Question

Simon Software Co. is trying to estimate its optimal capital structure. Right now, Simon has a capital structure that consists of 20 percent debt and 80 percent equity, based on market values. (Its D/S ratio is 0.25.) The risk-free rate is 6 percent and the market risk premium, rM – rRF, is 5 percent. Currently the company’s cost of equity, which is based on the CAPM, is 12 percent and its tax rate is 40 percent.

Find the new levered beta given the new capital structure (if it were to change its capital structure to 50 percent debt and 50 percent equity) using the Hamada equation.

0.81

1.00

1.22

1.45

1.67

Answer 1

Step 1: Calculation of current Beta

We have

Cost of Equity Ke = Rf + b ( Rm – Rf )

Where,

Rf – Risk free return

b – Beta

Rm – Expected return on market portfolio

Cost of Equity Ke = Rf + b ( Rm – Rf )

12 = 6 + b * 5

5b = 12-6 = 6

beta = 6 / 5 = 1.20

Step 2: Calculation of unlevered Beta (Aseet beta)

Asset Beta = Equity Beta / [(1+(1-tax rate)*(debt/equity)]

= 1.20 / [(1+.6*.2/.8]

= 1.2 / (1+.15)

Asset Beta = 1.0435

Step 3: Calculation of levered beta at 50% debt

levered beta = unlevered beta * (1+ (1-tax rate) (Debt/Equity))

= 1.0435* ( 1+ .6*.5/.5))

= 1.0435* (1+.6)

=1.0435 * 1.6

= 1.6696

?levered beta =1.67