Title: Determining the Payback Period of an Investment Project---**Problem Statement**:An investment project provides cash inflows of $1,325 per year for eight years. What is the project's payback period if the initial cost is $4,200? Or $5,250? Or $11,600?---**Explanation**:To determine the payback period, we must calculate how long it will take for the annual cash inflows to repay the initial cost of the investment.**Step-by-Step Solution**:1. **When the initial cost is $4,200**: - Annual cash inflow = $1,325 - Payback Period = Initial Investment / Annual Cash Inflow - Payback Period = $4,200 / $1,325 ≈ 3.17 years Therefore, it takes approximately 3.17 years to recover the initial investment of $4,200.2. **When the initial cost is $5,250**: - Annual cash inflow = $1,325 - Payback Period = Initial Investment / Annual Cash Inflow - Payback Period = $5,250 / $1,325 ≈ 3.96 years Therefore, it takes approximately 3.96 years to recover the initial investment of $5,250.3. **When the initial cost is $11,600**: - Annual cash inflow = $1,325 - Payback Period = Initial Investment / Annual Cash Inflow - Payback Period = $11,600 / $1,325 ≈ 8.75 years Therefore, it takes approximately 8.75 years to recover the initial investment of $11,600.**Conclusion**:By using the payback period formula, we are able to determine the amount of time needed to recover the initial investment for each of the given initial costs.---**Visual Explanation (Assume a graph might be included)**:_Graph/Diagram Description_:- **X-Axis**: Number of years- **Y-Axis**: Cumulative Cash Inflow ($)- **Lines representing each scenario**: - Line 1 representing scenario 1 ($4,200 initial cost) intersects the cumulative cash inflow at about 3.17 years. - Line 2 representing scenario 2 ($5,250 initial cost) intersects

Year cash flow 1 1 1,325.00 2…

Answered: An investment project provides cash…

An investment project provides cash inflows of $1325 per year for eight yea payback period if the initial cost is $4,200? Or $5250 or $11,600?

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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Question

Title: Determining the Payback Period of an Investment Project

---

**Problem Statement**:

An investment project provides cash inflows of $1,325 per year for eight years. What is the project's payback period if the initial cost is $4,200? Or $5,250? Or $11,600?

---

**Explanation**:

To determine the payback period, we must calculate how long it will take for the annual cash inflows to repay the initial cost of the investment.

**Step-by-Step Solution**:

1. **When the initial cost is $4,200**:
- Annual cash inflow = $1,325
- Payback Period = Initial Investment / Annual Cash Inflow
- Payback Period = $4,200 / $1,325 ≈ 3.17 years

Therefore, it takes approximately 3.17 years to recover the initial investment of $4,200.

2. **When the initial cost is $5,250**:
- Annual cash inflow = $1,325
- Payback Period = Initial Investment / Annual Cash Inflow
- Payback Period = $5,250 / $1,325 ≈ 3.96 years

Therefore, it takes approximately 3.96 years to recover the initial investment of $5,250.

3. **When the initial cost is $11,600**:
- Annual cash inflow = $1,325
- Payback Period = Initial Investment / Annual Cash Inflow
- Payback Period = $11,600 / $1,325 ≈ 8.75 years

Therefore, it takes approximately 8.75 years to recover the initial investment of $11,600.

**Conclusion**:
By using the payback period formula, we are able to determine the amount of time needed to recover the initial investment for each of the given initial costs.

---

**Visual Explanation (Assume a graph might be included)**:

_Graph/Diagram Description_:
- **X-Axis**: Number of years
- **Y-Axis**: Cumulative Cash Inflow ($)
- **Lines representing each scenario**:
- Line 1 representing scenario 1 ($4,200 initial cost) intersects the cumulative cash inflow at about 3.17 years.
- Line 2 representing scenario 2 ($5,250 initial cost) intersects

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