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

CFA® Level I · Corporate Issuers · 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.

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:

  1. 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.
  2. independent of its capital structure — correct
  3. 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:

  1. 11.33%Why not: This uses debt-to-total capital of one-third in place of the debt-to-equity ratio of 0.5.
  2. 10.00%Why not: This ignores the extra financial risk that leverage places on shareholders.
  3. 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

Under MM with corporate taxes, a firm has an unlevered cost of capital of 11%, a cost of debt of 5%, a tax rate of 25% and a debt-to-equity ratio of 0.8. Its cost of equity is closest to:

  1. 15.80%Why not: This omits the (1 - t) factor, applying the no-taxes version of Proposition II.
  2. 14.60% — correct
  3. 13.00%Why not: This uses the debt-to-total capital ratio of 0.444 in place of debt-to-equity.

r_e = r_0 + (r_0 - r_d)(1 - t)(D/E) = 11% + 6% x 0.75 x 0.8 = 14.6%. Taxes slow the rise in the cost of equity, so the WACC falls as leverage rises.

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