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business that are listed and traded in other markets “ European markets for Greece
and Latin American markets for Brazil. With commodity companies that trade in
global markets, like paper and oil companies, we can consider a global sample.

39 The details of this calculation will be explored later in this chapter.

Production Chain: Another way to expand the sample is to look for firms that either

provide supplies to the firm that you are analyzing or firms that feed off your firm.
For instance, when analyzing book retailers, we can consider book publishers as part
of the sample since the fortunes of the two are entwined. It is unlikely that one of
these groups can have a good year without the other partaking in the success
Customer specialization: Using the same rationale, the betas of firms that derive the

bulk of their revenues from a sector may be best estimated using firms in the sector.
Thus, the beta of a law firm that derives all of its revenues from investment banks
may be best estimated by looking at the betas of investment banks.

Illustration 4.6: Bottom-up Beta for Bookscape Books
We cannot estimate a regression beta for Bookscape Books, the private firm, since
it does not have a history of past prices. We can, however, estimate the beta for
Bookscape Books, using the bottom up approach. Since we were able to find only three
publicly traded book retailers in the United States, we expanded the sample to include
book publishers. We list the betas of these firms as well as debt, cash and equity values in
Table 4.9:
Table 4.9: Betas and Leverage of Publicly Traded Book Retailers and Publishers
Firm Beta Debt Equity Cash
Books-A-Million 0.532 $45 $45 $5
Borders Group 0.844 $182 $1,430 $269
Barnes & Noble 0.885 $300 $1,606 $268
Courier Corp 0.815 $1 $285 $6
Info Holdings 0.883 $2 $371 $54
John Wiley &Son-A 0.636 $235 $1,662 $33
Scholastic Corp 0.744 $549 $1,063 $11
0.7627 $1,314 $6,462 $645

While the firms in this sample are very different in terms of market capitalization, the
betas are consistent. To estimate the unlevered beta for the sector, we use the average
beta across the firms in conjunction with the aggregate values of debt and market value of
equity (with a marginal tax rate of 35%):
Debt to Equity Ratio for industry = 1314/6462 = 20.33%
Unlevered Beta = 0.7627/(1+(1-.35)(.2033)) = 0.6737

To correct for cash, we use the aggregate cash balance across the firms:
Unlevered Beta corrected for cash = 0.6737 (1 “ 645/(1314+6462)) = 0.7346
Since Bookscape has a negligible cash balance, the unlevered beta for book retailing is
also the unlevered beta for the firm.
Since the debt/equity ratios used are market debt equity ratios, and the only debt
equity ratio we can compute for Bookscape is a book value debt equity ratio, we have
assumed that Bookscape is close to the industry average debt to equity ratio of 20.33%.
Using a marginal tax rate of 40% (based upon personal income tax rates) for Bookscape,
we get a levered beta of 0.82.
Levered beta for Bookscape = 0.7346 (1 +(1-.40) (.2033)) = 0.82

Illustration 4.7: Bottom up Beta for Aracruz
The bottom up beta for Aracruz is difficult to estimate if we remain within its
home market, which is Brazil, for two reasons. First, there are only three publicly traded
firms within the market that are in the same line of business as Aracruz (i.e. paper and
pulp production). Second, the betas for all Brazilian firms are unreliable because the
index used to estimate these betas, the Bovespa, is a narrow one, dominated by a few
large companies.
There are three groups of comparable firms that we can use as comparable firms
in the bottom-up beta estimate:
Emerging Market Paper and Pulp companies: This is a much larger sample of

firms. While the individual firm betas may skewed by the limitations of the local
indices, the errors should average out over the sample.
U.S Paper and Pulp companies: The advantage gained is not just in terms of the

number of firms but also in terms of reliable betas. The peril in this approach is
that the risk in U.S. companies can be different from the risk in Brazilian because
of regulatory differences.40
Global Paper and Pulp companies: This is the largest group and includes a

diverse group of companies in both emerging and developed markets. Since betas

are measures of relative risk, we would argue that barring significant differences
in regulation and monopoly power across markets, it is reasonable to compare
betas across markets.
Number of Average Unlevered
Cash/Value for cash
firms Beta D/E Beta
Markets 111 0.6895 38.33% 0.5469 6.58% 0.5855
US 34 0.7927 83.57% 0.5137 2.09% 0.5246
Global 288 0.6333 38.88% 0.5024 6.54% 0.5375

