While the arguments for such actions may be couched in terms of offering competi-
tive advantage and flexibility, they do also reduce the operating leverage of the firm
and its exposure to market risk.
While operating leverage affects betas, it is difficult to measure the operating
leverage of a firm, at least from the outside, since fixed and variable costs are often
aggregated in income statements. It is possible to get an approximate measure of the
operating leverage of a firm by looking at changes in operating income as a function
of changes in sales.
For firms with high operating leverage, operating income should change more than
proportionately when sales change.
Generally, smaller firms with higher growth potential are viewed as riskier than
larger, more stable firms. While the rationale for this argument is clear when talking
about total risk, it becomes more difficult to see when looking at market risk or betas.
Should a smaller software firm have a higher beta than a larger software firm? One
reason to believe that it should is operating leverage. If there is a set-up cost associ-
ated with investing in infrastructure or economies of scale, smaller firms will have
higher fixed costs than larger firms, leading in turn to higher betas for these firms.
DEGREE OF FINANCIAL LEVERAGE. Other things remaining equal, an increase in financial
leverage will increase the beta of the equity in a firm. Intuitively, we would expect
that the fixed interest payments on debt result in high net income in good times and
low or negative net income in bad times. Higher leverage increases the variance in
net income and makes equity investment in the firm riskier. If all the firm’s risk is
borne by the stockholders (i.e., the beta of debt is zero)^13 and debt has a tax benefit
to the firm, then
where
D>EDebt>Equity ratiotCorporate tax ratebuUnlevered beta of the firm 1 i.e., the beta of the firm without any debt 2bLLevered beta for equity in the firmbLbua 1 11 t2aD
EbbDegree of operating leverage%Change in operating profit>%Change in sales9.2 ESTIMATING DISCOUNT RATES 9 • 21(^13) This formula was originally developed by Hamada in 1972. There are two common modifications.
One is to ignore the tax effects and compute the levered beta as:
If debt has market risk (i.e., its beta is greater than zero), the original formula can be modified to take it
into account. If the beta of debt is D, the beta of equity can be written as:
bLbua 1 11 t2a
D
E
bbbD 11 t2a
D
E
b
bLbua 1
D
E
b