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E(Rj) - Rf = Risk premium per unit of factor j risk
k = Number of factors
In a multi-factor model, the betas are estimated relative to the specified factors, using
historical data for each firm.


B. Fundamental Betas
The beta for a firm may be estimated from a regression but it is determined by
fundamental decisions that the firm has made on what business to be in, how much
operating leverage to use in the business and the degree to which the firm uses financial
leverage. In this section, we will examine an alternative way of estimating betas, where
we are less reliant on historical betas and more cognizant of the intuitive underpinnings
of betas.

Determinants of Betas
The beta of a firm is determined by three variables -(1) the type of business or
businesses the firm is in, (2) the degree of operating leverage in the firm and (3) the
firm's financial leverage. While much of the discussion in this section will be couched in
terms of CAPM betas, the same analysis can be applied to the betas estimated in the
APM and the multi-factor model as well.

Type of Business Since betas measure the risk of a firm relative to a market index, the
more sensitive a business is to market conditions, the
Cyclical Firm: A cyclical firm has
higher is its beta. Thus, other things remaining equal,
revenues and operating income that
cyclical firms can be expected to have higher betas
tend to move strongly with the
than non-cyclical firms. Other things remaining equal,
economy - up when the economy is
then, companies involved in housing and automobiles, doing well, and down during
two sectors of the economy which are very sensitive recessions.

to economic conditions, will have higher betas than
companies which are in food processing and tobacco, which are relatively insensitive to
business cycles.
Building on this point, we would also argue that the degree to which a product™s
purchase is discretionary will affect the beta of the firm manufacturing the product. Thus,
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the betas of food processing firms, such as General Foods and Kellogg™s, should be lower
than the betas of specialty retailers, since consumers can defer the purchase of the latter™s
products during bad economic times.
It is true that firms have only limited control over how discretionary the product
or service that they provide is to their customers. There are firms, however, that have
used this limited control to maximum effect to make their products less discretionary to
buyers, and by extension, lowered their business risk. One approach is to make the
product or service a much more integral and necessary part of everyday life, thus making
its purchase more of a requirement. A second approach is to effectively use advertising
and marketing to build brand loyalty. The objective in good advertising, as we see it, is to
make discretionary products or services seem like necessities to the target audience.
Thus, corporate strategy, advertising and marketing acumen can, at the margin, alter the
business risk and betas over time.

˜ 4.7: Betas and Business Risk
Polo Ralph Lauren, the upscale fashion designer, went public in 1997. Assume that you
were asked to estimate its beta. Based upon what you know about the firm™s
products, would you expect the beta to be
a. greater than one
b. about one
c. less than one
Why?

Degree of Operating Leverage The degree of operating leverage is a function of the cost
structure of a firm, and is usually defined in terms of the relationship between fixed costs
and total costs. A firm that has high operating leverage (i.e., high fixed costs relative to
total costs) will also have higher variability in
Operating Leverage: This is a
operating income than would a firm producing a
measure of the proportion of the
leverage.32
similar product with low operating Other operating expenses of a company
which are fixed costs.

32 Tosee why, compare two firms with revenues of $ 100 million and operating income of $ 10 million, but
assume that the first firm™s costs are all fixed whereas only half of the second firm™s costs are fixed. If
revenues increase at both firms by $ 10 million, the first firm will report a doubling of operating income
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things remaining equal, the higher variance in operating income will lead to a higher beta
for the firm with high operating leverage.
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.
Degree of Operating leverage = % Change in Operating Profit / % Change in
Sales
For firms with high operating leverage, operating income should change more than
proportionately, when sales change.
Can firms change their operating leverage? While some of a firm™s cost structure
is determined by the business it is in (an energy utility has to build expensive power
plants, and airlines have to lease expensive planes), firms in the United States have
become increasingly inventive in lowering the fixed cost component in their total costs.
Labor contracts that emphasize flexibility and allow the firm to make its labor costs more
sensitive to its financial success, joint venture agreements, where the fixed costs are
borne by someone else, and sub-contracting of manufacturing, which reduce the need for
expensive plant and equipment, are only some of the manifestations of this phenomenon.
While the arguments for such actions may be couched in terms of competitive advantage
and flexibility, they do reduce the operating leverage of the firm and its exposure to
“market” risk.

