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It is important to understand how capital structure impacts firm value and cost of capital in the ideal
world created by Modigliani and Miller‟s assumption of perfect and frictionless capital markets. In
this world capital structure is irrelevant, as firm value and cost of capital are not affected by capital
structure. We all know, however, that M&M‟s ideal world doesn‟t exist. There are market
imperfections and frictions, particularly income taxes and costly bankruptcy. By peeling back these
assumptions, we can see how and why capital structure can impact both firm value and cost of capital
in the real world.
We will begin with income taxes, particularly the tax-deductible nature of interest expense.
Deductible interest expense creates debt tax shields in any year equal to:
where τ C is the corporate income tax rate, k B is the cost of debt, and B is the amount borrowed.
As long as the firm is earning positive taxable income and paying income taxes, we can assume the
yearly debt tax shield has the same risk as the interest on the amount borrowed, so k B is also the
appropriate discount rate for the yearly debt tax shields. Assuming the cash flows are a perpetuity, the
present value of the debt tax shield is:
This debt tax shield decreases the amount of cash flow paid to tax authorities and therefore
increases the cash flow available to debt holders and equity holders. With more cash flow available for
investors, total firm value increases by the present value of the debt tax shield. In a world with income
taxes and tax-deductible interest expense, M&M‟s Proposition I changes to:
where V L is the value of the firm with financial leverage, V U is the value of the firm without
financial leverage, and τ C B is the present value of the debt tax shield assuming perpetual cash flows.
M&M‟s Proposition I now shows that the value of the firm with financial leverage is equal to the
value of the firm without financial leverage, plus the present value of the debt tax shield.
Income taxes and tax-deductible interest expense also change M&M‟s Proposition II. It is still true
that increasing the use of debt finance (increasing financial leverage) increases the risk to equity
holders and the cost of equity rises, but the Proposition II formula for cost of equity in this case now
looks like this:
The cost of equity is still a linear function of the firm‟s financial leverage, but the slope is not as
steep. The increase in cost of equity, therefore, is not large enough to entirely offset the benefit from
adding cheaper debt finance. In a world with income taxes and tax-deductible interest expense, an
increase in the use of debt finance increases firm value and decreases the firm‟s overall cost of capital.
If this were the only real-world condition that impacted firm value and cost of capital, the firm‟s
optimal capital structure would be heavily weighted toward debt finance. In fact, clever financial
managers would use as much debt finance as possible, as this would maximize firm value and
minimize the firm‟s cost of capital.