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Debt finance is the lower-cost method for raising capital for the firm, but it also creates debt
service, which increases firm risk, because missing its debt service can lead to dire consequences for
the firm. Equity finance is the higher-cost method for raising capital for the firm, but equity finance
does not create contractual obligations that the firm must meet, so equity finance is less risky for the
firm. One of the theories of capital structure, called the trade-off theory, is based on this logic.
Financial managers trade off the lower cost but higher risk of debt finance with the higher cost but
lower risk of equity finance, possibly searching for an optimal mix. We will work through the entire
development and logic of this theory in this section.
Any discussion of capital structure must begin with the work of Franco Modigliani and Merton
Miller. Modigliani and Miller 1 (M&M) proved that in a world with perfect and frictionless capital
markets, the value of any firm was independent of its capital structure, and was determined by
discounting the expected cash flows from the firm at an interest rate appropriate to the risk of this cash
flow stream. This is M&M‟s Proposition I, which states that the value of the levered firm, V L , the firm
with debt, is the same as the value of the unlevered firm, the firm without debt, V U :
Effectively, M&M showed that the value of any firm comes from the cash-flow-generating ability
of its assets, not from how it is financed. This result was dependent on several restrictive assumptions,
including that identical information is available to all investors and managers; investors and managers
have identical expectations from this information; there are no income taxes; companies and investors
are able to borrow and lend at the riskless rate of interest; and bankruptcy is costless and can be
entered and exited instantly. With these assumptions M&M showed with a mathematical proof and
through an arbitrage argument that, given two firms of the same risk class and with the same expected
cash flows, the value of the firms must be the same, no matter how the two firms are financed. This
result also allowed M&M to state, under the restrictive assumptions, that the cost of capital for any
firm is independent of its capital structure, which is often referred to as M&M‟s capital structure
irrelevancy proposition.
But we have already seen that debt finance has a lower cost than equity finance. Doesn‟t this refute
the M&M irrelevancy proposition? Wouldn‟t the use of more debt finance and less equity finance
reduce the firm‟s overall cost of capital? Using these same assumptions, M&M proved that the firm‟s
overall cost of capital does not change as more or less debt finance is used. Their Proposition II
showed that the required return to equity holders is positively related to the use of debt finance, also
called financial leverage, because the risk to equity holders increases with increasing financial
leverage. It is true that debt finance is less costly and using relatively more debt finance means using a
larger proportion of the lower-cost financing alternative. It is also true that using more debt finance
increases the risk to equity holders, so the cost of equity increases. M&M‟s Proposition II on the cost
of equity is expressed in the following formula:
where k S is the cost of equity, k O is the cost of capital for an all-equity firm, k B is the cost of debt, B
is the value of the firm‟s debt, and S is the value of the firm‟s equity.
The formula shows that the cost of equity is a linear function of the firm‟s financial leverage.
WACC is unaffected by financial leverage, even though you are adding cheaper debt finance, because
the cost of equity increases to precisely offset it. M&M prove the two effects exactly offset each other,
so the value of the firm and the WACC are not changed by the use of financial leverage.