Calculate the expected return (as a percentage) for Company X, which has a beta of 0.9 when the risk-free rate is 4.8% and you expect the equity risk premium to be 9.8%.
Question
Calculate the expected return (as a percentage) for Company X, which has a beta of 0.9 when the risk-free rate is 4.8% and you expect the equity risk premium to be 9.8%.
Solution
The expected return of a stock can be calculated using the Capital Asset Pricing Model (CAPM), which is expressed as:
Expected Return = Risk-free rate + Beta * (Market Return - Risk-free rate)
In this case, the risk-free rate is 4.8%, the beta is 0.9, and the equity risk premium (which is the Market Return - Risk-free rate) is 9.8%.
Step 1: Convert the percentages to decimals. 4.8% becomes 0.048, and 9.8% becomes 0.098.
Step 2: Substitute the values into the CAPM formula:
Expected Return = 0.048 + 0.9 * 0.098
Step 3: Calculate the value:
Expected Return = 0.048 + 0.0882 = 0.1362
Step 4: Convert the decimal back to a percentage:
Expected Return = 0.1362 * 100 = 13.62%
So, the expected return for Company X is 13.62%.
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