Chapter 13 Capital Structure and Leverage 415In practice,! nancial managers use! nancial statement forecasting models to
determine how changes in the debt ratio will affect the current ratio, times-
interest-earned ratio, and EBITDA coverage ratio.^5 They then discuss their pro-
jected ratios with bankers and bond rating agencies, who ask probing questions
and may make their own adjustments to the! rm’s forecasts. The bankers and rat-
ing agencies compare the! rm’s ratios with those of other! rms in its industry and
arrive at a “what if” rating and corresponding interest rate. Moreover, if the com-
pany plans to issue bonds to the public, the SEC requires that it inform investors
what the coverages will be after the new bonds have been sold. Recognizing all
this, sophisticated! nancial managers use their forecasted ratios to predict how
bankers and other lenders will judge their! rms’ risks and thus their costs of debt.
Experienced! nancial managers and investment bankers can judge quite accu-
rately the effects of capital structure on the cost of debt.
13-3b The Hamada Equation
Increasing the debt ratio increases the risks that bondholders face and thus the cost
of debt. More debt also raises the risk borne by stockholders, which raises the cost
of equity, rs. It is harder to quantify leverage’s effects on the cost of equity, but a
theoretical formula can help measure the effect.
To begin, recall from Chapter 8 that a stock’s beta is the relevant measure of
risk for a diversi! ed investor. Moreover, beta increases with! nancial leverage,
and Robert Hamada formulated the following equation to quantify this effect.^6
bL! bU[1 # (1 " T)(D/E)] 13-2
Here bL is the! rm’s current beta, which we now assume is based on the existence
of some! nancial leverage, and bU is the! rm’s beta if the! rm was debt-free, or
unlevered.^7 If the! rm was debt-free, its beta would depend entirely on its busi-
ness risk and thus would be a measure of the! rm’s “basic business risk.” D/E is
the measure of! nancial leverage as used in the Hamada equation, and T is the
corporate tax rate.^8
Now recall the CAPM version of the cost of equity:
rs! rRF # (RPM)bi
(^5) We discuss! nancial statement forecasts in Chapter 16.
(^6) See Robert S. Hamada, “Portfolio Analysis, Market Equilibrium, and Corporation Finance,” Journal of Finance,
March 1969, pp. 13–31.
(^7) Note that Equation 13-2 is the original equation that Hamada put forward, and it was based on a set of
assumptions. The most notable were (a) that the beta of the company’s debt is zero, (b) that the level of debt is
constant, and (c) that the values of the company’s interest tax shields are discounted at the before-tax cost of
debt. Other researchers have derived alternative equations that are based on di$ erent assumptions. For example,
one commonly used alternative assumes that the company’s debt ratio remains constant and that the interest
tax shields are discounted at the unlevered cost of equity. In this case, the resulting equation is as follows:
bL " bU[1! D/E]
See Eugene F. Brigham and Phillip R. Daves, Intermediate Financial Management, 9th ed. (Mason, OH: Thomson/
South-Western, 2007), Chapter 15, for further discussion of the Hamada equation and the di$ erent approaches
for levering and unlevering betas.
(^8) Recall from Chapter 4 that the debt/equity ratio, D/E, is directly related to the D/A ratio:
(^) ED " __ 1 #D/A D/A
For example, if the! rm has $40 of debt and $60 of equity, D/A = 0.4, E/A = 0.6, and
(^) ED " ____ 1 #0.4 0.4 " 0.4/0.6 " 0.6667
Thus, any D/A ratio can be directly translated into a D/E ratio. Note also that Hamada’s equation assumes that assets
are reported at market values rather than accounting book values. This point is discussed at length in Brigham and
Daves, op cit., where feedbacks among capital structure, stock prices, and capital costs are examined.