Illustration 4.3: Measuring Operating Leverage for Disney Corporation
In table 4.5, we estimate the degree of operating leverage for Disney from 1987 to
2003:
Table 4.5: Degree of Operating Leverage: Disney
Year Net Sales % Change in EBIT % Change in
Sales EBIT
1987 2877 756


(from $ 10 to $ 20 million) whereas the second firm will report a rise of 55% in its operating income (since
costs will rise by $ 4.5 million, 45% of the revenue increment).
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1988 3438 19.50% 848 12.17%
1989 4594 33.62% 1177 38.80%
1990 5844 27.21% 1368 16.23%
1991 6182 5.78% 1124 -17.84%
1992 7504 21.38% 1287 14.50%
1993 8529 13.66% 1560 21.21%
1994 10055 17.89% 1804 15.64%
1995 12112 20.46% 2262 25.39%
1996 18739 54.71% 3024 33.69%
1997 22473 19.93% 3945 30.46%
1998 22976 2.24% 3843 -2.59%
1999 23435 2.00% 3580 -6.84%
2000 25418 8.46% 2525 -29.47%
2001 25172 -0.97% 2832 12.16%
2002 25329 0.62% 2384 -15.82%
2003 27061 6.84% 2713 13.80%
1987-2003 15.83% 10.09%
1996-2003 11.73% 4.42%

The degree of operating leverage changes dramatically from year to year, because of
year-to-year swings in operating income. Using the average changes in sales and
operating income over the period, we can compute the operating leverage at Disney:
Operating Leverage = % Change in EBIT/ % Change in Sales
= 10.09% / 15.83% = 0.64
There are two important observations that can be made about Disney over the period,
though. First, the operating leverage for Disney is lower than the operating leverage for
other entertainment firms, which we computed to be 1.12.33 This would suggest that
Disney has lower fixed costs than its competitors. Second, the acquisition of Capital
Cities by Disney in 1996 may be affecting the operating leverage. Looking at the
numbers since 1996, we get an even lower estimate of operating leverage:
Operating Leverage1996-03 = 4.42%/11.73% = 0.38
We would not read too much into these numbers because Disney has such a wide range
of businesses. We would hypothesize that Disney™s theme part business has higher fixed
costs (and operating leverage) than it™s movie business.


33To compute this statistic, we looked at the aggregate revenues and operating income of entertainment
companies each year from 1987 to 2003.
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˜ 4.8: Social Policy and Operating Leverage
Assume that you are comparing a European automobile manufacturing firm with a U.S.
automobile firm. European firms are generally much more constrained in terms of
laying off employees, if they get into financial trouble. What implications does this
have for betas, if they are estimated relative to a common index?
a. The European firm will have much a higher beta than the U.S. firms
b. The European firms will have a similar betas to the U.S. firm
c. The European firms will have a much lower beta than the U.S. firms


Should small or high growth firms have higher betas than larger and more mature
firms?
Though the answer may seem obvious at first sight “ that smaller, higher growth
firms should are riskier than larger firms “ it is not an easy question to answer. If the
question were posed in terms of total risk, smaller and higher growth firms will tend to be
riskier simply because they have more volatile earnings streams (and their market prices
reflect that). When it is framed in terms of betas or market risk, smaller and higher
growth firms should have higher betas only if the products and services they offer are
more discretionary to their customers or if they have higher operating leverage. It is
possible that smaller firms operate in niche markets and sell products which customers
can delay or defer buying and that the absence of economies of scales lead to higher fixed
costs for these firms. These firms should have higher betas than their larger counterparts.
It is also possible that neither condition holds for a particular small firm. The answer will
therefore depend both on the company in question and the industry in which it operates.
In practice, analysts often add what is called a small firm premium to the cost of
equity for smaller firms. This small firm premium is usually estimated from historical
data to be the difference between the average annual returns on small market cap stocks
and the rest of the market “ about 3 to 3.5% when we look at the 1926-2003 period. This
practice can be dangerous for three reasons. The first is that the small firm premium has
been volatile and disappeared for an extended period in the 1980s. The second is that the
definition of a small market cap stock varies across time and that the historical small cap
premium is largely attributable to the smallest (among the small cap) stocks. The third is
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that using a constant small stock premium adjustment removes any incentive that the
analyst may have to examine the product characteristics and operating leverage of
individual small market cap companies more closely.

