Asked by Jeffrey Morales on Jun 26, 2024
Verified
T. Corporation has a standard deviation on its common stock of 75 percent and a correlation with market returns of 0.40. The market's standard deviation and expected return are 15 percent and 14 percent, respectively, and the risk-free rate of return is 8 percent. Calculate T. Corporation's required rate of return.
A) 1.867%
B) 9.867%
C) 19.20%
D) 14.06%
Required Rate
The lowest acceptable return on an investment, determined by the investor's risk tolerance and alternative investment options.
Standard Deviation
A statistical measure of the dispersion or variability in a dataset, often used in finance to quantify the risk of investment.
- Understand the components and the mechanism of the Capital Asset Pricing Model (CAPM).
- Discerning the link between risk and return.
Verified Answer
SC
stephany castroJun 30, 2024
Final Answer :
C
Explanation :
The formula for required rate of return using the Capital Asset Pricing Model (CAPM) is:
R = Rf + beta(Rm - Rf)
Where:
R = required rate of return
Rf = risk-free rate of return
beta = correlation of T. Corporation's stock returns with market returns
Rm = expected return on the market
First, we need to find T. Corporation's beta using the formula:
beta = (standard deviation of T. Corp. / standard deviation of market) * correlation
beta = (0.75 / 0.15) * 0.40 = 2
Plugging in the given values, we get:
R = 0.08 + 2(0.14 - 0.08)
R = 0.08 + 0.12
R = 0.20 or 20%
Therefore, the required rate of return for T. Corporation is 20%. The closest option is C, 19.20%.
R = Rf + beta(Rm - Rf)
Where:
R = required rate of return
Rf = risk-free rate of return
beta = correlation of T. Corporation's stock returns with market returns
Rm = expected return on the market
First, we need to find T. Corporation's beta using the formula:
beta = (standard deviation of T. Corp. / standard deviation of market) * correlation
beta = (0.75 / 0.15) * 0.40 = 2
Plugging in the given values, we get:
R = 0.08 + 2(0.14 - 0.08)
R = 0.08 + 0.12
R = 0.20 or 20%
Therefore, the required rate of return for T. Corporation is 20%. The closest option is C, 19.20%.
Learning Objectives
- Understand the components and the mechanism of the Capital Asset Pricing Model (CAPM).
- Discerning the link between risk and return.