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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 companyâ€™s balance sheet.

Given the mix of deposits, repurchase agreements, short term financing and other

liabilities that may appear on a financial service firmâ€™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

â€¢

Euros in 2003.

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

â€¢

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

â€¢

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

4.05%.

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

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

â€¢

the ratings of financial service firms.

The operating income for Deutsche Bank is assumed to drop if its rating drops. Table

â€¢

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 â€“ 0.10 C 14.00% -40.00%

0.10 â€“ 0.20 CC 12.50% -40.00%

0.20 - 0.30 CCC 10.50% -40.00%

0.30 â€“ 0.40 B- 6.25% -25.00%

0.40 â€“ 0.50 B 6.00% -20.00%

0.50 â€“ 0.60 B+ 5.75% -20.00%

0.60 â€“ 0.75 BB 4.75% -20.00%

0.75 â€“ 0.90 BB+ 4.25% -20.00%

0.90 â€“ 1.20 BBB 2.00% -20.00%

1.20 â€“ 1.50 A- 1.50% -17.50%

1.50 â€“ 2.00 A 1.40% -15.00%

2.00 â€“ 2.50 A+ 1.25% -10.00%

2.50 â€“ 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 Bankâ€™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 itâ€™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

firm.

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.

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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

this.

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. â˜ž: Bankruptcy Costs and Debt Ratios

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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

Explain.

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

factors.

Firm-Specific Factors

Determinants specific to the firm include the firmâ€™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

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Figure 8.4: Optimal Debt Ratio and Tax Rate

50%

45%

40%

35%

Optimal Debt Ratio

30%

25%

20%

15%

10%

5%

Bookscape

0%

Aracruz

0%

10%

20% Disney

30%

Tax Rate 40%

50%

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 firmâ€™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

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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

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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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