Given:
cost of equity of 14.6 percent
market risk premium is 8.4 percent
risk-free rate is 3.9 percent
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.
Re = rf + (rm – rf) * β
Where:
Re = the required rate of return on equity
rf = the risk free rate
rm – rf = the market risk premium
β = beta coefficient = unsystematic risk
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
14.6% = 3.9% + 8.4% * β
14.6% - 3.9% = 8.4% * β
10.7% / 8.4% = β
1.27 = β
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.
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%.
