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The value of the levered firm is estimated in Table 8.21 by aggregating the effects of the
tax savings and the expected bankruptcy costs.
Table 8.21: Value of Disney with Leverage
Expected
Bankruptcy
Unlevered Value of
Firm Value Tax Benefits Cost Levered Firm
Debt Ratio $ Debt
0% $0 $65,294 $0 $2 $64,555
10% $6,979 $65,294 $2,603 $2 $67,158
20% $13,958 $65,294 $5,206 $246 $69,517
30% $20,937 $65,294 $7,809 $1,266 $71,099
40% $27,916 $65,294 $8,708 $9,158 $64,107
50% $34,894 $65,294 $6,531 $14,218 $56,870
60% $41,873 $65,294 $6,531 $14,218 $56,870
70% $48,852 $65,294 $6,531 $14,218 $56,870
80% $55,831 $65,294 $6,531 $14,218 $56,870
90% $62,810 $65,294 $6,531 $14,218 $56,870

The firm value is maximized at between 20 and 30% debt, which is consistent with the
results of the other approaches. These results are, however, very sensitive to both the
estimate of bankruptcy cost as a percent of firm value and the probabilities of default.

apv.xls: This spreadsheet allows you to compute the value of a firm, with leverage,
using the adjusted present value approach.

Benefits and Limitations of the Adjusted Present Value Approach

The advantage of the APV approach is that it separates the effects of debt into
different components and allows the analyst to use different discount rates for each
component. In this method, we do not assume that the debt ratio stays unchanged forever,
which is an implicit assumption in the cost of capital approach. Instead, we have the



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flexibility to keep the dollar value of debt fixed and to calculate the benefits and costs of
the fixed dollar debt.
These advantages have to be weighed against the difficulty of estimating
probabilities of default and the cost of bankruptcy. In fact, many analyses that use the
adjusted present value approach ignore the expected bankruptcy costs, leading them to
the conclusion that firm value increases as firms borrow money. Not surprisingly, they
conclude that the optimal debt ratio for a firm is 100% debt.
In general, with the same assumptions, the APV and the Cost of Capital
conclusions give identical answers. However, the APV approach is more practical when
firms are evaluating a dollar amount of debt, while the cost of capital approach is easier
when firms are analyzing debt proportions.26

This spreadsheet allows you to compute the value of a firm, with leverage, using the

adjusted present value approach.


Comparative Analysis

The most common approach to analyzing the debt ratio of a firm is to compare its
leverage to that of similar firms. A simple way to perform this analysis is to compare a
firm's debt ratio to the average debt ratio for the industry in which the firm operates. A
more complete analysis would consider the differences between a firm and the rest of the
industry, when determining debt ratios. We will consider both ways below.

Comparing to Industry Average

Firms sometimes choose their financing mixes by looking at the average debt
ratio of other firms in the industry in which they operate. For instance, the table below
compares the debt ratios27 at Disney and Aracruz to other firms in their industries:
Paper and Pulp (Emerging
Disney Entertainment Aracruz Market)


26 See Inselbag and Kaufold (1997).
27 For purposes of this analysis, we looked at debt without operating leases being capitalized because of the
difficulty of doing this for all of the comparable firms.

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Market Debt Ratio 21.02% 19.56% 30.82% 27.71%
Book Debt Ratio 35.10% 28.86% 43.12% 49.00%
Source: Value Line
Based on this comparison, Disney is operating at a debt Comparable (Firm): This is a
ratio slightly higher than those of other firms in the firm that is similar to the firm being
analyzed in terms of underlying
industry in both market and book value terms, while
characteristics - risk, growth and
Aracruz has a market debt ratio slightly higher than the
cash flow patterns. The conventional
average firm but a book debt ratio slightly lower.
definition of comparable firm is one
The underlying assumptions in this comparison which is the same business as the
are that firms within the same industry are comparable, one being analyzed, and of similar
size.
and that, on average, these firms are operating at or
close to their optimal. Both assumptions can be questioned, however. Firms within the
same industry can have different product mixes, different amounts of operating risk,
different tax rates, and different project returns. In fact, most do. For instance, Disney is
considered part of the entertainment industry, but its mix of businesses is very different
from that of Lion™s Gate, which is primarily a movie company, or Liberty Media.
Furthermore, Disney's size and risk characteristics are very different from that of Pixar,
which is also considered part of the same industry group. There is also anecdotal
evidence that since firms try to mimic the industry average, the average debt ratio across
an industry might not be at or even close to its optimal.


dbtfund.xls: There is a dataset on the web that summarizes market value and
book value debt ratios, by industry, in addition to other relevant characteristics.

Controlling for Differences between Firms

Firms within the same industry can exhibit wide differences on tax rates, capacity
to generate operating income and cash flows, and variance in operating income.
Consequently, it can be dangerous to compare a firm™s debt ratio to the industry, and
draw conclusions about the optimal financing mix. The simplest way to control for
differences across firms, while using the maximum information available in the market, is




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to run a regression, regressing debt ratios against these variables, across the firms in a
industry:
Debt Ratio = ±0 + ±1 Tax Rate + ±2 Pre-tax Returns + ±3 Variance in operating income
There are several advantages to the crosssectional approach. Once the regression
has been run and the basic relationship established (i.e., the intercept and coefficients
have been estimated), the predicted debt ratio for any firm can be computed quickly using
the measures of the independent variables for this firm. If a task involves calculating the
optimal debt ratio for a large number of firms in a short time period, this may be the only
practical way of approaching the problem, since the other chapters described in this
chapter are time intensive.28
There are also limitations to this approach. The coefficients tend to shift over
time. Besides some standard statistical problems and errors in measuring the variables,
these regressions also tend to explain only a portion of the differences in debt ratios
between firms.29 However, the regressions provide significantly more information than
does a naive comparison of a firm's debt ratio to the industry average.

