Set out the Modigliani-Miller propositions and what they imply for the financing mix

CFA® Level I · Corporate Finance · Capital Structure · CI.1.d

The idea

Modigliani and Miller showed that, in perfect markets with no taxes, bankruptcy costs or information asymmetry, capital structure does not affect value. Proposition I without taxes: V_L = V_U, because splitting the same asset cash flows differently does not change their total. Proposition II without taxes: the cost of equity rises linearly with leverage, r_e = r_0 + (r_0 - r_d)(D/E), exactly offsetting cheaper debt so the WACC is unchanged. Adding corporate taxes changes the answer: V_L = V_U + tD, and r_e = r_0 + (r_0 - r_d)(1 - t)(D/E). Debt now adds value through the interest tax shield, the WACC falls as leverage rises, and the theory points to all-debt financing, a conclusion that breaks down once financial distress costs are recognised.

Formulas

Modigliani-Miller Proposition I with no taxes

V_L = V_U

V_L: the value of the firm that uses debt
V_U: the value of the same firm funded entirely by equity

With no taxes and no distress costs, the mix of debt and equity does not change what the business is worth. It only changes how the same cash flows are split.

Modigliani-Miller Proposition II with no taxes

r_e = r_0 + (r_0 − r_d) × (D ÷ E)

r_e: the return equity holders demand
r_0: the cost of capital for the firm with no debt
r_d: the interest rate on the debt
D: the market value of debt
E: the market value of equity

Cheap debt is offset exactly by dearer equity: more leverage raises the return owners demand, so the overall cost of capital stays at r_0.

Modigliani-Miller Proposition I with taxes

V_L = V_U + t × D

V_L: the value of the firm that uses debt
V_U: the value of the same firm with no debt
t: the corporate tax rate
D: the permanent debt

Interest is deductible, so debt adds the value of the tax saved, t × D when the debt is permanent. Taken alone it says to use almost all debt, which is why distress costs matter.

Modigliani-Miller Proposition II with taxes

r_e = r_0 + (r_0 − r_d) × (1 − t) × (D ÷ E)

r_e: the return equity holders demand
r_0: the cost of capital for the firm with no debt
r_d: the interest rate on the debt
t: the corporate tax rate
D: the market value of debt
E: the market value of equity

The tax shield softens the rise in the cost of equity, so the weighted average cost of capital falls as debt rises.

A practice question

From the question bank, with the reason each wrong option is wrong.

Modigliani-Miller Proposition I without taxes states that a company's value is:

maximised with 100% debt financingWhy not: That is the implication of MM with taxes, where the interest tax shield adds value for every unit of debt.
independent of its capital structure - correct
maximised with 100% equity financingWhy not: Without taxes MM finds no advantage to any mix, so all-equity financing is no better than any other.

In perfect markets with no taxes, value depends only on the cash flows generated by the firm's assets. Splitting those cash flows between debt and equity holders does not change their total, so V_L = V_U.

A harder one

Under MM Proposition II without taxes, a firm has an unlevered cost of capital of 10%, a cost of debt of 6% and a debt-to-equity ratio of 0.5. Its cost of equity is closest to:

11.33%Why not: This uses debt-to-total capital of one-third in place of the debt-to-equity ratio of 0.5.
10.00%Why not: This ignores the extra financial risk that leverage places on shareholders.
12.00% - correct

r_e = r_0 + (r_0 - r_d)(D/E) = 10% + (10% - 6%)(0.5) = 12%. The cost of equity rises with leverage by exactly enough to leave the WACC at 10%.

The hardest tier

MM with corporate taxes implies a firm should be financed almost entirely by debt. Firms do not do this in practice mainly because:

the cost of debt exceeds the cost of equityWhy not: Debt is cheaper than equity because it has priority and a tax shield; that is why MM with taxes favours it.
interest is not deductible beyond a set ratioWhy not: Limits on interest deductibility exist in some jurisdictions but are not the main reason the theory breaks down.
financial distress costs rise with leverage - correct

MM ignores the expected costs of financial distress, agency costs and information asymmetry. As debt rises, the probability and cost of distress rise, eventually offsetting the tax benefit, which is the basis of the static trade-off theory.

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