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Table 4.6 summarizes the beta estimates for different levels of financial leverage ranging
from 0 to 90% debt.
Table 4.6: Financial Leverage and Betas
Debt to Capital Debt/Equity Ratio Beta Effect of Leverage
0.00% 0.00% 0.86 0.00
10.00% 11.11% 0.92 0.06
20.00% 25.00% 1.00 0.14
30.00% 42.86% 1.09 0.23
40.00% 66.67% 1.22 0.36
50.00% 100.00% 1.40 0.54
60.00% 150.00% 1.67 0.81
70.00% 233.33% 2.12 1.26
80.00% 400.00% 3.02 2.16
90.00% 900.00% 5.72 4.86

As Disneyâ€™s financial leverage increases, the beta increases concurrently.

levbeta.xls: This spreadsheet allows you to estimate the unlevered beta for a firm
and compute the betas as a function of the leverage of the firm.

marginaltaxrate.xls: This data set on the web has marginal tax rates for different
countries.

In Practice: Dueling Tax Rates
The marginal tax rate, which is the tax rate on marginal income (or the last dollar
of income) is a key input not only for the levered beta calculation but also for the after-
tax cost of debt that we will be estimating later in this chapter. Estimating it can be
problematic because firms seldom report it in their financials. Most firms report an
effective tax rate on taxable income in their annual reports and filings with the SEC. This
rate is computed by dividing the taxes paid by the net taxable income, reported in the
financial statement. The effective tax rate can be different from the marginal tax rate for
several reasons:
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If it is a small firm and the tax rate is higher for higher income brackets, the average
â€¢
tax rate across all income will be lower than the tax rate on the last dollar of income.
For larger firms, where most of the income is at the highest tax bracket, this is less of
an issue.
Publicly traded firms, at least in the United States, often maintain two sets of books,
â€¢
one for tax purposes and one for reporting purposes. They generally use different
accounting rules for the two and report lower income to tax authorities and higher
income in their annual reports. Since taxes paid are based upon the tax books, the
effective tax rate will usually be lower than the marginal tax rate.
Actions that defer or delay the payment of taxes can also cause deviations between
â€¢
marginal and effective tax rates. In the period when taxes are deferred, the effective
tax rate will lag the marginal tax rate. In the period when the deferred taxes are paid,
the effective tax rate can be much higher than the marginal tax rate.
The best source of the marginal tax is the tax code of the country where the firm earns its
operating income. If there are state and local taxes, they should be incorporated into the
marginal tax rate as well. For companies in multiple tax locales, the marginal tax rate
used should be the average of the different marginal tax rates, weighted by operating
income by locale.

