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Cost of debt
9.15% 8.83% 8.59% 8.50% 10.20% 13.16% 14.36% 15.56% 16.76% 17.96%
Cost of Capital
Value (perpetual growth) $62,279 $66,397 $69,837 $71,239 $51,661 $34,969 $30,920 $27,711 $25,105 $22,948


Constrained Cost of Capital Approaches

The cost of capital approach that we have described is unconstrained, since our
only objective is to minimize the cost of capital. There are several reasons why a firm
may choose not to view the debt ratio that emerges from this analysis as optimal. First,
the firm™s default risk at the point at which the cost of capital is minimized may be high
enough to put the firm™s survival at jeopardy.
Investment Grade Bonds: An investment
Stated in terms of bond ratings, the firm may grade bond is one with a rating greater than
BBB. Some institutional investors, such as
have a below-investment grade rating. Second, pension funds, are constrained from holding
bonds with lower ratings.
the assumption that the operating income is
unaffected by the bond rating is a key one. If the
operating income declines as default risk increases, the value of the firm may not be
maximized where the cost of capital is minimized. Third, the optimal debt ratio was
computed using the operating income from the most recent financial year. To the extent
that operating income is volatile and can decline, firms may want to curtail their
borrowing. In this section, we will consider ways in which we can bring each of these
considerations into the cost of capital analysis.

Bond Rating Constraint
One way of using the cost of capital approach, without putting firms into financial
jeopardy, is to impose a “bond rating constraint” on the cost of capital analysis. Once this
constraint has been imposed, the optimal debt ratio is the one that has the lowest cost of
capital, subject to the constraint that the bond rating meets or exceeds a certain level.
While this approach is simple, it is essentially subjective and is therefore open to
manipulation. For instance, the management at Disney could insist on preserving a AA
rating and use this constraint to justify reducing its debt ratio. One way to make managers
more accountable in this regard is to measure the cost of a rating constraint.
Cost of Rating Constraint = Maximum Firm Value without constraints
- Maximum Firm Value with constraints


If Disney insisted on maintaining a AA rating, its constrained optimal debt ratio would be
10%. The cost of preserving the constraint can then be measured as the difference
between firm value at 30% and at 20%.
Cost of Rating Constraint = Value at 30% Debt - Value at 10% Debt
= $71,239 - $ 66,397
= $ 4,842 million
This loss in value is probably overstated since we are keeping operating income fixed.
Notwithstanding this concern, the loss in value that can accrue from having an
unrealistically high rating constraint can be viewed as the cost of being too conservative
when it comes to debt policy.

8.4. ˜: Agency Costs and Financial Flexibility
In the last chapter, we consider agency costs and lost flexibility as potential costs of using
debt. Where in the cost of capital approach do we consider these costs?
a. These costs are not considered in the cost of capital approach
b. These costs are fully captured in the cost of capital through the costs of equity and
debt, which increase as you borrow more money.
c. These costs are partially captured in the cost of capital through the costs of equity and
debt, which increase as you borrow more money.

Sensitivity Analysis
The optimal debt ratio we estimate for a firm is a function of all the inputs that go
into the cost of capital computation “ the beta of the firm, the riskfree rate, the risk
premium and the default spread. It is also, indirectly, a function of the firm™s operating
income, since interest coverage ratios are based upon this income, and these ratios are
used to compute ratings and interest rates.
The determinants of the optimal debt ratio for a firm can be divided into variables
specific to the firm, and macro economic variables. Among the variables specific to the
firm that affect its optimal debt ratio are the tax rate, the firm™s capacity to generate
operating income and its cash flows. In general, the tax benefits from debt increase as the
tax rate goes up. In relative terms, firms with higher tax rates will have higher optimal
debt ratios than will firms with lower tax rates, other things being equal. It also follows

