## Modigliani-Miller (MM) Approach — With Corporate Taxes
### Key Adjustment
When corporate taxes are introduced, the MM model recognises the tax-deductibility of interest, which creates a tax shield on debt. This makes the value of a levered firm higher than an unlevered firm.
### Relationship between Financial Leverage and Cost of Equity (with tax)
$$
\boxed{K_{eg} = K_{eu} + (K_{eu} - K_d) \times \frac{Debt(1-t)}{Equity}}
$$
Where:
| Symbol | Meaning |
|---|---|
| $K_{eg}$ | Cost of equity in a levered company |
| $K_{eu}$ | Cost of equity in an unlevered company |
| $K_d$ | Cost of debt |
| $t$ | Corporate tax rate |
| Debt | Market value of debt |
| Equity | Market value of equity |
### Interpretation
- Cost of equity (K_eg) increases linearly with the debt-equity ratio.
- However, the increase is dampened by the (1−t) factor because tax savings on debt reduce the effective financial risk borne by equity holders.
- Compared to the no-tax model, K_eg rises less steeply when taxes are introduced.
### Value of the Firm (with tax)
$$
V_L = V_U + (D \times t)
$$
Where D × t = present value of the interest tax shield.
> Conclusion: With corporate taxes, MM theory implies that a firm should use the maximum amount of debt to maximise its value (since each additional rupee of debt adds tax shield value).