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makes future investment
uncertain.

Based upon this analysis, qualitative though it might be, we would argue that all three
firms could benefit from borrowing, as long as the borrowing does not push it below an
acceptable default risk threshold.

No Optimal Capital Structure
We have just argued that debt has advantages, relative to equity, as well as
disadvantages. Will trading off the costs and benefits of debt yield an optimal mix of debt
and equity for a firm? In this section, we will present arguments that it will not, and the
resulting conclusion that there is no such optimal mix. The seeds of this argument were
sown in one of the most influential papers ever written in corporate finance, containing
one of corporate finance™s best-known theorems, the Modigliani-Miller Theorem.
When they first looked at the question of whether there is an optimal capital
structure, Miller and Modigliani drew their conclusions in a world void of taxes,
transactions costs, and the possibility of default. Based upon these assumptions, they
concluded that the value of a firm was unaffected by its leverage and that investment and
financing decisions could be separated. Their conclusion can be confirmed in several
ways; we present two in this section. We will also present a more complex argument for
why there should be no optimal capital structure even in a world with taxes, made by
Miller almost two decades later.

The Irrelevance of Debt in a Tax-free World

In their initial work, Miller and Modigliani made three significant assumptions
about the markets in which their firms operated. First, they assumed there were no taxes.
Second, they assumed firms could raise external financing from debt or equity, with no
issuance costs. Third, they assumed there were no costs “direct or indirect “ associated
with bankruptcy. Finally, they operated in an environment in which there were no agency
costs; managers acted to maximize stockholder wealth, and bondholders did not have to
worry about stockholders expropriating wealth with investment, financing or dividend
decisions.

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In such an environment, reverting back to the trade off that we summarized in
Table 7.3, it is quite clear that all the advantages and disadvantages disappear, leaving
debt with no marginal benefits and no costs. In Table 18.5, we modify table 18.1 to
reflect the assumptions listed above:
Table 7.6: The Trade Off on Debt: No Taxes, Default Risk and Agency Costs
Advantages of Debt Disadvantages of Debt
1. Tax Benefit: 1. Bankruptcy Cost:
Zero, because there are no taxes Zero, because there are no bankruptcy
costs
2. Added Discipline: 2. Agency Cost:
Zero, because managers already maximize Zero, because bondholders are fully
Stockholder wealth. protected from wealth transfer
3. Loss of Future Financing Flexibility:
Not costly, because firms can raise
external financing costlessly.

Debt creates neither benefits nor costs and thus has a neutral effect on value. In such an
environment, the capital structure decision becomes irrelevant.
In a later paper, Miller and Modigliani preserved the environment they introduced
above but made one change, allowing for a tax benefit for debt. In this scenario, where
debt continues to have no costs, the optimal debt ratio for a firm is 100% debt. In fact, in
such an environment the value of the firm increases by the present value of the tax
savings for interest payments (See Figure 18.4).
Value of Levered Firm = Value of Unlevered Firm + tc B
where tc is the corporate tax rate and B is the dollar borrowing. Note that the second term
in this valuation is the present value of the interest tax savings from debt, treated as a
perpetuity. Figure 7.8 graphs the value of a firm with just the tax benefit from debt.




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Figure 7.8: Value of Levered Firm: MM with Taxes


Firm
Value

VL
Tax Benefit of borrowing
tc B
Vu




Debt ($ B)
Miller and Modigliani presented an alternative proof of the irrelevance of leverage,
based upon the idea that debt does not affect the underlying cash flows of the firm, in the
absence of taxes. Consider two firms that have the same cash flow (X) from operations.
Firm A is an all-equity firm, while firm B has both equity and debt. The interest rate on
debt is r. Assume you are an investor and you buy a fraction(±) of the equity in firm A,
and the same fraction of both the equity and debt of firm B. Table 7.7 summarizes the
cash flows that you will receive in the next period.
Table 7.7: Cash Flows to Investor from Levered and All-Equity Firm
Firm A Firm B

Type of firm All-Equity firm (Vu = E) Has some Equity and Debt

Actions now Investor buys a fraction a of Investor buys a fraction a of
the firm (± Vu) both equity and debt of the
firm
± EL + ± DL

Next period Investor receives a fraction a Investor receives the following
of the cash flow (± X) ±(X-rDL) + ± r DL = ± X
Since you receive the same total cash flow in both firms, the price you will pay for either
firm has to be the same. This equivalence in values of the two firms implies that leverage
does not affect the value of a firm. Note that this proof works only if the firm does not

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receive a tax benefit from debt; a tax benefit would give Firm B a higher cash flow than
Firm A.

