M&M Theory: Proposition I
M&M Proposition I says that in a perfect market with no taxes, a firm's value does not depend on how it is financed. Splitting the same cash flows between lenders and shareholders doesn't make the pie bigger. Investors can borrow on their own, so they won't pay extra for corporate leverage.
M&M Proposition I explained simply
M&M Proposition I says that in a perfect market with no taxes, a firm's value doesn't depend on how it's financed: V_L = V_U. Splitting the same cash flows between lenders and shareholders doesn't make the pie bigger. In the example, both firms are worth $1,000, and Firm L's equity is worth $600 after its $400 of debt.
What this M&M Proposition I lesson covers
- What M&M Proposition I says and the perfect-market assumptions behind it
- Why a levered firm is worth the same as an unlevered one: V_L = V_U
- How homemade leverage lets investors copy any capital structure
- Why the size of the pie matters, not how you slice it
- What breaks the result in practice: taxes and financial distress costs
M&M Proposition I formula, explained
- V_L
- value of the levered firm (D + E)
- V_U
- value of the same firm with no debt
- EBIT
- expected operating income, assumed constant forever
- r_A
- required return on the firm's assets (the all-equity cost of capital)
How to apply M&M Proposition I step by step (worked example)
Firms U and L are identical, each earning EBIT of $100 a year forever. Firm U has no debt; Firm L has $400 of debt at 6%. The return required on the assets is 10%. No taxes. What are the firms and Firm L's equity worth?
- Value Firm U: V_U = 100 ÷ 0.10 = $1,000.
- By M&M Proposition I, V_L = V_U = $1,000.
- Firm L's equity = V_L − D = 1,000 − 400 = $600.
- Cash flow check: L pays $24 interest and $76 to shareholders, still $100 in total.
- Homemade leverage check: buying 10% of U for $100 with $40 borrowed at 6% costs $60 and pays 10 − 2.40 = $7.60, the same as 10% of L's equity ($60 for $7.60).
Answer: Both firms are worth $1,000, and Firm L's equity is worth $600. If L's equity traded above $600, investors would use homemade leverage on U instead, pushing prices back in line.
M&M Proposition I without and with taxes
| No taxes | With corporate taxes | |
|---|---|---|
| Firm value | V_L = V_U | V_L = V_U + T_c × D |
| Does debt add value? | No | Yes, through the tax shield |
| Main point | Financing only splits the pie | The government's slice shrinks |
If debt doesn't change value, why fear it? David's take
In M&M's world, with no taxes, firms U and L are both worth $1,000. Debt doesn't make you richer or poorer; it only changes who owns what. Add taxes and debt starts to help. So where did the idea that being debt-free is always the responsible choice come from? I believed it for decades myself. It isn't in this theory. Debt is like fire: deadly out of control, very useful under control.
From David's concept: Reconsidering the Debt-Free Convention. This is David's opinion, alongside the standard textbook answer above.
Harder M&M Proposition I questions
What are the firms worth with a 25% corporate tax rate?
Firm U: 100 × (1 − 0.25) ÷ 0.10 = $750. Firm L: 750 + 0.25 × 400 = $850, so L's equity is worth 850 − 400 = $450. The $100 difference is the present value of the tax shield.
Which assumptions does Proposition I depend on?
No taxes, no bankruptcy costs, investors and firms borrow at the same rate, and everyone has the same information. Relaxing them is what makes capital structure matter in real life.
Common M&M Proposition I questions
What does Modigliani Miller Proposition 1 say?
It says that, without taxes or other market frictions, the total value of a firm is set by its assets and their cash flows, not by how those cash flows are split between debt and equity. So a levered firm is worth exactly the same as an identical unlevered firm.
What are the assumptions of the M&M theorem?
The classic version assumes no taxes, no bankruptcy or distress costs, no transaction costs, that investors can borrow and lend at the same rate as firms, that everyone has the same information, and that the firm's investment decisions don't change when its financing changes.
What is homemade leverage?
Homemade leverage means investors borrowing or lending on their own account to recreate the payoff of a levered or unlevered firm. Because anyone can do this, a firm can't raise its value just by changing its debt ratio. Investors won't pay a premium for something they can do themselves.
Does M&M Proposition 1 hold with taxes?
No. Once interest is tax-deductible, debt saves the firm taxes every year. M&M with corporate taxes says V_L = V_U + T_c × D for permanent debt, so the levered firm is worth more by the present value of its interest tax shield.