Illustration 8.9: Estimating Disney™s debt ratio using the cross sectional approach
This approach can be applied to look at differences within a industry or across the
entire market. We can illustrate looking at the Disney against firms in the entertainment
sector first and then against the entire market.
To look at the determinants of debt ratios within the entertainment industry, we
regressed debt ratios of firms in the industry against two variables “ the growth in sales
over the previous five years and the EBITDA as a percent of the market value of the firm.
Based on our earlier discussion of the determinants of capital structure, we would expect
firms with higher operating cashflows (EBITDA) as a percent of firm value to borrow
more money. We would also expect higher growth firms to weigh financial flexibility




28 There are some who have hypothesized that under-leveraged firms are much more likely to be taken over
than firms that are over-leveraged or correctly leveraged. If we want to find the 100 firms on the New York
Stock Exchange that are most under-leveraged, the cross-sectional regression and the predicted debt ratios
that come out of this regression can be used to find this group.
29 The independent variables are correlated with each other. This multi-collinearity makes the coefficients
unreliable and they often have signs that go counter to intuition.

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more in their debt decision and borrow less. The results of the regression are reported
below, with t statistics in brackets below the coefficients:
Debt to Capital = 0.2156 - 0.1826 (Growth in Sales) + 0.6797 (EBITDA/ Firm Value)
(4.91) (1.91) (2.05)
The dependent variable is the market debt to capital ratio, and the regression has an R-
squared of 14%. While there is statistical significance, it is worth noting that the
predicted debt ratios will have substantial standard errors associated with them. Even so,
if we use the current values for these variables for Dinsey in this regression, we get a
predicted debt ratio:
DFRDisney= 0.2156 - 0.1826 (.0668) + 0.6797 (.0767) = 0.2555 or 25.55%
At their existing debt ratio of 21%, Disney is slightly under levered. Thus, relative to the
industry in which it operates and its specific characteristics, Disney could potentially
borrow more.
One of the limitations of this analysis is that there are only a few firms within
each industry. This analysis can be extended to all firms in the market. While firms in
different businesses differ in terms of risk and cash flows, and these differences can
translate into differences in debt ratios, we can control for the differences in the
regression. To illustrate, we regressed debt ratios of all listed firms in the United States
against four variables “
The effective tax rate of the firm, as a proxy for the tax advantages associated

with debt.
Closely held shares as a percent of shares outstanding (CLSH) as a measure of

how much separation there is between managers and stockholders (and hence as a
proxy for debt as a disciplinary mechanism).
EBITDA as a percent of enterprise value (E/V) as a measure of the cash flow

generating capacity of a firm
Capital expenditures as a percent of total assets (CPXFR) as a measure of how

much firms value flexibility




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The results of the regression are presented below30:
DFR = 0.0488 + 0.810 Tax Rate “0.304 CLSH + 0.841 E/V “2.987 CPXFR
(1.41a) (8.70a) (3.65b) (7.92b) (13.03a)
where DFR is debt as a percentage of the market value of the firm (debt + equity). The R-
Squared for this regression is 53.3%. If we plug in the values for Disney into this
regression, we get a predicted debt ratio:
DFRDisney= 0.0488 + 0.810 (0.3476) “0.304 (0.022) + 0.841 (.0767) “2.987 (.0209)
= 0.3257 or 32.57%
Based upon the debt ratios of other firms in the market and Disney™s financial
characteristics, we would expect Disney to have a debt ratio of 32.57%. Since its actual
debt ratio is 21.02%, Disney is under levered.

8.7. ˜: Optimal Debt Ratios based upon Comparable Firms
The predicted debt ratio from the regression shown above will generally yield
(a) a debt ratio similar to the optimal debt ratio from the cost of capital approach
(b) a debt ratio higher than the optimal debt ratio from the cost of capital approach
(c) a debt ratio lower than the optimal debt ratio from the cost of capital approach
(d) any of the above, depending upon ...
Explain.




dbtreg.xls: There is a dataset on the web that summarizes the latest debt ratio
regression across the entire market.


Selecting the Optimal Debt Ratio
Using the different approaches for estimating optimal debt ratios, we do come up
with different estimates of the right financing mix for Disney and Aracruz. Table 8.22
summarizes them:




30 The numbers in brackets below the coefficients represent t statistics. The * indicates statistical
significance.

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Table 8.22: Summary of Predicted Debt Ratios
Disney Aracruz
Actual Debt Ratio 21.02% 30.82%
Optimal
I. Operating Income 30.00% -
II. Cost of Capital
With no constraints 30.00% 30.00%
With BBB constraint 30.00% 30.00%
III. APV 30.00% 30.00%
V. Comparable
To Industry 25.55% 28.56%
To Market 32.57% -
While there are differences in the estimates across the different approaches, a few
consistent conclusions emerge: Disney, at its existing debt ratio, is slightly underlevered,
though the increase in value from moving to the optimal is small. Aracruz is slightly
over levered, based upon normalized operating income.
Bookscape also has excess debt capacity, if we estimate the optimal debt ratio
using the cost of capital approach. However, bankruptcy may carry a larger cost to the
private owner of Bookscape than it would to the diversified investors of the Disney or
Aracruz. We would therefore be cautious about using this excess debt capacity.

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