Bottom Up Betas
Breaking down betas into their business, operating leverage and financial leverage
components provides us with an alternative way of estimating betas, where we do not
need past prices on an individual firm or asset to estimate its beta.
To develop this alternative approach, we need to introduce an additional feature
that betas possess that proves invaluable. The beta of two assets put together is a
weighted average of the individual asset betas, with the weights based upon market value.
Consequently, the beta for a firm is a weighted average of the betas of all of different
businesses it is in. Thus, the bottom-up beta for a firm, asset or project can be estimated
as follows.
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1. Identify the business or businesses that make up the firm, whose beta we are trying to
estimate. Most firms provide a breakdown of their revenues and operating income by
business in their annual reports and financial filings.
2. Estimate the average unlevered betas of other publicly traded firms that are primarily
or only in each of these businesses. In making this estimate, we have to consider the
following estimation issues:
Comparable firms: In most businesses, there are at least a few comparable firms
â€¢
and in some businesses, there can be hundreds. Begin with a narrow definition of
comparable firms, and widen it if the number of comparable firms is too small.
Beta Estimation: Once a list of comparable firms has been put together, we need
â€¢
to estimate the betas of each of these firms. Optimally, the beta for each firm will
be estimated against a common index. If that proves impractical, we can use betas
estimated against different indices.
Unlever first or last: We can compute an unlevered beta for each firm in the
â€¢
comparable firm list, using the debt to equity ratio and tax rate for that firm, or we
can compute the average beta, debt to equity ratio and tax rate for the sector and
unlever using the averages. Given the standard errors of the individual regression
betas, we would suggest the latter approach.
Averaging approach: The average beta across the comparable firms can be either
â€¢
a simple average or a weighted average, with the weights based upon market
capitalization. Statistically, the savings in standard error are larger if a simple
averaging process is used.
Adjustment for Cash: Investments in cash and marketable securities have betas
â€¢
close to zero. Consequently, the unlevered beta that we obtain for a business by
looking at comparable firms may be affected by the cash holdings of these firms.
To obtain an unlevered beta cleansed of cash:
Unlevered Beta
Unlevered Beta corrected for Cash =
(1 - Cash/ Firm Value)
3. To calculate the unlevered beta for the firm, we take a weighted average of the
unlevered betas, using the proportion of firm value derived from each business as the
!
weights. These firm values will have to be estimated since divisions of a firm usually
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do not have market values available.37 If these values cannot be estimated, we use
operating income or revenues as weights. This is also take into account the cash
holdings of the firm by computing it as a percent of firm value and attaching a beta of
zero if the cash is invested in riskless securities (like commercial paper or treasury
bills) or a higher beta if it is invested in riskier securities (like corporate bonds). This
weighted average is called the bottom-up unlevered beta.
4. Calculate the current debt to equity ratio for the firm, using market values if available.
If not, use the target leverage specified by the management of the firm or industry-
typical debt ratios.
5. Estimate the levered beta for the firm (and each of its businesses) using the unlevered
beta from step 3 and the leverage from step 4.
Clearly, this process rests on being able to identify the unlevered betas of individual
There are three advantages associated with using bottom-up betas and they are
significant:
We can estimate betas for firms that have no price history since all we need is an
â€¢
identification of the business they operate in. In other words, we can estimate bottom
up betas for initial public offerings, private businesses and divisions of companies.
Since the beta for the business is obtained by averaging across a large number of
â€¢
regression betas, it will be more precise than any individual firmâ€™s regression beta
estimate. The standard error of the average beta estimate will be a function of the
number of comparable firms used in step 2 above and can be approximated as
follows:
Average " Beta
" Average Beta =
Number of firms
Thus, the standard error of the average of the betas of 100 firms, each of which has a
standard error of 0.25, will be only 0.025. (0.25/âˆš100).
!
The bottom-up beta can reflect recent and even forthcoming changes to a firmâ€™s
â€¢
business mix and financial leverage, since we can change the mix of businesses and
the weight on each business in making the estimate.

37 The exception is when you have stock tracking each division traded separately in financial markets.
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This data set on the web has updated betas and unlevered betas by business
sector in the United States.

