M&M Theory: Proposition II
M&M Proposition II explains what happens to shareholders' required return when a firm borrows. Debt is cheaper, but it makes equity riskier, so the cost of equity rises in a straight line with the debt-to-equity ratio. With no taxes, the two effects cancel and WACC stays the same.
M&M Proposition II explained simply
M&M Proposition II says the cost of equity rises in a straight line as a firm borrows: r_E = r_A + (D ÷ E) × (r_A − r_D). Debt is cheaper, but it makes equity riskier, and without taxes the two effects cancel. In the example, the cost of equity is 12% and WACC stays at 10%.
What this M&M Proposition II lesson covers
- The M&M Proposition II formula for the cost of equity
- Why cheap debt does not lower WACC in a world without taxes
- How financial risk pushes up the return shareholders demand
- How to check your answer by recomputing WACC
- How the formula changes once corporate taxes are added
M&M Proposition II formulas, explained
- r_E
- cost of equity (required return on the levered firm's shares)
- r_A
- return on assets, the cost of capital if the firm had no debt (also written r_0 or r_U)
- r_D
- cost of debt
- D ÷ E
- debt-to-equity ratio at market values
- V
- total firm value, D + E
- r_U
- unlevered cost of equity
- T_c
- corporate tax rate
How to apply M&M Proposition II step by step (worked example)
A firm's return on assets is 10% and its debt costs 6%. It has a debt-to-equity ratio of 0.5. No taxes. Find the cost of equity and check WACC.
- Write the formula: r_E = r_A + (D ÷ E) × (r_A − r_D).
- Plug in: r_E = 10% + 0.5 × (10% − 6%) = 10% + 2% = 12%.
- D ÷ E = 0.5 means D ÷ V = 1/3 and E ÷ V = 2/3.
- WACC = (1/3 × 6%) + (2/3 × 12%) = 2% + 8% = 10%.
Answer: The cost of equity is 12%. WACC is still 10%, equal to r_A, so borrowing cheap debt did not lower the overall cost of capital.
M&M Proposition I vs Proposition II
| Proposition I | Proposition II | |
|---|---|---|
| Question | Does debt change firm value? | What does debt do to the cost of equity? |
| Answer (no taxes) | No | It rises with D/E |
| Formula | V_L = V_U | r_E = r_A + (D ÷ E) × (r_A − r_D) |
| Effect on WACC (no taxes) | — | Unchanged |
Harder M&M Proposition II questions
What is the cost of equity at a debt-to-equity ratio of 1.0?
r_E = 10% + 1.0 × (10% − 6%) = 14%. WACC is still 0.5 × 6% + 0.5 × 14% = 10%.
How do corporate taxes change the result?
With a 25% tax rate and D/E of 0.5: r_E = 10% + 0.5 × (10% − 6%) × (1 − 0.25) = 11.5%. The cost of equity rises more slowly, and WACC falls as the firm borrows.
Common M&M Proposition II questions
What does M&M Proposition 2 say?
It says the cost of equity rises linearly with the debt-to-equity ratio. Shareholders demand extra return because debt makes their claim riskier. In a no-tax world, this rise exactly offsets the benefit of using cheaper debt, so the firm's WACC does not change.
Why does the cost of equity increase with debt?
Lenders get paid first and their payments are fixed, so all the ups and downs of the business land on a smaller equity base. That extra financial risk means shareholders need a higher expected return, which shows up as a higher cost of equity and a higher equity beta.
What is the difference between M&M Proposition 1 and 2?
Proposition I is about value: the firm is worth the same whatever its debt ratio. Proposition II is about returns: it shows how the cost of equity must rise with leverage so that the overall cost of capital, and therefore firm value, stays constant.
How does M&M Proposition 2 change with taxes?
With corporate taxes, the slope is multiplied by (1 − T_c): r_E = r_U + (D ÷ E)(r_U − r_D)(1 − T_c). The cost of equity still rises with debt, but more slowly, and after-tax WACC falls as the firm borrows more.