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estimated separately for financial service firms; applying manufacturing company
spreads will result in absurdly low ratings for even the safest banks, and very low optimal
debt ratios. Furthermore, the relationship between interest coverage ratios and ratings
tend to be much weaker for financial service firms than it is for manufacturing firms. The
second is a measurement problem that arises partly from the difficulty in estimating the
debt on a financial service company™s balance sheet.
Given the mix of deposits, repurchase agreements, short term financing and other
liabilities that may appear on a financial service firm™s balance sheet, one solution is to
focus only on long term debt, defined tightly, and to use interest coverage ratios defined
using only long term interest expenses. The third problem is that financial service firms
are regulated, and have to meet capital ratios that are defined in terms of book value. If,
in the process of moving to an optimal market value debt ratio, these firms violate the
book capital ratios, they could put themselves in jeopardy.

Illustration 8.7: Applying the Cost of Capital Approach to Deutsche Bank
We analyze the optimal capital structure for Deutsche Bank using data from 2004.
To begin, we make the following assumptions:
The earnings before long-term interest expenses and taxes amounted to 7,405 million

Euros in 2003.
Deutsche Bank was ranked AA- and paid 5.05% on its long-term debt in 2004. It had

82 billion in long term-debt outstanding at the end of the year.
Deutsche Bank had 581.85 million shares outstanding, trading at 70.40 Euros per

share, and the bottom-up beta of 0.98 that we estimated for the company in chapter 4
is the current beta. The tax rate for the firm is 38% and the riskless Euro rate is

20 Davis and Lee (1997) consider some of the issues related to estimating the optimal debt ratio for a bank.


The interest coverage ratios used to estimate the bond ratings are adjusted to reflect

the ratings of financial service firms.
The operating income for Deutsche Bank is assumed to drop if its rating drops. Table

8.16 summarizes the interest coverage ratios and estimated operating income drops
for different ratings classes.
Table 8.16: Interest Coverage Ratios, Ratings and Operating Income Declines
Long Term Interest Coverage Rating is Spread is Operating Income
Ratio Decline
< 0.05 D 16.00% -50.00%
0.05 “ 0.10 C 14.00% -40.00%
0.10 “ 0.20 CC 12.50% -40.00%
0.20 - 0.30 CCC 10.50% -40.00%
0.30 “ 0.40 B- 6.25% -25.00%
0.40 “ 0.50 B 6.00% -20.00%
0.50 “ 0.60 B+ 5.75% -20.00%
0.60 “ 0.75 BB 4.75% -20.00%
0.75 “ 0.90 BB+ 4.25% -20.00%
0.90 “ 1.20 BBB 2.00% -20.00%
1.20 “ 1.50 A- 1.50% -17.50%
1.50 “ 2.00 A 1.40% -15.00%
2.00 “ 2.50 A+ 1.25% -10.00%
2.50 “ 3.00 AA 0.90% -5.00%
> 3.00 AAA 0.70% 0.00%
Thus, we assume that the operating income will drop 5% if Deutsche Bank™s rating drops
to AA and 20% if it drops to BBB. The drops in operating income were estimated by
looking at the effects of ratings downgrades on banks21.
Based upon these assumptions, the optimal long term debt ratio for Deutsche
Bank is estimated to be 40%, lower than it™s current long term debt ratio of 67%. Table
8.17 below summarizes the cost of capital and firm values at different debt ratios for the
Table 8.17: Debt Ratios, Cost of Capital and Firm Value: Deutsche Bank
Debt Cost of Bond Interest rate Tax Cost of Debt Firm
Ratio Beta Equity Rating on debt Rate (after-tax) WACC Value (G)
0% 0.44 6.15% AAA 4.75% 38.00% 2.95% 6.15% $111,034

21 We were able to find a few down-graded banks upto BBB. Below BBB, we found no banks that
remained independent, since the FDIC stepped in to protect depositors. We made the drop in operating
income large enough to rule out ratings below BBB.


10% 0.47 6.29% AAA 4.75% 38.00% 2.95% 5.96% $115,498
20% 0.50 6.48% AAA 4.75% 38.00% 2.95% 5.77% $120,336
30% 0.55 6.71% AAA 4.75% 38.00% 2.95% 5.58% $125,597
40% 0.62 7.02% AAA 4.75% 38.00% 2.95% 5.39% $131,339
50% 0.71 7.45% A+ 5.30% 38.00% 3.29% 5.37% $118,770
60% 0.84 8.10% A 5.45% 38.00% 3.38% 5.27% $114,958
70% 1.07 9.19% A 5.45% 38.00% 3.38% 5.12% $119,293
80% 1.61 11.83% BB+ 8.30% 32.43% 5.61% 6.85% $77,750
90% 3.29 19.91% BB 8.80% 27.19% 6.41% 7.76% $66,966

The optimal debt ratio is the point at which the firm value is maximized. Note that the
cost of capital is actually minimized at 70% debt but the firm value is highest at a 40%
debt ratio. This is so because the operating income changes as the debt ratio changes.
While the cost of capital continues to decline as the debt ratio increases beyond 40%, the
decline in operating income more that offsets this drop.

