Capital structure: Modigliani and Miller, and why their answer is a checklist
The most famous result in corporate finance says that how a company is financed does not change what it is worth. It is true under stated conditions, and the conditions are the whole lesson: each one that fails in practice is a reason financing decisions matter.
01the theorems
- Proposition I, no taxes
VL = VUThe levered firm is worth the same as the unlevered one.- Proposition II
rE = rA + (D/E)·(rA − rD)rA the return on the assets, rD on the debt, rE on the equity.- The average does not move
rA = (E/V)·rE + (D/V)·rD
Financing does not change value, in a perfect market1,2
Modigliani and Miller's first theorem, from 1958: neither the amount nor the structure of a firm's debt affects its value, provided financial markets work perfectly, there are no taxes and there are no bankruptcy costs. Value comes from the expected returns on the assets, discounted for their risk, whoever holds the claims.
Leverage raises the cost of equity2
The same theorem implies that the expected return on a firm's shares - its cost of equity - rises linearly with the ratio of debt to equity. Borrowing looks cheap because debt costs less than equity, but it makes the remaining equity riskier by exactly enough to leave the average cost unchanged.
Dividend policy does not change value either1,2
A later paper extended the argument: for a given investment policy, a firm's value does not depend on its dividends. A higher dividend raises shareholders' income but lowers the share price by the same amount.
The arbitrage behind it2
The theory rests on shareholders being able to borrow and lend on the same terms as firms. If they can, any leverage a company chooses can be undone or copied in an investor's own portfolio, so nobody pays extra for it.
Proposition II, worked (illustrative)2
Take assets that earn 10% and debt that costs 5%. With no debt the shares earn the asset return, 10%. Finance half with debt (D/E = 1) and the cost of equity becomes 10% + 1 × (10% − 5%) = 15%. The average is 0.5 × 15% + 0.5 × 5% = 10%, exactly where it started: the cheap debt is paid for by dearer equity, which is the theorem in one line of arithmetic.
02why capital structure does matter
- Annual interest tax shield
tax shield = t × interest = t × rD × D- Value of a permanent tax shield
PV = t × rD × D / rD = t × DAssumes the debt is kept forever and the shield is as risky as the debt.
Interest is tax-deductible, which is why the after-tax cost of debt in a WACC is multiplied by one minus the tax rate. The no-taxes assumption is the first to fail in any real valuation.
What the deduction is worth (computed)3
A company with 1,000 of permanent debt at 5% pays 50 of interest a year. At a 25% tax rate that saves 12.5 of tax each year, and discounting a perpetuity of 12.5 at the 5% the debt costs gives 12.5 / 0.05 = 250, which is 25% × 1,000. Against that saving sits the cost of financial distress, the next assumption on this list to fail.
The theorem assumes financial distress costs nothing. Restructuring advisers exist because it costs a great deal; the restructuring page covers the group that works on it.
A leveraged buyout is the theory's test case3,4
An LBO funds a purchase with substantial debt. In the theorem's perfect market that leverage could not add value by itself, so whatever it does add has to come through the conditions the theorem assumes away - taxes first. That is why the LBO questions in the bank are, underneath, questions about this page.