Capital Structure in a Perfect Market (MM I)

The starting question

Should a firm be financed mostly with debt, mostly with equity, or some mix? Common intuition says debt is “cheaper”: interest rates on Treasuries are 4%, but expected stock returns are 10%. So loading up on debt should lower cost of capital and raise firm value. Right?

In 1958, Franco Modigliani and Merton Miller showed: not in a perfect market. With no taxes, no bankruptcy costs, no agency costs, and no information asymmetry, the firm’s total value is the same regardless of capital structure.

This is MM Proposition I:

$$V_L = V_U.$$

Where $V_L$ is the value of a levered firm and $V_U$ is the value of the same firm if it were all-equity-financed. They’re equal.

Why? An arbitrage proof

Suppose two firms are identical except for capital structure. Firm U is all equity, worth $V_U$. Firm L is partly debt, partly equity, total worth $V_L$. Suppose $V_L > V_U$.

You could:

1. Buy a fraction $\alpha$ of Firm U’s equity (cost: $\alpha V_U$).
2. Borrow $\alpha \cdot D_L$ personally at the same rate Firm L borrows at (since identical risk).
3. Use the loan + the equity stake to replicate Firm L’s payoff to equity holders.

The replica costs $\alpha V_U - \alpha D_L = \alpha(V_U - D_L)$: you pay $\alpha V_U$ for the equity, and the personal loan brings in $\alpha D_L$ of cash. Buying a fraction $\alpha$ of Firm L’s equity directly costs $\alpha E_L = \alpha(V_L - D_L)$. If $V_L > V_U$, the direct stake is the dearer of the two, so you sell Firm L’s equity and buy the cheaper homemade replica, banking $\alpha(V_L - V_U) > 0$ risk-free. Arbitrage.

The market punishes the price discrepancy and pulls $V_L$ down to $V_U$. The logic also works in reverse if $V_L < V_U$. In equilibrium, $V_L = V_U$.

What this says (and doesn’t say)

MM I says: in the absence of frictions, the size of the pie doesn’t depend on how you slice it. Slicing the pie into more debt slices and fewer equity slices doesn’t change the pie’s size.

What it doesn’t say:

• It does not say capital structure doesn’t matter in the real world. The real world has taxes (next lesson), bankruptcy costs, agency costs, information asymmetries, all of which break MM.
• It does not say debt is “free.” Debt and equity claim different slices of the same pie; the value the firm forgoes to debt holders is exactly the value debt holders receive.

But MM I matters because it tells us where to look for capital- structure effects: in the frictions. If a corporate-finance change adds value, ask which MM assumption it relaxes.

MM Proposition II

MM I implies that adding debt doesn’t change firm value. So if WACC stays constant (since neither value nor cash flow changes), then adding cheap debt must mechanically raise the cost of equity by exactly enough to offset.

Formally, MM Proposition II:

$$r_E = r_U + \frac{D}{E}\,(r_U - r_D).$$

Where $r_U$ is the cost of capital of the unlevered (all-equity) firm. As $D/E$ rises, $r_E$ rises linearly. WACC stays at $r_U$ regardless of leverage:

$$\text{WACC} = \frac{E}{V} r_E + \frac{D}{V} r_D = r_U.$$

(Algebra: substitute MM II into WACC and simplify.)

The intuition: more debt → more risk to equity holders (their claim is junior to a bigger pile of debt) → higher required equity return. The lower cost of debt and the higher cost of equity exactly offset.

Drag the leverage up and watch the two effects cancel. The cost of equity climbs, but the WACC line never moves:

Unlevered cost of capital r_U: 12.00%Cost of debt r_D: 5.00%

At D/E = 1: r_E ≈ 19.0%, WACC = 12.0% (= r_U)

Reset

Raise leverage and the red cost of equity climbs in a straight line, yet the green WACC never moves: it stays pinned at r_U. The firm trades cheap debt for costlier equity in exactly offsetting amounts, so its total value is untouched. That flat green line is Modigliani-Miller.

Baseline: unlevered cost of capital r_U = 12%, cost of debt r_D = 5%. The flat green WACC line at 12% is the whole MM result; the next lessons add taxes and distress that bend it.

Where MM breaks (preview of next 3 lessons)

Five major real-world frictions:

1. Taxes (next lesson). Interest is tax-deductible; dividends aren’t. So debt has a tax shield that adds value. MM with taxes says firm value rises monotonically with debt.
2. Financial distress costs (Lesson 22). Levered firms can go bankrupt, which destroys value (legal fees, asset fire-sales, customer and employee defections).
3. Agency costs. Debt disciplines managers; debt can also create perverse incentives.
4. Information asymmetry. Issuing equity signals firm overvaluation; issuing debt signals confidence. The market reacts.
5. Capital-market imperfections. Borrowing rates differ across firms; not everyone has access to the same capital markets at the same terms.

MM is the benchmark. Real-world deviations from MM are the substance of capital-structure theory.

A worked numerical example

Consider an all-equity firm with cost of capital $r_U = 12\%$. It generates an expected perpetual EBIT of $100M per year. With no taxes, firm value V_U = 100M / 0.12 = \833M$.

Now suppose the firm issues $300M of debt at 5% and uses the proceeds to buy back equity. Capital structure: $D = 300, E = V − D$.

MM I: $V_L = V_U = 833M$. So $E = 833 − 300 = 533M$.

MM II: $r_E = 0.12 + (300/533) \times (0.12 − 0.05) = 0.12 + 0.039 = 15.9\%$.

WACC check:

$$\text{WACC} = (533/833)(0.159) + (300/833)(0.05) = 0.102 + 0.018 = 12.0\%.$$

Equal to $r_U$. Value unchanged. Cost of equity rose. WACC stayed flat. MM at work.

Where this leads

The MM benchmark gives us a clean baseline. The next four lessons add the frictions back in one at a time and watch the optimal capital structure emerge.