$100,000

N: 1

I: 10

Calculate PV: 90,909.09

End of 2nd year:

FV: \$300,000

N: 2

I: 10

Calculate PV: 247,933.88

End of 3rd year:

FV: \$250,000

N: 3

I: 10

Calculate PV: 187,828.7

Next we need to add up all present values from operating cash inflows to obtain total PV of operating cash inflows:

= 90,909.09 + 247,933.88 + 187,828.7

Total PV of operating cash inflows = 526,671.67

Next we will follow equation for Profitability Index (PI):

PI = Total present value of cash inflows/Initial investment

PI=526,671.67/\$500,000

PI=1.05

Therefore, the profitability index (PI) for project C is 1.05.

2. To find NPV, we follow the formula for NPV:

NPV=Present value of cash inflows – Initial investment

Therefore, NPV for project C = \$526,671.67 – \$500,000

NPV for project C = \$26,671.67

3. Since NPV is more than zero (\$26,671.67), project C is acceptable according to NPV technique.

4. Since Profitability Index (PI) is greater than 1 (1.05), the project may be considered to be acceptable.

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