Degree of Financial Leverage Other things remaining equal, an increase in financial
leverage will increase the equity beta of a firm. Intuitively, we would expect that the
fixed interest payments on debt to increase earnings per share in good times and to push it
down in bad times.34 Higher leverage increases the variance in earnings per share and
makes equity investment in the firm riskier. If all of the firm's risk is borne by the
stockholders (i.e., the beta of debt is zero)35, and debt creates a tax benefit to the firm,
then,
βL = βu (1 + (1-t) (D/E))
where
βL = Levered Beta for equity in the firm
βu = Unlevered beta of the firm ( i.e., the beta of the firm without any debt)
t = Marginal tax rate for the firm
D/E = Debt/Equity Ratio
The marginal tax rate is the tax rate on the last dollar of income earned by the firm
generally will not be equal to the effective or average rates, and it is used because interest
expenses save taxes on the marginal income. Intuitively, we expect that as leverage
increases (as measured by the debt to equity ratio), equity investors bear increasing
amounts of market risk in the firm, leading to higher betas. The tax factor in the equation
captures the benefit created by the tax deductibility of interest payments.
The unlevered beta of a firm is determined by the types of the businesses in which
it operates and its operating leverage. This unlevered beta is often also referred to as the
asset beta since its value is determined by the assets (or businesses) owned by the firm.


34 Interest expenses always lower net income, but the fact that the firm uses debt instead of equity implies
that the number of shares will also be lower. Thus, the benefit of debt shows up in earnings per share.
35 to ignore the tax effects and compute the levered beta as
βL = βu (1+ D/E)
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 βD , the beta of equity can be written as:
βL = βu (1+(1-t)(D/E)) - βD (1-t)D/E
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Thus, the equity beta of a company is determined both by the riskiness of the business it
operates in, as well as the amount of financial leverage risk it has taken on. Since
financial leverage multiplies the underlying business risk, it stands to reason that firms
that have high business risk should be reluctant to take on financial leverage. It also
stands to reason that firms which operate in relatively stable businesses should be much
more willing to take on financial leverage. Utilities, for instance, have historically had
high debt ratios, but have not had high betas, mostly because their underlying businesses
have been stable and fairly predictable.
Breaking risk down into business and financial leverage components also
provides some insight into why companies have high betas, since they can end up with
high betas in one of two ways - they can operate in a risky business, or they can use very
high financial leverage in a relatively stable business.

Illustration 4.4: Effects of Financial Leverage on betas: Disney
From the regression for the period from 1999 to 2003, Disney had a beta of 1.01.
To estimate the effects of leverage on Disney, we began by estimating the average
debt/equity ratio between 1999 and 2003, using market values for debt and equity.
Average Market Debt/Equity Ratio between 1999 and 2003 = 27.5%
The unlevered beta is estimated using a marginal corporate tax rate of 37.3%:36
Unlevered Beta = Current Beta / (1 + (1 - tax rate) (Average Debt/Equity))
= 1.01 / (1 + (1 - 0.373)) (0.275) = 0.8615
The levered beta at different levels of debt can then be estimated:
Levered Beta = Unlevered Beta * [1 + (1 - tax rate) (Debt/ Equity)]
For instance, if Disney were to increase its debt equity ratio to 10%, its equity beta will
be
Levered Beta (@10% D/E) = 0.8615*(1+ (1 - 0.373) (0.10)) = 0.9155
If the debt equity ratio were raised to 25%, the equity beta would be
Levered Beta (@25% D/E) = 0.8615 *(1+ (1 - 0.373) (0.25)) = 1.00


36 The marginal corporate tax rate in the United States in 2003 was 35%. The marginal state and local tax
rates, corrected for federal tax savings, is estimated by Disney in its annual report to be 2.3%. Disney did
report some offsetting tax benefits that reduced their effective tax rate to 35%. We assumed that these
offsetting tax benefits were temporary.
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