Consider the following two projects: Year 2 Cash Flow Cash Flow Cash Flow Cash Flow Cash Flow Year 1 Year 3 Year 4 Project Year 0 Discount Rate A - 100 40 50 60 N/A 0.13 в - 73 30 30 30 30 0.13 The net present value (NPV) of project B is closest to: O A. 17.9 О В. 20.3 O C. 40.6 O D. 16.2
Consider the following two projects: Year 2 Cash Flow Cash Flow Cash Flow Cash Flow Cash Flow Year 1 Year 3 Year 4 Project Year 0 Discount Rate A - 100 40 50 60 N/A 0.13 в - 73 30 30 30 30 0.13 The net present value (NPV) of project B is closest to: O A. 17.9 О В. 20.3 O C. 40.6 O D. 16.2
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 Evaluation and NPV Calculation
### Project Overview
Consider the following two projects, each with designated cash flows over a five-year period and an associated discount rate. The cash flows are documented in the table below:
**Project Cash Flows and Discount Rates:**
| Project | Year 0 Cash Flow | Year 1 Cash Flow | Year 2 Cash Flow | Year 3 Cash Flow | Year 4 Cash Flow | Discount Rate |
|---------|------------------|------------------|------------------|------------------|------------------|----------------|
| A | -100 | 40 | 50 | 60 | N/A | 0.13 |
| B | -73 | 30 | 30 | 30 | 30 | 0.13 |
**Key Concepts:**
- **Cash Flow (CF)**: Represents the net amount of cash being transferred in and out of the project at different years.
- **Discount Rate**: The rate used to calculate the present value of future cash flows.
### Net Present Value (NPV)
The net present value of a project evaluates the profitability by accounting for the time value of money. It calculates the present values (PV) of incoming and outgoing cash flows using the formula:
\[ PV = \frac{CF_t}{(1 + r)^t} \]
Where:
- \( CF_t \) is the cash flow at time t.
- \( t \) is the time period.
- \( r \) is the discount rate.
The NPV is the sum of all these present values.
### Calculation and Options
Given the cash flows for Project B:
- **Year 0**: -73
- **Year 1**: 30
- **Year 2**: 30
- **Year 3**: 30
- **Year 4**: 30
And a discount rate of 0.13, we compute the NPV as follows:
\[ NPV = -73 + \frac{30}{(1+0.13)^1} + \frac{30}{(1+0.13)^2} + \frac{30}{(1+0.13)^3} + \frac{30}{(1+0.13)^4} \]
The NPV calculation yields:
- \(\frac{30}{(1.13)^1}](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6b2d2087-0413-432e-842b-e7bfa6e336f7%2F03642fb7-9fda-4b96-aab9-4eaad9b0f330%2F9ydlwqi_processed.png&w=3840&q=75)
Transcribed Image Text:## Project Evaluation and NPV Calculation
### Project Overview
Consider the following two projects, each with designated cash flows over a five-year period and an associated discount rate. The cash flows are documented in the table below:
**Project Cash Flows and Discount Rates:**
| Project | Year 0 Cash Flow | Year 1 Cash Flow | Year 2 Cash Flow | Year 3 Cash Flow | Year 4 Cash Flow | Discount Rate |
|---------|------------------|------------------|------------------|------------------|------------------|----------------|
| A | -100 | 40 | 50 | 60 | N/A | 0.13 |
| B | -73 | 30 | 30 | 30 | 30 | 0.13 |
**Key Concepts:**
- **Cash Flow (CF)**: Represents the net amount of cash being transferred in and out of the project at different years.
- **Discount Rate**: The rate used to calculate the present value of future cash flows.
### Net Present Value (NPV)
The net present value of a project evaluates the profitability by accounting for the time value of money. It calculates the present values (PV) of incoming and outgoing cash flows using the formula:
\[ PV = \frac{CF_t}{(1 + r)^t} \]
Where:
- \( CF_t \) is the cash flow at time t.
- \( t \) is the time period.
- \( r \) is the discount rate.
The NPV is the sum of all these present values.
### Calculation and Options
Given the cash flows for Project B:
- **Year 0**: -73
- **Year 1**: 30
- **Year 2**: 30
- **Year 3**: 30
- **Year 4**: 30
And a discount rate of 0.13, we compute the NPV as follows:
\[ NPV = -73 + \frac{30}{(1+0.13)^1} + \frac{30}{(1+0.13)^2} + \frac{30}{(1+0.13)^3} + \frac{30}{(1+0.13)^4} \]
The NPV calculation yields:
- \(\frac{30}{(1.13)^1}
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