Question
A stock has a Beta of 1.39. The current risk free rate in the economy is 1.68%, while the market portfolio risk premium is 6%. Find the cost of equity for this stock.
Answers
GPT-4o mini
The cost of equity can be calculated using the Capital Asset Pricing Model (CAPM), which is given by the formula:
\[
\text{Cost of Equity} = \text{Risk-Free Rate} + \beta \times \text{Market Risk Premium}
\]
Where:
- \(\text{Risk-Free Rate}\) = 1.68%
- \(\beta\) = 1.39
- \(\text{Market Risk Premium}\) = 6%
Now, substituting the values into the formula:
\[
\text{Cost of Equity} = 1.68\% + 1.39 \times 6\%
\]
Calculating the market risk premium component:
\[
1.39 \times 6\% = 8.34\%
\]
Now add this to the risk-free rate:
\[
\text{Cost of Equity} = 1.68\% + 8.34\% = 10.02\%
\]
Therefore, the cost of equity for the stock is **10.02%**.
\[
\text{Cost of Equity} = \text{Risk-Free Rate} + \beta \times \text{Market Risk Premium}
\]
Where:
- \(\text{Risk-Free Rate}\) = 1.68%
- \(\beta\) = 1.39
- \(\text{Market Risk Premium}\) = 6%
Now, substituting the values into the formula:
\[
\text{Cost of Equity} = 1.68\% + 1.39 \times 6\%
\]
Calculating the market risk premium component:
\[
1.39 \times 6\% = 8.34\%
\]
Now add this to the risk-free rate:
\[
\text{Cost of Equity} = 1.68\% + 8.34\% = 10.02\%
\]
Therefore, the cost of equity for the stock is **10.02%**.