In Practice: Building in Regulatory, Self Imposed and Lender Constraints
In most analyses of optimal capital structure, an analyst will be faced with a series of
constraints, some of which come from regulatory requirements, some of which are self
imposed and some of which are imposed by existing lenders to the firm. One very
common constraint imposed by all three is a constraint that the book value debt ratio not
exceed a specified number. Since the analysis we have done so far has focused on market
value debt ratios, there is the risk that the book value constraint may be violated. There
are two solutions:
1. The first is to do the entire analysis using book value of debt and equity, looking for
the optimal debt ratio. Since the approach we have described is driven by cash flows,
the optimal dollar debt that is computed should not be affected significantly by doing
2. The second and more general approach (since it can be used to analyze any kind of
constraint) is to keep track of the book value debt ratio in the traditional analysis, and
view the optimal capital structure as the one the minimizes the cost of capital subject
to the book value debt ratio being lesser than the specified constraint.

8.6. ˜: Bankruptcy Costs and Debt Ratios

The optimal debt ratio obtained by minimizing the cost of capital is too high
because it does not consider bankruptcy costs.
a. True
b. False

Determinants of Optimal Debt Ratio

The preceding analysis highlights some of the determinants of the optimal debt
ratio. We can then divide these determinants into firm-specific and macroeconomic

Firm-Specific Factors
Determinants specific to the firm include the firm™s tax rate, pre-tax returns and
variance in operating income.

(a) Firm's tax rate:
In general, the tax benefits from debt increase as the tax rate goes up. In relative
terms, firms with higher tax rates have higher optimal debt ratios than do 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. We can illustrate this by computing the optimal debt
ratio for Disney, Aracruz and Bookscape, holding all else constant and just changing the
tax rate in Figure 8.4


Figure 8.4: Optimal Debt Ratio and Tax Rate




Optimal Debt Ratio






20% Disney
Tax Rate 40%

At a 0% tax rate, the optimal debt ratio is zero for all three firms. Without the benefits
that accrue from taxes, the rationale for using debt disappears. As the tax rate increases,
the optimal debt ratios increase for all three firms but at different rates. For Aracruz and
Disney, the optimal debt ratio does not increase above 30% even if the tax rate increases
because the operating income at both firms is not high enough to sustain much higher
debt ratios; in other words, there is not enough earnings to claim additional tax benefits.
For Bookscape, though, the optimal continues to increase and reaches 50% when the tax
rate is 50%.

(b) Pre-Tax Returns on the Firm (in Cash Flow Terms):
The most significant determinant of the optimal debt ratio is a firm™s earnings
capacity. In fact, the operating income as a percentage of the market value of the firm
(debt plus equity) is usually good indicator of the optimal debt ratio. When this number is
high (low), the optimal debt ratio will also be high (low). A firm with higher pre-tax
earnings 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 earnings. Disney, for
example, has operating income of $2,805 million, which is 4.02 % of the market value of


the firm of $69,769 million in the base case, and an optimal debt ratio of 30%. Doubling
this to 8.04% will increase the optimal debt ratio to 50%.

(c) Variance in Operating Income
The variance in operating income enters the base case analysis in two ways. First,
it plays a role in determining the current beta: firms with high (low) variance in operating
income have high (low) betas. Second, the volatility in operating income can be one of
the factors determining bond ratings at different levels of debt: ratings drop off much
more dramatically for higher variance firms as debt levels are increased. It follows that
firms with higher (lower) variance in operating income will have lower (higher) optimal
debt ratios. The variance in operating income also plays a role in the constrained analysis,
since higher variance firms are much more likely to register significant drops in operating
income. Consequently, the decision to increase debt should be made much more
cautiously for these firms.

Macro-economic Factors
Should macroeconomic conditions affect optimal debt ratios? Obviously. In good
economic times, firms will generate higher earnings and be able to service more debt. In
recessions, earnings will decline and with it the capacity to service debt. That is why
prudent firms borrow based upon normalized earnings rather than current earnings.
Holding operating income constant, macroeconomic variables can still affect optimal
debt ratios. In fact, both the level of riskfree rate and the magnitude of default spreads can
affect optimal debt ratios.

(a) Level of Rates
As interest rates decline, the conventional wisdom is that debt should become cheaper
and more attractive for firms. While this may seem intuitive, the effect is muted by the
fact that lower interest rates also reduce the cost of equity. In fact, changing the riskfree
rate has a surprisingly small effect on the optimal debt ratio, as long as interest rates


move within a normal range.22 When interest rates exceed normal levels, optimal debt
ratios do decline partly because we keep operating income fixed. The higher interest
payments at every debt ratio reduce bond ratings and affect the capacity of firms to
borrow more.

(b) Default Spreads
The default spreads for different ratings classes tend to increase during recessions
and decrease during recoveries. Keeping other things constant, as the spreads increase
(decrease) optimal debt ratios decrease (increase), for the simple reason that higher
spreads penalize firms which borrow more money and have lower ratings. In fact, the
default spreads on corporate bonds between 1992 and 2000, leading to higher optimal
debt ratios for all firms. In 2001 and 2002, as the economy slowed, default spreads
widened again, leading to lower optimal debt ratios.

There is a dataset on the web that summarizes operating margins and returns on


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