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, Rf, is 5%; the market risk premium, RPM, is 6%; and the firm's tax rate is 40%. Currently, Cyclone's cost of equity is 14%, which is determined by the CAPM. What would be Cyclone's estimated cost of equity if it changed its capital structure to 50% debt and 50% equity? based on cost of equity estimations, Should the firm change its capital structure?

 

Cost of Equity = Riskfree rate + (Market Risk Premium)(Leveraged Beta)

Substituting to the formula, we get

14%= 5% + (6%)(Beta leveraged at 25% Debt)

9=(6%)(Beta leveraged at 25% Debt)

Make the Beta Leverage at 25% Debt the subject of the formula

First Divide 6%

9/6 = (6%)(Beta leveraged at 25% Debt)/6

9/6 = (6%)(Beta leveraged at 25% Debt)/6

(Beta leveraged at 25% Debt)=1.5%

Therefore the Beta leveraged for 25% Debt = 1.5

Now calculate the value of unleveraged beta

Remember we have the Leveraged Beta which is 1.5

The formula for the Unleveraged Beta is

Unleveraged Beta = (Leveraged Beta)/[1+(1-T)(D/E)]

Here Leveraged Beta which is 1.5, tax rate is 40%, debt rate is 25%, and Equity rate is 75%

Substituting in the formula, we get

= 1.5/[1+(1-40%)(25%/75%)]

= 1.25

If unleveraged Beta is 1.25 at 25% debt, we can use it find

We can still use the formula Unleveraged Beta = (Leveraged Beta)/[1+(1-T)(D/E)]

However, Debt rate is now 50% and equity is 50% not 75%

Substituting in the formula

Beta leveraged at 50% Debt = 1.25x[1+(1-40%)(50%/50%)]

= 2

Now substitute the value of Beta leveraged at 50% Deb in the original formula of calculating cost of equity

Cost of equity, rs= Riskfree rate + (Market Risk Premium)(Beta leveraged at 50% Debt)

= 5% + (6%)(2)

= 17%

Step-by-step explanation

Usually the cost of equity equals to Risk free rate plus market Risk Premium multplied the Leveraged Beta

substitute the values in the formula

Cost of Equity = Riskfree rate + (Market Risk Premium)(Leveraged Beta)

We get Leveraged Beta to be 1.5

However, our interest is to find the unleveraged Beta and the final cost of equity at 50%

Therefore we substitute the values as discussed above in the answer section

Unleveraged Beta = (Leveraged Beta)/[1+(1-T)(D/E)]

Here Leveraged Beta which is 1.5, tax rate is 40%, debt rate is 25%, and Equity rate is 75%

We get Unleveraged Beta as 1.25

We can use this value to get the Beta leveraged at 50% Debt as calculated above

The answer is 2

now substitute this in the original formula to calculate the cost of equity

The answer is 17%