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Microlesson · 5-min read

Modigliani-Miller (MM) Approach — With Tax (1963)

## MM Approach With Tax (1963)

In 1963 MM amended their model to incorporate corporate tax. Once taxes exist, the value of the firm increases (and KO decreases) with leverage, because interest on debt is tax-deductible (the interest tax shield).

### Key result

  • Value of Levered firm > Value of Unlevered firm, due to the tax advantage on interest payments.

### Formulas

1. Value of Levered Firm

$$V_L = V_{UL} + (D \times T)$$

where $V_{UL}$ = value of unlevered firm, $D$ = debt, $T$ = tax rate. The term (D × T) is the present value of the tax shield.

2. Cost of equity in a levered company

$$Ke_g = Ke_u + (Ke_u - Kd)\times \frac{Debt}{Debt + Equity}$$

where $Ke_g$ = cost of equity of levered firm, $Ke_u$ = cost of equity of unlevered firm.

3. WACC in a levered company

$$Ko_g = Ke_u\,(1 - tL)$$

where $t$ = tax rate and $L = \dfrac{Debt}{Debt + Equity}$.

Worked example

### Example 1

Value of levered firm: An unlevered firm is worth ₹40,00,000. It takes on ₹10,00,000 of debt; tax rate is 30%. Then:

V_L = 40,00,000 + (10,00,000 × 0.30) = 40,00,000 + 3,00,000 = ₹43,00,000.

The ₹3,00,000 gain is the value of the interest tax shield.

### Example 2

Levered WACC: If Ke_u = 15%, tax rate t = 30%, and L = Debt/(Debt+Equity) = 0.40, then:

Ko_g = 15% × (1 − 0.30 × 0.40) = 15% × (1 − 0.12) = 15% × 0.88 = 13.2%.

WACC falls below the unlevered cost of equity because of the tax shield.

⚠️ Common exam mistakes

  • Using (D × T) incorrectly — it is added to the UNlevered value, and T must be the tax rate (decimal), not the debt amount.
  • In the WACC formula Ko_g = Ke_u(1 − tL), forgetting that L itself is a fraction, so the product tL is small — students sometimes multiply by t only.
  • Assuming levered = unlevered value under the with-tax model — with tax, the levered firm is always worth more (by the tax shield).
Reference:
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