The tax rates used were 32% for emerging market companies, 35% for U.S. companies
and 33% for Global companies, based upon averaging the marginal tax rates in each
group. The unlevered beta of emerging market companies is slightly higher than the U.S.
and global groupings. While the average beta for U.S. companies is higher than the rest
of the sample, the difference is entirely due to the higher debt to equity ratios of these
companies. We will use an emerging market unlevered beta of 0.59 as the beta for the
paper and pulp business that Aracruz is involved in.
We can estimate the unlevered beta for Aracruz in two steps. First, we consider
the asset composition for Aracruz. In addition to being in the paper business, Aracruz has
a cash balance of 1,018 million BR, which is roughly 7.07% of the firm value. Since this
is much larger than the typical cash balances of the companies on our comparable firm
list, and the beta of cash is zero, the unlevered beta for Aracruz can be estimated as
Unlevered Beta for Aracruz = (0.9293) (0.585) + (0.0707) (0) = 0.5440
Aracruz had gross debt outstanding of 4.093 million BR at the end of 2003 and a market
value of equity of 9,189 million BR leading to a debt/equity ratio of 44.59%. Allowing
for a tax rate of 34% (the Brazilian marginal tax rate), the levered beta for Aracruz can
then be estimated as follows:
Levered Beta for Aracruz = 0.5440 (1+ (1-.34) (.4459)) = 0.7040

40 As a counterpoint, paper and pulp companies are commodity companies and are governed by the
vagaries of the price of paper and pulp. In other words, there is a reasonable argument to be made that
paper and pulp companies globally are governed by the same primary risk factors.

If we wanted a levered beta for just the paper business of Aracruz, we would use the
levered beta for the paper and pulp business and the gross debt to equity ratio for the
Levered Beta for paper business = 0.585 (1+ (1-.34) (.4459))) = 0.7576
In Practice: Gross Debt or Net Debt
Many analysts in Europe and Latin America prefer to subtract the cash from the
gross debt to arrive at a net debt figure. While there is no conceptual problem with this
approach, they should remain consistent. Consider, the calculation of unlevered and
levered betas in illustration 4.7. First, the computation of unlevered beta for the emerging
market paper and pulp companies would have been based upon the net debt to equity
ratio for firms in the sector rather than the debt to equity ratio:
Net Debt/Equity = (Gross Debt “ Cash)/ Equity = 29.22%
Unlevered Beta = Levered Beta / (1 + (1- tax rate) (Net D/E))
= 0.6895/ (1 + (1-.32)(.2922)) = 0.5751
This unlevered beta is already corrected for cash and no further adjustments are needed.
To make the levered beta calculation for Aracruz, we would use the net debt to equity
ratio for the company. The net debt is computed by subtracting Aracruz™s cash balance of
1,018 million BR from its gross debt of 4,093 million BR yielding a net debt to equity
ratio of 33.47%.
Levered Beta for Aracruz = Unlevered Beta (1 + (1 “ tax rate) (Net D./E))
= 0.5751 (1 + (1-.34)(.3347)) = 0.7022
Again, we can dispense with the adjustment for cash since the net debt to equity ratio
captures the cash holdings.
Notice that the levered beta of 0.7040 computed for Aracruz in illustration 4.7
does not exactly match the computation using the net debt to equity ratio. The reason lies
in an implicit assumption that we make when we net cash against debt. We assume that
both debt and cash are riskless and that the tax benefit from debt is exactly offset by the
tax paid on interest earned on cash. It is generally not a good idea to net debt if the debt is
very risky or if the interest rate earned on cash is substantially lower than the interest rate
paid on debt.

With a net debt to equity ratio, there is one more potential complication. Any firm
that has a cash balance that exceeds its debt will have negative net debt and using this
negative net D/E ratio will yield an unlevered beta that exceeds the levered beta. While
this may trouble some, it makes sense because the unlevered beta reflects the beta of the
business that the firm operates in. Firms that have vast cash balances that exceed their
borrowing can have levered betas that are lower than the unlevered betas of the
businesses they operate in.

Illustration 4.8: Bottom Up Beta for Deutsche Bank
There are a few banks in Germany that can be viewed as competitors to Deutsche
Bank, though none of them are as large as it is, or have as large of a stake in investment
banking. Since the rules and regulatory constraints governing banking in the United
States are different from the rules governing banks in much of the Eurozone, we will look
at the betas of European banks with market capitalizations exceeding $ 5 billion to
estimate the beta for the commercial banking arm of Deutsche Bank. To estimate the beta
of Deutsche Bank™s investment banking arm, which includes Morgan Grenfell and
Banker™s Trust, we use the betas of investment banking firms in the United States. The
results are presented below:
Comparable Firms Number of Average Beta
Large commercial Banks in 58 0.7345
U.S. investment banks 9 1.5167
Note that we do not adjust for differences in leverage, since regulatory constraints and the
needs of the business keep the leverage of most commercial banks at similar levels.41 The
beta for Deutsche Bank as a firm can be estimated as a weighted average of these two
betas. Using estimating market value weights of 69% for the commercial banking and

41 Regulators often specify capital ratios, specified in terms of book values of debt and equity that banks
must meet to stay in business. Most banks stay close to these ratios though some tend to be better
capitalized than others.

