## Modigliani-Miller (MM) Approach
### Why MM Matters
The NOI approach is definitional/conceptual and lacks behavioural significance — it asserts irrelevance but offers no operational justification. MM provides the behavioural justification for a constant overall cost of capital (and therefore a constant total value of the firm).
There are two versions:
- MM 1958 — Without Tax
- MM 1963 — With Tax
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## MM Approach WITHOUT Tax (1958)
- Given by Modigliani and Miller in 1958.
- Similar to the NOI approach — capital structure decisions are IRRELEVANT.
- VF and K₀ always remain constant, unaffected by any increase/decrease in debt weight (W_d).
### The Three Propositions
Proposition 1 — Value Irrelevance
$$VF = \frac{EBIT \;(NOI)}{K_0}$$
- Total value of the firm and K₀ remain constant.
- Therefore: Value of Levered firm = Value of Unlevered firm ($V_L = V_U$).
Proposition 2 — Cost of Equity Rises with Leverage
- K_e increases in a linear fashion as debt is added, exactly offsetting the cheaper debt, so K₀ stays constant. (Mirrors the NOI offset mechanism.)
Proposition 3 — Investment Decision Rule
- The cut-off rate for investment is completely independent of how the investment is financed.
### The Behavioural Justification — Arbitrage
MM's contribution over NOI is the arbitrage process: if two identical firms (one levered, one unlevered) had different values, investors would use personal (homemade) leverage to arbitrage — buying the undervalued firm and selling the overvalued one — until the two values become equal. This is what forces $V_L = V_U$.
### Graphical View
Like NOI: K₀ is a flat horizontal line, K_e slopes upward with leverage, K_d is constant.