Compute the payback period statistic for Project X and recommend whether the firm should accept or reject the project with the cash flows shown in the chart if the maximum allowable payback is four years.
0	-$1,450
1	$250
2	$380
3	$620
4	$1,000
5	$100


To compute the payback period for Project X, we need to determine how long it will take for the project to recover its initial investment of $1,450 through the net cash inflows over the years.

### Step-by-Step Calculation:

1. **Initial Investment**: 
   \[
   \text{Initial Investment} = -\$1,450
   \]

2. **Cumulative Cash Flows**:
   - **Year 0**: 
     \[
     \text{Cumulative Cash Flow} = -\$1,450
     \]
   - **Year 1**: 
     \[
     \text{Cumulative Cash Flow} = -\$1,450 + \$250 = -\$1,200
     \]
   - **Year 2**: 
     \[
     \text{Cumulative Cash Flow} = -\$1,200 + \$380 = -\$820
     \]
   - **Year 3**: 
     \[
     \text{Cumulative Cash Flow} = -\$820 + \$620 = -\$200
     \]
   - **Year 4**: 
     \[
     \text{Cumulative Cash Flow} = -\$200 + \$1,000 = \$800
     \]
   - **Year 5**: 
     \[
     \text{Cumulative Cash Flow} = \$800 + \$100 = \$900
     \]

3. **Determining the Payback Period**:
   - By the end of Year 3, the project still has not recovered the initial investment, with a cumulative cash flow of -$200.
   - In Year 4, the cumulative cash flow becomes positive, reaching $800.
   - Therefore, the payback period occurs between Year 3 and Year 4.

   To find the exact payback period:
   \[
   \text{Payback Period} = 3 + \frac{\$200}{\$1,000} = 3 + 0.2 = 3.2 \text{ years}
   \]

### Conclusion:
- The payback period for Project X is **3.2 years**.
- Since this payback period is **less than the maximum allowable payback period of 4 years**, the firm **should accept** the project.

Would you like more details or have any questions?

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Here are 5 related questions you might find helpful:

1. What is the difference between the payback period and the discounted payback period?
2. How does the payback period compare with other capital budgeting metrics like NPV or IRR?
3. What are the limitations of using the payback period as a decision-making tool?
4. How would the payback period change if cash flows were uneven or occurred at different times during the year?
5. Can the payback period method be applied to projects with no initial cash outlay?

**Tip:** While the payback period is simple and useful for quick assessments, it does not account for the time value of money or cash flows beyond the payback point. Consider using it alongside other metrics like NPV or IRR for more comprehensive project evaluation.

Learn how to compute the payback period for Project X using cash flow analysis. This problem involves determining if a project should be accepted based on a maximum allowable payback period of four years. Detailed step-by-step calculations and analysis provided.

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