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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 Lionâ€™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 firmâ€™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 = Î±0 + Î±1 Tax Rate + Î±2 Pre-tax Returns + Î±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 Disneyâ€™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 â€“ 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 â€“

The effective tax rate of the firm, as a proxy for the tax advantages associated

â€¢

with debt.

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

â€¢

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

â€¢

generating capacity of a firm

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

â€¢

much firms value flexibility

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The results of the regression are presented below30:

DFR = 0.0488 + 0.810 Tax Rate â€“0.304 CLSH + 0.841 E/V â€“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) â€“0.304 (0.022) + 0.841 (.0767) â€“2.987 (.0209)

= 0.3257 or 32.57%

Based upon the debt ratios of other firms in the market and Disneyâ€™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. â˜ž: 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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