The Irrelevance of Debt with Taxes

It is clear, in the Miller-Modigliani model, that when taxes are introduced into the
model, debt does affect value. In fact, introducing both taxes and bankruptcy costs into
the model creates a trade off, where the financing mix of a firm affects value, and there is
an optimal mix. In an address in 1979, however, Merton Miller argued that the debt
irrelevance theorem could apply even in the presence of corporate taxes, if taxes on the
equity and interest income individuals receive from firms were included in the analysis.
To demonstrate the Miller proof of irrelevance, assume that investors face a tax
rate of td on interest income and a tax rate of te on equity income. Assume also that the
firm pays an interest rate of r on debt and faces a corporate tax rate of tc. The after-tax
return to the investor from owning debt can then be written as:
After-tax Return from owning Debt = r (1-td)
The after-tax return to the investor from owning equity can also be estimated. Since cash
flows to equity have to be paid out of after-tax cash flows, equity income is taxed twice “
“ once at the corporate level and once at the equity level:
After-tax Return from owning Equity = ke (1 - tc) (1 - te)
The returns to equity can take two forms ““ dividends or capital gains; the equity tax rate
is a blend of the tax rates on both. In such a scenario, Miller noted that the tax benefit of
debt, relative to equity becomes smaller, since both debt and equity now get taxed, at
least at the level of the individual investor.
Tax Benefit of Debt, relative to Equity = {1 - (1-tc) (1-te)}/(1-td)
With this relative tax benefit, the value of the firm, with leverage, can be written as:
VL = Vu + [1- (1-tc) (1-te))/(1-td)] B
where VL is the value of the firm with leverage, VU is the value of the firm without
leverage, and B is the dollar debt. With this expanded equation, that includes both
personal and corporate taxes, there are several possible scenarios:




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a. Personal tax rates on both equity and dividend income are zero: if we ignore
personal taxes, this equation compresses to the original equation for the value of a
levered firm, in a world with taxes but no bankruptcy costs:
VL = Vu + tc B
b. The personal tax rate on equity is the same as the tax rate on debt: If this were the
case, the result is the same as the original one ““ the value of the firm increases
with more debt.
VL = Vu + tc B
c. The tax rate on debt is higher than the tax rate on equity: In such a case, the
differences in the tax rates may more than compensate for the double taxation of
equity cash flows. To illustrate, assume that the tax rate on ordinary income is
70%, the tax rate on capital gains on stock is 28% and the tax rate on corporations
is 35%. In such a case, the tax liabilities for debt and equity can be calculated for
a firm that pays no dividend as follows:
Tax Rate on Debt Income = 70%
Tax Rate on Equity Income = 1 - (1-0.35) (1-.28) = 0.532 or 53.2%
This is a plausible scenario, especially considering tax law in the United States
until the early 1980s. In this scenario, debt creates a tax disadvantage to investors.
d. The tax rate on equity income is just low enough to compensate for the double
taxation: In this case, we are back to the original debt irrelevance theorem.
(1 - td) = (1-tc) (1-te) ................ Debt is irrelevant
Miller™s analysis brought investor tax rates into the analysis for the first time and
provided some insight into the role of investor tax preferences on a firm™s capital
structure. As Miller himself notes, however, this analysis does not reestablish the
irrelevance of debt under all circumstances; rather, it opens up the possibility that debt
could still be irrelevant, despite its tax advantages.

