Capital Structure Theories^283= ba
=b + b -b
-^(^) + ...(32)
We can observe from Equation (32) that the equity beta increases linearly with leverage
(D/S) since it adds financial risk to the shareholderís return.
Illustration 1: Unlevered Firm has no corporate tax. The observed beta on its equity
is 1.20. The beta of debt is 0.20. The company has a debt-equity ratio of 0.40.
Calculate the companyís asset beta.
be = ba + (bd-be )D/S
1.20 = ba + (ba-0.20)0.40
be + 0.4ba = 1.20 + 0.08
ba = 1.28/1.4 = 0.914
Debt has low risk. If we assume that debt is risk-free, then bd= 0. If bd =0, then ba
(asset beta) is given as follows:
be = ba + (bd-bd )D/S
be = ba + ba D/S (since bd = 0)
ba = +!
b
...(33)
Corporate Tax and Interest Tax Shield
Firms in practice pay taxes, and interest paid on debt is tax deductible. The asset beta
should be adjusted for the tax effect. The adjustment factors will be the tax rate and
the firmís leverage (debt ratio). The adjusted beta will be as follows:
b =b +b
(^) -
...(34)
where V is total market value of debt and equity (i.e. S + D).
As we have stated earlier, the risk of debt holders is quite low. If they have no risk,
they will earn risk-free rate and bd will be zero. Thus, Equation (34) can be expressed
as follows:ba = # !"
b
(since bd = 0) $ $
# !"# !" =b -=b -
...(35)
where L is D/V. From Equation (35), we can express be as follows: