A project costs $30,000 and is expected to return cash flows of $9,500 per year for six years. What is the payback period of this project?

Group of answer choices

c. 3.21 years

d. 3.32 years

a. 3.07 years

b. 3.16 years

To calculate the payback period for the project, we need to determine how long it takes for the cash flows to recover the initial investment of $30,000.

### Cash Flows:
- Annual cash flow: $9,500
- Initial investment: $30,000

### Payback Period Calculation:
1. **Cumulative Cash Flows**: 
   - Year 1: $9,500
   - Year 2: $19,000 ($9,500 + $9,500)
   - Year 3: $28,500 ($19,000 + $9,500)
   - Year 4: $38,000 ($28,500 + $9,500)

After 3 years, the total cash flow is $28,500, which is not enough to cover the initial investment of $30,000. By the end of year 4, the total cash flow is $38,000.

2. **Calculating the exact payback period**:
   - The amount still needed after 3 years is: 
     \[
     30,000 - 28,500 = 1,500
     \]
   - In year 4, it will take a portion of the year to recover the remaining $1,500:
   \[
   \text{Time to recover remaining amount} = \frac{1,500}{9,500} \approx 0.158 \text{ years}
   \]
   
3. **Total Payback Period**:
   \[
   \text{Total payback period} = 3 + 0.158 \approx 3.158 \text{ years}
   \]

This rounds to approximately **3.16 years**.

### Answer:
**b. 3.16 years**

Would you like more details on this calculation or have any other questions? Here are some related questions you might consider:

1. What factors might affect the cash flow estimates for this project?
2. How would a longer payback period influence investment decisions?
3. What is the significance of the payback period in project evaluation?
4. How does the payback period differ from other investment appraisal methods?
5. What other financial metrics could be useful alongside the payback period? 

**Tip**: Always consider the time value of money when assessing project profitability.

A project costs $30,000 and is expected to return cash flows of $9,500 per year for six years. What is the payback period of this project?

Discover how to calculate the payback period for a project with a cost of $30,000 and expected annual cash flows of $9,500 over six years. This problem illustrates key financial concepts, including cumulative cash flows and payback period determination, with a solution arriving at approximately 3.16 years.

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