that a firm's optimal debt ratio will increase as its tax rate increases. Firms that generate
higher operating income and cash flows, as a percent of firm market value, also can
sustain much more debt as a proportion of the market value of the firm, since debt
payments can be met much more easily from prevailing cash flows.
The macroeconomic determinants of optimal debt ratios include the level of
interest rates and default spreads. As interest rates increase, the costs of debt and equity
both increase. However, optimal debt ratios tend to be lower when interest rates are
higher, perhaps because interest coverage ratios drop at higher rates. The default spreads
commanded by different ratings classes tend to increase during recessions and decrease
during recoveries. Keeping other things constant, as the spreads increase, optimal debt
ratios decrease, for the simple reason that higher default spreads result in higher costs of
How does sensitivity analysis allow a firm to choose an optimal debt ratio? After
computing the optimal debt ratio with existing inputs, firms may put it to the test by
changing both firm-specific inputs (such as operating income) and macro-economic
inputs (such as default spreads). The debt ratio the firm chooses as its optimal then
reflects the volatility of the underlying variables, and the risk aversion of the firm™s

Illustration 8.4: Sensitivity Analysis on Disney™s Optimal Debt Ratio
In the base case, in illustration 8.2, we used Disney™s operating income in 2003 to
find the optimal debt ratio. We could argue that Disney's operating income is subject to
large swings, depending upon the vagaries of the economy and the fortunes of the
entertainment business, as shown in Table 8.11.
Table 8.11: Disney's Operating Income History: 1987 “ 2003
Year EBIT % Change in
1987 756
1988 848 12.17%
1989 1177 38.80%
1990 1368 16.23%
1991 1124 -17.84%
1992 1287 14.50%
1993 1560 21.21%


1994 1804 15.64%
1995 2262 25.39%
1996 3024 33.69%
1997 3945 30.46%
1998 3843 -2.59%
1999 3580 -6.84%
2000 2525 -29.47%
2001 2832 12.16%
2002 2384 -15.82%
2003 2713 13.80%

There are several ways of using the information in such historical data to modify the
analysis. One approach is to look at the firm's performance during previous downturns.
In Disney's case, the operating income in 2002 dropped by 15.82% as the firm struggled
with the aftermath of terrorism. In 2000, Disney™s self-inflicted wounds, from over
investment in the internet business and poor movies, caused operating income to
plummet almost 30%. A second approach is to obtain a statistical measure of the
volatility in operating income, so that we can be more conservative in choosing debt
levels for firms with more volatile earnings. In Disney™s case, the standard deviation in
percentage changes in operating income is 19.54%. Table 8.12 illustrates the impact of
lowering operating from current levels on the optimal debt level.
Table 8.12: Effects Of Operating Income On Optimal Debt Ratio
% Drop in EBITDA EBIT Optimal Debt Ratio
0% $ 2,805 30%
5% $ 2,665 20%
10% $ 2,524 20%
15% $ 2385 20%
20% $ 2,245 20%
The optimal debt ratio declines to 20% when the operating income decreases by 5% but
the optimal stays at 20% for larger decreases in operating income (up to 40%).
In Practice: EBIT versus EBITDA
In recent years, analysts have increasingly turned to using EBITDA as a measure
of operating cashflows for a firm. It may therefore seem surprising that we focus on
operating income or EBIt far more than EBITDA when computing the optimal capital


structure. The interest coverage ratios, for instance, are based upon operating income and
not EBITDA. While it is true that depreciation and amortization are non-cash expenses
and should be added back to cash flows, it is dangerous for a firm with ongoing
operations to depend upon the cashflows generated by these items to service debt
payments. After all, firms with high depreciation and amortization expenses usually have
high ongoing capital expenditures. If the cash inflows from depreciation and amortization
are redirected to make interest payments, the reinvestment made by firms will be
insufficient to generate future growth or to maintain existing assets.

