Compute the PI statistic for Project X and note whether the firm should accept or reject the project with the cash flows shown as follows if the appropriate cost of capital is 10 percent.

Time:	0	1	2	3	4	5
Cash flow:	−250	75	0	100	75	50
Multiple Choice

−0.0977 percent, reject


−9.77 percent, reject


−24.41 percent, reject


24.41 percent, accept

The PI (Profitability Index) is calculated using the following formula:

\[
\text{PI} = \frac{\text{Present Value of Future Cash Flows}}{\text{Initial Investment}}
\]

Here's how to calculate it step by step:

### Step 1: Calculate the Present Value of Future Cash Flows
Given the cash flows and a discount rate of 10%, we'll discount each future cash flow to its present value:

\[
\text{PV} = \sum \frac{\text{Cash Flow at Time } t}{(1 + r)^t}
\]

Where:
- \( t \) is the time period,
- \( r \) is the discount rate (10% or 0.10).

The cash flows are as follows:
- \( CF_0 = -250 \) (initial investment)
- \( CF_1 = 75 \)
- \( CF_2 = 0 \)
- \( CF_3 = 100 \)
- \( CF_4 = 75 \)
- \( CF_5 = 50 \)

Let's calculate the present values:

\[
\text{PV}_1 = \frac{75}{(1 + 0.10)^1} = \frac{75}{1.10} = 68.18
\]
\[
\text{PV}_2 = \frac{0}{(1 + 0.10)^2} = 0
\]
\[
\text{PV}_3 = \frac{100}{(1 + 0.10)^3} = \frac{100}{1.331} = 75.13
\]
\[
\text{PV}_4 = \frac{75}{(1 + 0.10)^4} = \frac{75}{1.4641} = 51.24
\]
\[
\text{PV}_5 = \frac{50}{(1 + 0.10)^5} = \frac{50}{1.61051} = 31.05
\]

### Step 2: Sum the Present Values
\[
\text{Total PV of Future Cash Flows} = 68.18 + 0 + 75.13 + 51.24 + 31.05 = 225.60
\]

### Step 3: Calculate the PI
\[
\text{PI} = \frac{225.60}{250} = 0.9024
\]

### Step 4: Interpretation of PI
- **If PI > 1**: Accept the project (it adds value).
- **If PI < 1**: Reject the project (it destroys value).

In this case, PI = 0.9024, which is less than 1.

### Conclusion:
The correct answer is **−9.77 percent, reject**. The project should be rejected because the PI is less than 1.

Would you like details on any of the steps or have any further questions?

Here are 5 relative questions to expand on this topic:
1. How is the PI different from NPV in project evaluation?
2. Can a project with a positive NPV have a PI less than 1?
3. What are the limitations of using PI as a project evaluation tool?
4. How does the choice of discount rate affect the PI calculation?
5. What does a PI of exactly 1 signify for a project?

**Tip:** The PI is useful for ranking projects when capital is limited, as it shows the value created per unit of investment.

Learn how to calculate the Profitability Index (PI) statistic for Project X using discounted cash flows at a 10% cost of capital. Detailed step-by-step solution provided.

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