Modigliani-Miller and Capital Structure

Cut a pizza into 6 slices or 8, and you still have the same pizza. That is the whole idea behind Modigliani-Miller (MM): slicing a company's cash flows into "debt" and "equity" claims doesn't change the size of the pizza, only how many pieces it's divided into. The company's total value is set by what its assets earn, not by how the claims on those earnings are labeled.

This runs against instinct because debt looks cheap — interest rates are lower than the returns equity investors demand. Surely borrowing more and using less equity should raise firm value? MM's insight was that as leverage rises, the equity that remains becomes riskier and equity holders demand a higher return to compensate, and the two effects exactly offset in a frictionless world.

The two propositions

Proposition I says total firm value is unaffected by leverage:

$$V_L = V_U$$

Here $V_L$ is the value of the levered firm (some debt, some equity) and $V_U$ is the value of the identical firm with no debt at all. In words: adding debt does not enlarge the pie.

Proposition II says the cost of equity rises linearly with leverage to compensate for the added risk:

$$r_E = r_U + \frac{D}{E}\left(r_U - r_D\right)$$

Here $r_E$ is the required return on equity, $r_U$ is the return required if the firm had no debt at all, $D$ and $E$ are the market values of debt and equity, and $r_D$ is the cost of debt. In words: every extra dollar of debt relative to equity pushes equity's required return up by the spread between the unlevered return and the (cheaper) cost of debt.

Worked example: releverage a coffee chain

An all-equity coffee chain is worth $100 million, funded by $100 million of equity, with an unlevered cost of capital $r_U$ of 10 percent. Management issues $40 million of debt at $r_D$ of 5 percent and uses the cash to buy back $40 million of stock, leaving $60 million of equity.

$$r_E = 0.10 + \frac{40}{60}(0.10 - 0.05) = 0.10 + 0.0333 = 0.1333$$

Cost of equity rises from 10 percent to 13.3 percent. Now check that the blended cost of capital hasn't moved:

$$\text{WACC} = \frac{60}{100}(0.1333) + \frac{40}{100}(0.05) = 0.08 + 0.02 = 0.10$$

Exactly 10 percent, unchanged. The firm did not get cheaper to finance; it just moved risk from the balance sheet's right side onto a smaller slice of equity.

What this means in practice

No real firm actually lives in MM's frictionless world, and that is the point of the theorem: it is a baseline, not a prediction. Interest is tax-deductible, so debt creates a real tax shield; bankruptcy is costly and more likely at high leverage; and managers know more than outside investors, which shapes financing choices (see pecking-order theory). Every serious capital-structure argument is really a claim about which of MM's assumptions fails hardest for a given company, and by how much.

Key terms

• $V_U$ / $V_L$ — value of the unlevered and levered versions of the same firm.
• $r_U$ — the return required on the firm's assets with no debt at all.
• WACC — the blended cost of capital across debt and equity, weighted by market value.
• Tax shield — the value created because interest payments reduce taxable income, the main real-world crack in MM's Proposition I.