Illustration 4.5: Bottom Up Beta for Disney
Disney is an entertainment firm with diverse holdings. In addition to its theme
parks, it has significant investments in broadcasting and movies. To estimate Disneyâ€™s
beta today, we broke their business into four major components -
1. Studio Entertainment, which is the production and acquisition of motion pictures for
distribution in theatrical, television and home video markets as well as television
programming for network and syndication markets. Disney produces movies under
five imprints â€“ Walt Disney Pictures, Touchstone Pictures, Hollywood Pictures,
Miramax and Dimension.
2. Media Networks, which includes the ABC Television and Radio networks, and
reflects the acquisition made in 1995. In addition, Disney has an extensive exposure
in the cable market through the Disney channel, A & E and ESPN among others.
3. Park Resorts, which include Disney World (in Orlando, Florida) and Disney Land (in
Anaheim, California), as well as royalty holdings in Tokyo Disneyland and
Disneyland Paris. The hotels and villas at each of these theme parks are considered
part of the theme parks, since they derive their revenue almost exclusively from
visitors to these parks.
4. Consumer Products, which includes a grab bag of businesses including Disneyâ€™s
retail outlets, its licensing revenues, software, interactive products and publishing.
This breakdown reflects Disneyâ€™s reporting in its annual report. In reality, there are a
number of smaller businesses that Disney is in that are embedded in these four businesses
including:
Cruise lines: Disney operates two ships â€“ Disney Magic and Disney Wonder â€“
â€¢
that operate out of Florida and visit Caribbean ports.
Internet operations: Disney made extensive investments in the GO network and
â€¢
other online operations. While much of this investment was written off by 2002,
they still represent a potential source of future revenues.
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Sports franchises: Disney owns the National Hockey League franchise, the
â€¢
Mighty Ducks of Anaheim; in 2002 it sold itâ€™s stake in the Anaheim Angels, a
Major League Baseball team.
Absent detailed information on the operations of these businesses, we will assume that
they represent too small a portion of Disneyâ€™s overall revenues to make a significant
difference in the risk calculation. For the four businesses for which we have detailed
information, we estimated the unlevered beta by looking at comparable firms in each
business. Table 4.7 summarizes the comparables used and the unlevered beta for each of
Table 4.7: Estimating Unlevered Betas for Disneyâ€™s Business Areas
Unlevered
Average beta
Comparable Number levered Median Unlevered Cash/Firm corrected
for cash
Business firms of firms beta D/E beta Value
Networks companies 24 1.22 20.45% 1.0768 0.75% 1.0850
Theme park &
Parks and Entertainment
Resorts firms 9 1.58 120.76% 0.8853 2.77% 0.9105
Studio Movie
Entertainment companies 11 1.16 27.96% 0.9824 14.08% 1.1435
Toy and
apparel
retailers;
Entertainment
Consumer
Products software 77 1.06 9.18% 0.9981 12.08% 1.1353

To obtain the beta for Disney, we have to estimate the weight that each business is
of Disney as a company. The value for each of the divisions was estimated by applying
the typical revenue multiple at which comparable firm trade at to the revenue reported by
Disney for that segment in 2003.38 The unlevered beta for Disney as a company in 2003

38 We first estimated the enterprise value for each firm by adding the market value of equity to the book
value of debt and subtracting out cash. We divided the aggregate enterprise value by revenues for all of the
comparable firms to obtain the multiples. We did not use the averages of the revenue multiples of the
individual firms because a few outliers skewed the results. While Disney has about \$1.2 billion in cash, it
represents about 1.71% of firm value and will have a negligible impact on the beta. We have ignored it in
computing the beta for Disneyâ€™s equity.
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is a value-weighted average of the betas of each of the different business areas. Table 4.8
summarizes this calculation.
Table 4.8: Estimating Disneyâ€™s Unlevered Beta
Revenues in Estimated Firm Value Unlevered
Business 2002 EV/Sales Value Proportion beta
Media Networks \$10,941 3.41 \$37,278.62 49.25% 1.0850
Parks and Resorts \$6,412 2.37 \$15,208.37 20.09% 0.9105
Studio
Entertainment \$7,364 2.63 \$19,390.14 25.62% 1.1435
Consumer Products \$2,344 1.63 \$3,814.38 5.04% 1.1353
Disney \$27,061 \$75,691.51 100.00% 1.0674

The equity beta can then be calculated using the current financial leverage for Disney as a
firm. Combining the market value of equity of \$ 55,101 million an estimated market
value of debt of \$14,668 million39, we arrive at the current beta for Disney:
Equity Beta for Disney = 1.0674 (1+(1-.373)(14, 668/55,101) = 1.2456
This contrasts with the beta of 1.01 that we obtained from the regression, and is, in our
view, a much truer reflection of the risk in Disney.

In Practice: Canâ€™t find comparable firms?
A problem faced by analysts using the bottom up approach for some firms is a
paucity of comparable firms, either because the firm is unique in terms of the product it
offers or because the bulk of the firms in the sector are private businesses. Rather than
fall back on the regression approach, which is likely to yield a very wide range for the
beta, we would suggest the following to expand the comparable firm sample:
Geographic expansion: When analyzing firms from smaller markets, such as Brazil or
â€¢
Greece, the number of comparable firms will be small if we restrict ourselves only to
firms in the market. One way to increase sample size is to consider firms in the same
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