To calculate the beta (β) of the stock, we can use the Capital Asset Pricing Model (CAPM), which is expressed by the following formula:
\[ \text{Expected Return} = \text{Risk-Free Rate} + \beta \times \text{Market Risk Premium} \]
From the information provided:
- Expected Return (ER) = 13.00% = 0.13
- Risk-Free Rate (RFR) = 3.99% = 0.0399
- Market Risk Premium (MRP) = 7.58% = 0.0758
We can plug these values into the CAPM formula and solve for β:
\[ 0.13 = 0.0399 + \beta \times 0.0758 \]
Subtract the risk-free rate from both sides:
\[ 0.13 - 0.0399 = \beta \times 0.0758 \]
\[ 0.0901 = \beta \times 0.0758 \]
Now, solve for β by dividing both sides by the market risk premium:
\[ \beta = \frac{0.0901}{0.0758} \]
\[ \beta \approx 1.188 \]
Thus, the beta (β) of the stock is approximately 1.19.
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