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Microlesson · 5-min read

Modigliani-Miller (MM) Approach — Without Tax (1958)

## MM Approach Without Tax (1958)

The NOI approach is definitional/conceptual — it asserts irrelevance but offers no behavioural justification. The Modigliani-Miller (MM) approach supplies that behavioural justification for why KO (and therefore VF) stays constant.

There are two MM models:

  • MM 1958 — without tax
  • MM 1963 — with tax

### MM Without Tax — Core Idea

  • Similar in conclusion to the NOI approach: capital structure decisions are irrelevant.
  • VF and KO always remain constant, unaffected by changes in the debt weight (Wd).

### The Three Propositions

Proposition 1 — Value of the firm

$$VF = \frac{EBIT\ (NOI)}{KO}$$

  • Total value of the firm and KO remain constant.
  • Therefore Value of levered firm = Value of unlevered firm.

Proposition 2 — Cost of equity rises with leverage

$$Ke = KO + (KO - Kd)\times \frac{Debt}{Equity}$$

  • As the debt-equity ratio rises, Ke rises linearly — this is exactly what keeps KO constant.

Proposition 3 — What drives the cost of capital

  • Capital structure does NOT affect KO.
  • KO is affected only by business risk, not by financial risk.

Worked example

### Example 1

Applying Proposition 2: Suppose KO = 12%, Kd = 8%, and the firm uses a Debt:Equity ratio of 0.5 (i.e. Debt/Equity = 0.5). Then:

Ke = 12% + (12% − 8%) × 0.5 = 12% + 4% × 0.5 = 12% + 2% = 14%.

The cost of equity rises from 12% (all-equity) to 14% as leverage is introduced — the rise exactly offsets the cheaper debt, so KO stays at 12%.

### Example 2

Applying Proposition 1: If a firm has EBIT (NOI) of ₹6,00,000 and KO = 12%, then VF = 6,00,000 / 0.12 = ₹50,00,000 — and this value is identical whether the firm is levered or unlevered (no tax).

⚠️ Common exam mistakes

  • Stating that VF increases with debt under MM-without-tax — without tax, levered value = unlevered value.
  • Forgetting the multiplier (Debt/Equity) in Proposition 2 and using just (KO − Kd).
  • Confusing business risk and financial risk — under Proposition 3 only business risk drives KO.
Reference:
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