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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 firm™s
maximum acceptable probability of default. Based upon the distribution of operating
income, we then determine how much debt the firm can carry.


Steps in Applying Operating Income Approach

We begin with an analysis of a firm™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 firm™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 Disney™s
historical earnings and estimate operating income changes from 1988 to 2003 and present
it in figure 8.1.


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









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 Disney™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 million“
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 2003““ $ 666 million ““ as well as the operating lease expenses from 2003 - $

1 This is Disney™s current bond rating.


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) / σOI (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 “ 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.


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

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 firm™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.


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,

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

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

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 firm™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 ““ including debt, equity and hybrid securities ““ 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

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.


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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