Given:
<span>cost of equity of 14.6 percent
</span><span>market risk premium is 8.4 percent
</span><span>risk-free rate is 3.9 percent
</span><span>increase company's beta to 1.4 after purchase.
We will use the CAPM or Capital Asset Pricing Model formula to solve the new cost of equity.
</span>
Re = rf + (rm – rf) * β
Where:
<span>Re = the required rate of return on equity
<span>rf = the risk free rate
</span><span>rm – rf = the market risk premium
</span>β = beta coefficient = unsystematic risk</span><span>
</span>We need to solve for the original beta coefficient using the given cost of equity, market risk premium and risk free rate.
Re = rf + (rm – rf) * β<span>
14.6% = 3.9% + 8.4% * </span>β
14.6% - 3.9% = 8.4% * β
10.7% / 8.4% = β
1.27 = β
<span>
The initial beta coefficient is 1.27.
Using the same risk free rate, market risk premium, and a new beta coefficient of 1.4, we need to solve the cost of equity.
</span>Re = 3.9% + 8.4% * 1.4
Re = 3.9% + 11.76%
Re = 15.66%
The new cost of equity after purchasing a company is 15.66%. It increase from 14.6% by 1.06%.
