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CHAPTER 8

CAPITAL STRUCTURE: THE OPTIMAL FINANCIAL MIX

What is the optimal mix of debt and equity for a firm? While in the last chapter

we looked at the qualitative trade off between debt and equity, we did not develop the

tools we need to analyze whether debt should be 0%, 20%, 40% or 60% of capital. Debt

is always cheaper than equity, but using debt increases risk in terms of default risk to

lenders, and higher earnings volatility for equity investors. Thus, using more debt can

increase value for some firms and decrease value for others, and for the same firm, debt

can be beneficial up to a point and destroy value beyond that point. We have to consider

ways of going beyond the generalities in the last chapter to specific ways of identifying

the right mix of debt and equity.

In this chapter, we explore three ways to find an optimal mix. The first approach

begins with a distribution of future operating income; we can then decide how much debt

to carry by defining the maximum possibility of default we are willing to bear. The

second approach is to choose the debt ratio that minimizes the cost of capital. Here, we

review the role of cost of capital in valuation and discuss its relationship to the optimal

debt ratio. The third approach, like the second, also attempts to maximize firm value, but

it does so by adding the value of the unlevered firm to the present value of tax benefits

and then netting out the expected bankruptcy costs. The final approach is to base the

financing mix on the way comparable firms finance their operations.

Operating Income Approach

The operating income approach is the simplest and one of the most intuitive ways

of determining how much a firm can afford to borrow. We determine the firmâ€™s

maximum acceptable probability of default. Based upon the distribution of operating

income, we then determine how much debt the firm can carry.

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Steps in Applying Operating Income Approach

We begin with an analysis of a firmâ€™s operating income and cash flows, and we

consider how much debt it can afford to carry based upon its cash flows. The steps in the

operating income approach are as follows:

1. We assess the firmâ€™s capacity to generate operating income based upon both current

conditions and past history. The result is a distribution for expected operating income,

with probabilities attached to different levels of income.

2. For any given level of debt, we estimate the interest and principal payments that have

to be made over time.

3. Given the probability distribution of operating cash flows and the debt payments, we

can estimate the probability that the firm will be unable to make those payments.

4. We set a limit on the probability of its being unable to meet debt payments. Clearly,

the more conservative the management of the firm, the lower this probability constraint

will be.

5. We compare the estimated probability of default at a given level of debt to the

probability constraint. If the probability of default is higher than the constraint, the firm

chooses a lower level of debt; if it is lower than the constraint, the firm chooses a higher

level of debt.

Illustration 8.1: Estimating Debt Capacity Based Upon Operating Income Distribution

In the following analysis, we apply the operating income approach to analyzing

whether Disney should issue an additional $ 5 billion in new debt.

Step 1: We derive a probability distribution for expected operating income from Disneyâ€™s

historical earnings and estimate operating income changes from 1988 to 2003 and present

it in figure 8.1.

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Figure 8.1: Disney: Operating Income Changes - 1988-2003

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3.5

3

2.5

2

1.5

1

0.5

0

Drop more than Decline 10%- Decline 0-10% Increase 0-10% Increase 10- Increase 20- Increase 30- Increase more

20% 20% 20% 30% 40% than 40%

Percentage change in annual operating income

The average change in operating income on an annual basis over the period was 10.09%,

and the standard deviation in the annual changes is 19.54%. If we assume that the

changes are normally distributed, these statistics are sufficient for us to compute the

approximate probability of being unable to meet the specified debt payments.

Step 2: We estimate the interest and principal payments on a proposed bond issue of $ 5

billion by assuming that the debt will be rated BBB, lower than Disneyâ€™s current bond

rating of BBB+1. Based upon this rating, we estimated an interest rate of 5.5% on the

debt. In addition, we assume that the sinking fund payment set aside to repay the bonds is

5% of the bond issue. This results in an annual debt payment of $ 550 millionâ€“

Additional Debt Payment = Interest Expense + Sinking Fund Payment

= 0.055 * 5,000 + .05 * 5,000 = $ 525 million

The total debt payment then can be computed by adding the interest payment on existing

debt in 2003â€“â€“ $ 666 million â€“â€“ as well as the operating lease expenses from 2003 - $

1 This is Disneyâ€™s current bond rating.

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556 million - to the additional debt payment that will be created by taking on $ 5 billion

in additional debt.

Total Debt Payment = Interest on Existing Debt + Operating lease expense + Additional

Debt Payment = $ 666 million + $ 556 million + $ 525 million = $ 1,747 million

Step 3: We can now estimate the probability2 of default from the distribution of operating

income by assuming that the percentage changes in operating income are normally

distributed and by considering the operating income of $ 2,713 million that Disney

earned in 2003 as the base year income.

T statistic = (Current EBIT- Debt Payment) / ÏƒOI (Current Operating Income)

= ($ 2,713- $ 1747 million) / (.1954 * $2713) = 1.82

Based upon the t statistic, the probability that Disney will be unable to meet its debt

payments in the next year is 3.42%.

