For the given cash flows, suppose the firm uses the NPV decision rule. Year Cash Flow -$ 155,000 61,000 78,000 62,000 1 2 3 At a required return of 10 %, what is the NPV of the project? At a required return of 19%, what is the NPV of the project?
For the given cash flows, suppose the firm uses the NPV decision rule. Year Cash Flow -$ 155,000 61,000 78,000 62,000 1 2 3 At a required return of 10 %, what is the NPV of the project? At a required return of 19%, what is the NPV of the project?
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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![**Project Cash Flow Analysis Using NPV Decision Rule**
**Objective:**
To determine the Net Present Value (NPV) of a given project based on projected cash flows at different required rates of return.
**Given Data:**
The firm evaluates the project using the NPV decision rule based on the following cash flows:
| Year | Cash Flow |
|------|--------------|
| 0 | -$155,000 |
| 1 | $61,000 |
| 2 | $78,000 |
| 3 | $62,000 |
**Questions:**
1. **At a required return of 10%, what is the NPV of the project?**
2. **At a required return of 19%, what is the NPV of the project?**
**Explanation:**
To answer these questions, we need to calculate the Net Present Value (NPV) at the given required returns. NPV is calculated using the following formula:
\[ \text{NPV} = \sum_{t=0}^{n} \frac{C_t}{(1 + r)^t} \]
where \(C_t\) is the cash flow at time \(t\),
\(r\) is the required return,
and \(t\) is the time period.
**Details of Calculations:**
1. **For a required return of 10%:**
- Year 0: Present Value (PV) = \(-\$155,000 / (1 + 0.10)^0\)
- Year 1: PV = \( \$61,000 / (1 + 0.10)^1 \)
- Year 2: PV = \( \$78,000 / (1 + 0.10)^2 \)
- Year 3: PV = \( \$62,000 / (1 + 0.10)^3 \)
2. **For a required return of 19%:**
- Year 0: Present Value (PV) = \(-\$155,000 / (1 + 0.19)^0\)
- Year 1: PV = \( \$61,000 / (1 + 0.19)^1 \)
- Year 2: PV = \( \$78,000 / (1 + 0.19)^2 \)
- Year 3: PV = \( \$62](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fce618159-930e-4ade-8eed-109751c2dc39%2Fb45745c2-0a53-42c8-be4f-2064cdbd9d6a%2F64i9by.png&w=3840&q=75)
Transcribed Image Text:**Project Cash Flow Analysis Using NPV Decision Rule**
**Objective:**
To determine the Net Present Value (NPV) of a given project based on projected cash flows at different required rates of return.
**Given Data:**
The firm evaluates the project using the NPV decision rule based on the following cash flows:
| Year | Cash Flow |
|------|--------------|
| 0 | -$155,000 |
| 1 | $61,000 |
| 2 | $78,000 |
| 3 | $62,000 |
**Questions:**
1. **At a required return of 10%, what is the NPV of the project?**
2. **At a required return of 19%, what is the NPV of the project?**
**Explanation:**
To answer these questions, we need to calculate the Net Present Value (NPV) at the given required returns. NPV is calculated using the following formula:
\[ \text{NPV} = \sum_{t=0}^{n} \frac{C_t}{(1 + r)^t} \]
where \(C_t\) is the cash flow at time \(t\),
\(r\) is the required return,
and \(t\) is the time period.
**Details of Calculations:**
1. **For a required return of 10%:**
- Year 0: Present Value (PV) = \(-\$155,000 / (1 + 0.10)^0\)
- Year 1: PV = \( \$61,000 / (1 + 0.10)^1 \)
- Year 2: PV = \( \$78,000 / (1 + 0.10)^2 \)
- Year 3: PV = \( \$62,000 / (1 + 0.10)^3 \)
2. **For a required return of 19%:**
- Year 0: Present Value (PV) = \(-\$155,000 / (1 + 0.19)^0\)
- Year 1: PV = \( \$61,000 / (1 + 0.19)^1 \)
- Year 2: PV = \( \$78,000 / (1 + 0.19)^2 \)
- Year 3: PV = \( \$62
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