eBook Assume that the risk-free rate is 2.5% and the required return on the market is 9%. What is the required rate of return on a stock with a beta of 2? Round your answer to two decimal places. %
eBook Assume that the risk-free rate is 2.5% and the required return on the market is 9%. What is the required rate of return on a stock with a beta of 2? Round your answer to two decimal places. %
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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![### Transcription for Educational Use:
**Title: Understanding Required Rate of Return in Finance**
**Scenario:**
- The risk-free rate is given as 2.5%.
- The required return on the market is 9%.
- Calculate the required rate of return on a stock with a beta of 2.
**Instructions:**
Round your answer to two decimal places.
---
**Note:** This scenario presents an example of using the Capital Asset Pricing Model (CAPM) to determine the required rate of return on a stock. The CAPM formula is:
\[ \text{Required Rate of Return} = \text{Risk-Free Rate} + \beta \times (\text{Market Return} - \text{Risk-Free Rate}) \]
**Calculation:**
Given:
- Risk-Free Rate (\(R_f\)) = 2.5%
- Market Return (\(R_m\)) = 9%
- Beta (\(\beta\)) = 2
Plug these values into the CAPM formula:
\[ \text{Required Rate of Return} = 2.5\% + 2 \times (9\% - 2.5\%) \]
Calculate the market risk premium:
\[ \text{Market Risk Premium} = 9\% - 2.5\% = 6.5\% \]
Then:
\[ \text{Required Rate of Return} = 2.5\% + 2 \times 6.5\% \]
\[ = 2.5\% + 13\% = 15.5\% \]
**Answer:**
The required rate of return on the stock is **15.5%**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbb5aba3c-4931-42d1-80b4-3d9f41ab8cf8%2F7fbaef4e-3bbf-4912-90ed-41b85942bd01%2F0wek7gy_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Transcription for Educational Use:
**Title: Understanding Required Rate of Return in Finance**
**Scenario:**
- The risk-free rate is given as 2.5%.
- The required return on the market is 9%.
- Calculate the required rate of return on a stock with a beta of 2.
**Instructions:**
Round your answer to two decimal places.
---
**Note:** This scenario presents an example of using the Capital Asset Pricing Model (CAPM) to determine the required rate of return on a stock. The CAPM formula is:
\[ \text{Required Rate of Return} = \text{Risk-Free Rate} + \beta \times (\text{Market Return} - \text{Risk-Free Rate}) \]
**Calculation:**
Given:
- Risk-Free Rate (\(R_f\)) = 2.5%
- Market Return (\(R_m\)) = 9%
- Beta (\(\beta\)) = 2
Plug these values into the CAPM formula:
\[ \text{Required Rate of Return} = 2.5\% + 2 \times (9\% - 2.5\%) \]
Calculate the market risk premium:
\[ \text{Market Risk Premium} = 9\% - 2.5\% = 6.5\% \]
Then:
\[ \text{Required Rate of Return} = 2.5\% + 2 \times 6.5\% \]
\[ = 2.5\% + 13\% = 15.5\% \]
**Answer:**
The required rate of return on the stock is **15.5%**.
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