Step 4: Assume that the management at Disney set a constraint that the probability of

default be no greater than 5%.

Step 5: Since the estimated probability of default is indeed less than 5%, Disney can

afford to borrow more than $ 5 billion. If the distribution of operating income changes is

normal, we can estimate the level of debt payments Disney can afford to make for a

probability of default of 5%.

T statistic for 5% probability level = 1.645

Consequently, the debt payment can be estimated as

($2,713 - X)/ (.1954* $2,713) = 1.645

Solving for X, we estimate a breakeven debt payment of -

Break Even Debt Payment = $ 1,841 million

Subtracting out the existing interest and lease payments from this amount yields a break-

even additional debt payment of $619 million

Break-Even Additional Debt Payment = 1841- 666 â€“ 556 = $619 million

2 This is the probability of defaulting on interest payments in one period. The cumulative probability of

default over time will be much higher.

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If we assume that the interest rate remains unchanged at 5.5% and the sinking fund will

remain at 5% of the outstanding debt, this yields an optimal debt level of $ 5,895 million.

Optimal Debt Level = Break Even Debt Payment / (Interest Rate + Sinking Fund Rate)

= $ 619 / (.055 + .05) = $ 5,895 million

The optimal debt level will be lower if the interest rate increases as Disney borrows more

money.

Limitations of the Operating Income Approach

Although this approach may be intuitive and simple, it has some drawbacks. First,

estimating a distribution for operating income is not as easy as it sounds, especially for

firms in businesses that are changing and volatile. For instance, the operating income of

firms can vary widely from year to year, depending upon the success or failure of

individual products. Second, even when we can estimate a distribution, the distribution

may not fit the parameters of a normal distribution, and the annual changes in operating

income may not reflect the risk of consecutive bad years. This can be remedied by

calculating the statistics based upon multiple years of data. For Disney, in the above

example, if operating income is computed over rolling two-year periods3, the standard

deviation will increase and the optimal debt ratio will decrease..

This approach is an extremely conservative way of setting debt policy because it

assumes that debt payments have to be made out of a firmâ€™s cash balances and operating

income and that the firm has no access to financial markets. Finally, the probability

constraint set by management is subjective and may reflect management concerns more

than stockholder interests. For instance, management may decide that it wants no chance

of default and refuse to borrow money as a consequence.

Refinements on the Operating Income Approach

The operating income approach described in this section is simplistic because it is

based upon historical data and the assumption that operating income changes are

3 By rolling two-year periods, we mean 1980 & 1981, 1981 & 1982, 1982 & 1983 .... The resulting

standard deviation is corrected for the multiple counting of the same observations.

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normally distributed. We can make it more sophisticated and robust by making relatively

small changes:

You can look at simulations of different possible outcomes for operating income,

â€¢

rather than looking at historical data; the distributions of the outcomes are based

both upon past data and upon expectations for the future.

Instead of evaluating just the risk of defaulting on debt, you can consider the

â€¢

indirect bankruptcy costs that can accrue to a firm, if operating income drops

below a specified level.

You can compute the present value of the tax benefits from the interest payments

â€¢

on the debt, across simulations, and thus compare the expected cost of bankruptcy

to the expected tax benefits from borrowing.

With thee changes, you can look at different financing mixes for a firm, and estimate

the optimal debt ratio as that mix that maximizes the firmâ€™s value.4

Cost of Capital Approach

In chapters 3 and 4, we estimated the minimum acceptable hurdle rates for equity

investors (the cost of equity), and for all investors in the firm - (the cost of capital). We

defined the cost of capital to be the weighted average of the costs of the different

components of financing â€“â€“ including debt, equity and hybrid securities â€“â€“ used by a

firm to fund its financial requirements. By altering the weights of the different

components, firms might be able to change their cost of capital5. In the cost of capital

approach, we estimate the costs of debt and equity at different debt ratios, use these costs

to compute the costs of capital, and look for the mix of debt and equity that yields the

lowest cost of capital for the firm. At this cost of capital, we will argue that firm value is

maximized.6.

4 Opler, Grinblatt and Titman have an extended discussion of this approach.

5 If capital structure is irrelevant, the cost of capital will be unchanged as the capital structure is altered.

6 If capital structure is irrelevant, the cost of capital will be unchanged as the capital structure is altered.

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Definition of the Weighted Average Cost of Capital (WACC)

The weighted average cost of capital (WACC) is defined as the weighted average

of the costs of the different components of financing used by a firm.

WACC = ke ( E/ (D+E+PS)) + kd ( D/ (D+E+PS)) + kps ( PS/ (D+E+PS))

where WACC is the weighted average cost of capital, ke, kd and kps are the costs of

equity, debt and preferred stock, and E, D and PS are their respective market values.

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