According to Modigliani and Miller, in a world with no corporate taxes a firm cannot change its total value by altering the proportions of debt and equity in its capital structure.

Question

BlackTom AI · Accepted Answer

Modigliani–Miller Proposition I (no taxes) states that the market value of a firm is independent of its capital structure.

1) Relevant knowledge points and concepts
- MM Proposition I (no corporate taxes): in perfect capital markets, leverage does not change firm value. 
- MM Proposition II: cost of equity rises linearly with debt-to-equity to offset benefits of cheaper debt. 
- Key assumptions: no corporate taxes, no bankruptcy costs, frictionless markets (no transaction costs), symmetric information, investors can borrow/lend at same rates as firms.

2) Complete reasoning process step by step
- Start with an unlevered firm cost of capital r0 (the required return on assets).
- If a firm introduces debt, equity holders require a higher return r_e to compensate for increased risk.
- MM II gives the relation between r_e and leverage:
  r_e = r0 + (D/E) (r0 - r_d)
  where r_d is debt cost, D debt, E equity.
- Compute weighted average cost of capital (WACC) after leverage:
  WACC = (E/V) r_e + (D/V) r_d, where V = D + E.

3) Calculations and intermediate steps
- Substitute r_e into WACC:
  WACC = (E/V)[r0 + (D/E)(r0 - r_d)] + (D/V) r_d
       = (E/V) r0 + (D/V)(r0 - r_d) + (D/V) r_d
       = (E/V) r0 + (D/V) r0
       = r0 ( (E+ D)/V ) = r0.
- Therefore WACC remains r0 regardless of D/E.
- Firm value based on perpetual EBIT (or free cash flow) is V = EBIT / r0, independent of capital structure.

4) Why the correct answer is correct
- Because under MM assumptions the increase in equity cost exactly offsets cheaper debt so overall firm value and WACC are unchanged by capital structure. Arbitrage arguments reinforce this: if a levered and unlevered firm had different values, investors could replicate leverage themselves and arbitrage away the difference.

5) Why the other option (False) is incorrect
- Saying "False" would imply capital structure can change firm value even in a no-tax world, contradicting MM Proposition I. In reality capital structure affects value only when assumptions break: with corporate taxes (tax shield V_L = V_U + T_c D), bankruptcy costs, agency costs, or market frictions.

6) Conclusion
- Therefore the correct statement is True, which matches the provided answer.

According to Modigliani and Miller, in a world with no corporate taxes a firm cannot change its total value by altering the proportions of debt and equity in its capital structure.True/False

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