Normalized Operating Income
A key input that drives the optimal capital Normalized Income: This is a
measure of the income that a firm can
structure is the current operating income. If this
make in a normal year, where there are no
income is depressed, either because the firm is a
extraordinary gains or losses either from
cyclical firm or because there are firm-specific
firm-specific factors (such as write offs
factors that are expected to be temporary, the and one-time sales) or macro economic
optimal debt ratio that will emerge from the factors (such as recessions and economic
analysis will be much lower than the firm™s true booms).
optimal. For example, automobile manufacturing firms would have had very low debt
ratios if the optimal debt ratios had been computed based upon the operating income in
2001 and 2002, which were recession years. If the drop in operating income is
permanent, however, this lower optimal debt ratio is, in fact, the correct estimate.
When evaluating a firm with depressed current operating income, we must first
decide whether the drop in income is temporary or permanent. If the drop is temporary,
we must estimate the normalized operating income for the firm. The normalized
operating income is an estimate of how much the firm would earn in a normal year, i.e., a
year without the specific events that are depressing earnings this year. Most analysts
normalize earnings by taking the average earnings over a period of time (usually 5 years).

mgnroc.xls: There is a dataset on the web that summarizes operating margins
and returns on capital by industry group in the United States for the most recent quarter.


Operating Income as a Function of Default Risk
In the analysis we just completed for the Disney, we assumed that operating
income would remain constant while the debt ratios changed. While this assumption
simplifies our analysis substantially, it is not realistic. The operating income, for many
firms, will drop as the default risk increases; this, in fact, is the cost we labeled as an
indirect bankruptcy cost in the last chapter. The drop is likely to become more
pronounced as the default risk falls below an acceptable level; for instance, a bond rating
below investment grade may trigger significant losses in revenues and increases in
A general model for optimal capital structure would allow both operating income
and cost of capital to change as the debt ratio changes. We have already described how
we can estimate cost of capital at different debt ratios, but we could also attempt to do the
same with operating income. For instance, we could estimate how the operating income
for the Aracruz would change as debt ratios and default risk changes by looking at the
effects of rating downgrades on the operating income of other paper and pulp companies.
If both operating income and cost of capital change, the optimal debt ratio may no
longer be the point at which the cost of capital is minimized. Instead, the optimal has to
be defined as that debt ratio at which the value of the firm is maximized. We will
consider an example of such an analysis in a few pages, when we estimate the optimal
debt ratio for J.P. Morgan.

Illustration 8.5: Applying the Cost of Capital Approach with Normalized Operating
Income to Aracruz Cellulose
Aracruz Cellulose, the Brazilian pulp and paper manufacturing firm, reported
operating income of 887 million BR on revenues of 3176 million BR in 2003. This was
significantly higher than it™s operating income of 346 million BR in 2002 and 196 million
Br in 2001. We estimated the optimal debt ratio for Aracruz, based upon the following
In 2003, Aracruz had depreciation of 553 million BR and capital expenditures

amounted to 661 million BR.
Aracruz had debt outstanding of 4,094 million BR with a dollar cost of debt of 7.25%.


The corporate tax rate in Brazil is estimated to be 34%.

Aracruz had 859.59 million shares outstanding, trading 10.69 BR per share. The beta

of the stock is estimated, using comparable firms, to be 0.70.
In chapter 4, we estimated Aracruz™s current dollar cost of capital to be 10.33%, using an
equity risk premium of 12.49% for Brazil:
Current $ Cost of Equity = 4% + 0.70 (12.49%) = 12.79%
Market Value of Equity = 10.69 BR/share * 859.59= 9,189 million BR
Current $ Cost of Capital
= 12.79% (9,189/(9,189+4,094)) + 7.25% (1-.34) (4,094/(9189+4,094) = 10.33%
We made three significant changes in applying the cost of capital approach to Aracruz as
opposed to Disney:
The operating income at Aracruz is a function of the price of paper and pulp in

global markets. While 2003 was a very good year for the company, its income
history over the last decade reflects the volatility created by pulp prices. We
computed Aracruz™s average pre-tax operating margin over the last 10 years to be
25.99%. Applying this lower average margin to 2003 revenues generates a
normalized operating income of 796.71 million BR. We will compute the optimal


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