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
![**Project Payback Period Calculation**
Worthington Inc. is evaluating a project based on the following cash flow data. The objective is to determine the payback period of the project.
**Cash Flow Data:**
- **Year 0:** Initial Investment = -$500
- **Year 1:** Cash Inflow = $150
- **Year 2:** Cash Inflow = $200
- **Year 3:** Cash Inflow = $300
**Payback Period Options:**
- 2.03 years
- 2.25 years
- 2.50 years
- 2.75 years
- 3.03 years
**Explanation:**
To calculate the payback period, we look at how long it takes for the initial investment of $500 to be recovered through the net cash inflows.
1. **Year 1:**
- Cumulative cash flow = -$500 (initial) + $150 = -$350
2. **Year 2:**
- Cumulative cash flow = -$350 + $200 = -$150
3. **Year 3:**
- Cumulative cash flow = -$150 + $300 = $150
The initial investment is fully recovered between Year 2 and Year 3. To be precise, calculate the fraction of Year 3 required to recover the remaining $150:
\[ \text{Fraction of Year 3} = \frac{\text{Unrecovered Investment at End of Year 2}}{\text{Cash Inflow of Year 3}} = \frac{150}{300} = 0.5 \]
Thus, the total payback period is 2.5 years.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe5b2b20d-049f-4dcf-af25-64fd11186c52%2F240e7a27-a8fd-4946-a316-e877348a13fb%2Fgcsqzh_processed.png&w=3840&q=75)
Transcribed Image Text:**Project Payback Period Calculation**
Worthington Inc. is evaluating a project based on the following cash flow data. The objective is to determine the payback period of the project.
**Cash Flow Data:**
- **Year 0:** Initial Investment = -$500
- **Year 1:** Cash Inflow = $150
- **Year 2:** Cash Inflow = $200
- **Year 3:** Cash Inflow = $300
**Payback Period Options:**
- 2.03 years
- 2.25 years
- 2.50 years
- 2.75 years
- 3.03 years
**Explanation:**
To calculate the payback period, we look at how long it takes for the initial investment of $500 to be recovered through the net cash inflows.
1. **Year 1:**
- Cumulative cash flow = -$500 (initial) + $150 = -$350
2. **Year 2:**
- Cumulative cash flow = -$350 + $200 = -$150
3. **Year 3:**
- Cumulative cash flow = -$150 + $300 = $150
The initial investment is fully recovered between Year 2 and Year 3. To be precise, calculate the fraction of Year 3 required to recover the remaining $150:
\[ \text{Fraction of Year 3} = \frac{\text{Unrecovered Investment at End of Year 2}}{\text{Cash Inflow of Year 3}} = \frac{150}{300} = 0.5 \]
Thus, the total payback period is 2.5 years.
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