A firm's equity beta is 1.4, the risk-free rate is 3%, and the expected market return is 9%. Calculate the firm's cost of equity using the CAPM.
Understand the Problem
The question is asking for the calculation of a firm's cost of equity using the Capital Asset Pricing Model (CAPM), given the firm's equity beta, the risk-free rate, and the expected market return.
Answer
The firm's cost of equity is $11.4\%$.
Answer for screen readers
The firm's cost of equity using the CAPM is $11.4%$.
Steps to Solve
- Identify the CAPM Formula
The Capital Asset Pricing Model (CAPM) formula is given by:
$$ r_e = r_f + \beta \times (r_m - r_f) $$
where:
- ( r_e ) = cost of equity
- ( r_f ) = risk-free rate
- ( \beta ) = equity beta
- ( r_m ) = expected market return
- Substitute the Known Values
Plug in the values from the problem:
- ( r_f = 3% = 0.03 )
- ( \beta = 1.4 )
- ( r_m = 9% = 0.09 )
Now, substitute these values into the CAPM formula:
$$ r_e = 0.03 + 1.4 \times (0.09 - 0.03) $$
- Calculate the Market Risk Premium
Calculate the market risk premium, which is the difference between the expected market return and the risk-free rate:
$$ r_m - r_f = 0.09 - 0.03 = 0.06 $$
- Multiply Beta by the Market Risk Premium
Now, multiply the equity beta by the market risk premium:
$$ 1.4 \times 0.06 = 0.084 $$
- Calculate the Cost of Equity
Finally, add the risk-free rate to the result from the previous step:
$$ r_e = 0.03 + 0.084 = 0.114 $$
Convert this back to percentage:
$$ r_e = 11.4% $$
The firm's cost of equity using the CAPM is $11.4%$.
More Information
Using CAPM, the cost of equity is a critical measure for evaluating the required return an investor expects for providing capital to a firm.
Tips
- Failing to convert percentages to decimals when performing calculations.
- Neglecting to add the risk-free rate back to the calculated risk premium.
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