31% for the investment banking arms (based upon the revenues that Deutsche Bank made
from each in the most recent year), we arrive at a beta for Deutsche Bank™s equity:42
Deutsche Bank™s beta = 0.7345 (0.69) + 1.5167 (0.31) = 0.9767
This beta will change over time as the weights on the businesses change.

Calculating Betas after A Major Restructuring
The bottom-up process of estimating betas provides a solution when firms go
through a major restructuring, where they change both their financial mix and leverage.
In these cases, the regression betas are misleading because they do not reflect fully the
effects of these changes. Disney™s beta, estimated from the bottom up approach, is likely
to provide a more precise estimate than the beta from a regression, given Disney™s
acquisition of Capital Cities and its increase in leverage. In fact, a firm™s beta can be
estimated even before the restructuring becomes effective using this approach. In the
illustration that follows, for instance, we estimate Disney™s beta just before and after its
acquisition of Capital Cities/ABC, allowing for the changes in both the business mix and
the leverage.

Illustration 4.9: Beta of a Firm After an Acquisition: Disney / Capital Cities
In 1995, Disney announced that it was acquiring Capital Cities, the owner of the
ABC television and radio network, for approximately $ 120 per share, and that it would
finance the acquisition partly through the issue of $ 10 billion in debt. At the time of the
acquisition, Disney had a market value of equity of $31.1 billion, debt outstanding of
$3.186 billion and a levered beta of 1.15. Capital Cities, based upon the $120 offering
price, had a market value of equity of $18.5 billion, debt outstanding of $ 615 million and
a levered beta of 0.95.
In order to evaluate the effects of the acquisition on Disney™s beta, we do the
analysis in two parts. First, we examine the effects of the merger on the business risk of
the combined firm, by estimating the unlevered betas of the two companies, and
calculating the combined firm™s unlevered beta.

42Deutsche Bank does not explicitly break down income into commercial banking and investment banking
components. The firm reported 5,470 million in Euros in trading revenues (investment banking), $ 15,179
million in net interest revenues and fiduciary commissions (commercial banking).

Disney™s unlevered beta = 1.15/(1+0.64*0.10) = 1.08
Capital Cities unlevered beta = 0.95/(1+0.64*0.03) = 0.93
The unlevered beta for the combined firm can be calculated as the weighted average of
the two unlevered betas, with the weights being based upon the market values of the two
Value of Disney = 31,100 + 3,186 = $ 34, 286 million
Value of Capital Cities = 18,500 + 615 = $ 19, 115 million
Unlevered Beta for combined firm = 1.08 (34286/53401) + 0.93 (19115/53401)
= 1.026
Then, we examine the effects of the financing of the merger on the betas, by calculating
the debt/equity ratio for the combined firm after the acquisition. Since Disney is
assuming the old debt of Capital Cities, we add that debt to Disney™s existing debt and
add the additional $ 10 billion in debt used to fund this acquisition:44
Debt = Capital Cities Old Debt + Disney™s Old Debt + New Debt
= $ 615 + $ 3,186 + $ 10,000 = $ 13,801 million
Equity = Disney™s Old Equity + New Equity used for Acquisition
= $ 31,100 + $ 8,500 = $ 39,600 million
where New Equity = Total Cost of Acquisition - New Debt Issued
= $ 18,500 - $ 10,000 = $ 8,500 million
Notice that the equity in Capital Cities of $18,500 million disappears after the acquisition
and is replaced with new debt of $ 10,000 million and new Disney equity of $ 8,500
million. The debt/equity ratio can then be computed as follows “
D/E Ratio = 13,801/39600 = 34.82%
This debt/equity ratio in conjunction with the new unlevered beta for the combined firm
yields a new beta of
New Beta = 1.026 (1 + 0.64 (.3482)) = 1.25

43 Unlevered betas should always be weighted based upon firm values. With levered (equity) betas, the
values of equity can be used as weights.
44 If Disney had paid off Capital Cities™ old debt instead of assuming it, we could have ignored it in the
debt calculation. However, Disney would then have had to raise an extra $615 million in financing to fund
this acquisition.


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