The Consequences of Debt Irrelevance

If the financing decision is irrelevant, as proposed by Miller and Modigliani,
corporate financial analysis is simplified in a number of ways. The cost of capital, which
is the weighted average of the cost of debt and the cost of equity, is unaffected by


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changes in the proportions of debt and equity. This might seem unreasonable, especially
since the cost of debt is much lower than the cost of equity. In the Miller-Modigliani
world, however, any benefits incurred by substituting cheaper debt for more expensive
equity are offset by increases in both their costs, as shown in Figure 7.9.

Figure 7.9: Cost of Capital in the MM World




Cost of Equity
Cost of equity rises as
leverage increases
Cost of Capital

Cost of Debt

Cost of debt rises as
default risk increases

Debt Ratio
The value of the firm is also unaffected by the amount of leverage it has. Thus, if the
firm is valued as an all-equity entity, its value will remain unchanged if it is valued with
any other debt ratio. (This actually follows from the implication that the cost of capital is
unaffected by changes in leverage and from the assumption that the operating cash flows
are determined by investment decisions rather than financing decisions.)
Finally, the investment decision can be made independently of the financing decision.
In other words, if a project is a bad project when evaluated as an all-equity project, it will
remain so using any other financing mix.

The Contribution of the Miller-Modigliani Theorem

It is unlikely that capital structure is irrelevant in the real world, given the tax
preferences for debt and existence of default risk. In spite of this, Miller and Modigliani
were pioneers in moving capital structure analysis from an environment in which firms
picked their debt ratios based upon comparable firms and management preferences, to
one that recognized the trade-offs. They also drew attention to the impact of good
investment decisions on firm value. To be more precise, a firm that invests in poor

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projects cannot hope to recoup the lost value by making better financing decisions; a firm
that takes good projects will succeed in creating value, even if it uses the wrong financing
mix. Finally, while the concept of a world with no taxes, default risk, or agency problems
may seem a little far-fetched, there are some environments in which the description might
hold. Assume, for instance, that the U.S. government decides to encourage small
businesses to invest in urban areas by relieving them of their tax burden and providing a
back-up guarantee on loans (default protection). Firms that respond to these initiatives
might find that their capital structure decisions do not affect their value.
Finally, surveys of financial managers indicate that, in practice, they do not attach
as much weight to the costs and benefits of debt as we do in theory. In a survey by
Pinegar and Wilbricht, managers were asked to cite the most important inputs governing
their financial decisions. Their responses are ranked in the order of the importance
managers attached to them in Table 7.8.
Table 7.8: Inputs into Capital Structure Decisions
Percentage of Responses Within Each Rank
Least Important...................¦¦¦...Most Important
Inputs/Assumptions by 1 2 3 4 5 Not Ranked Mean
Order of Importance
1. Projected cash flow from 1.7% 1.1% 9.7% 29.5% 58.0% 0.0% 4.41
asset to be financed
2. Avoiding dilution of 2.8% 6.3% 18.2% 39.8% 33.0% 0.0% 3.94
common equity™s claims
3. Risk of Asset to be 2.8% 6.3% 20.5% 36.9% 33.0% 0.6% 3.91
financed
4. Restrictive covenants on 9.1% 9.7% 18.7% 35.2% 27.3% 0.0% 3.62
senior securities
5. Avoiding mispricing of 3.4% 10.8% 27.3% 39.8% 18.7% 0.0% 3.60
securities to be issued.
6. Corporate Tax Rate 4.0% 9.7% 29.5% 42.6% 13.1% 1.1% 3.52
7. Voting Control 17.6% 10.8% 21.0% 31.2% 19.3% 0.0% 3.24
8. Depreciation & Other 8.5% 17.6% 40.9% 24.4% 7.4% 1.1% 3.05
Tax shields
9. Correcting mispricing of 14.8% 27.8% 36.4% 14.2% 5.1% 1.7% 2.66
securities
10. Personal tax rates of 31.2% 34.1% 25.6% 8.0% 1.1% 0.0% 2.14
debt and equity holders
11. Bankruptcy Costs 69.3% 13.1% 6.8% 4.0% 4.5% 2.3% 1.58

Financial managers seem to weigh financial flexibility and potential dilution much more
heavily than bankruptcy costs and taxes in their capital structure decisions.
In Practice: The Dilution Bogey


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