Hamada Equation: Cyclone Software Co. is trying to establish its optimal capital structure. Its current capital structure consists of 25% debt and 75% equity; however, the CEO believes that the firm should use more debt. The risk-free rate, r_RF, is 5%; the market risk premium, RP_M is 6%; and the tax rate is 40%. Currently, Cyclones cost of equity is 14%, which is determined by the CAPM. What would be Cyclones estimated cost of equity if it changed its capital structure to 50% debt and 50% equity.

This is the solution below:

Cost of Equity = Riskfree rate + (Market Risk Premium)(Leveraged Beta) 14 = 5% + (6%)(Beta leveraged at 25% Debt) Beta leveraged for 25% Debt = 1.5 Unleveraged Beta = (Leveraged Beta)/[1+(1-T)(D/E)] = 1.5/[1+(1-40%)(25%/75%)] = 1.25 Beta leveraged at 50% Debt = 1.25x[1+(1-40%)(50%/50%)] = 2 Cost of equity, rs= Riskfree rate + (Market Risk Premium)(Beta leveraged at 50% Debt) = 5% + (6%)(2) = 17%

Where did 1.5 as debt come from. Can someone explain. Thank you.