# Modigliani-Miller (MM) Approach - Without Tax

MM (without tax) states that in a perfect capital market with no taxes and no transaction costs, the value and overall cost of capital of a firm remain unchanged regardless of capital structure.

## Assumptions

1. Perfect capital markets - information is freely available; no transaction costs.

2. All investors are rational.

3. Firms can be grouped into equivalent risk classes based on business risk.

4. No corporate taxes.

## The Three Propositions

### Proposition I - Value of the Firm

Total market value of a firm equals expected NOI capitalised at the discount rate appropriate to its risk class.

V(levered) = V(unlevered) = NOI / K0

### Proposition II - Cost of Equity

A firm with debt has a higher cost of equity than an unlevered firm. The cost of equity includes a risk premium for financial risk.

### Proposition III - Overall Cost of Capital

The capital structure (financial leverage) does not affect the overall cost of capital (K0). K0 is determined only by business risk.

## The Intuition - Arbitrage

Any difference in value between identical levered and unlevered firms would be eliminated by investors through personal arbitrage (homemade leverage), restoring V_L = V_U.

Worked example

### Example 1

Conceptual Example: Two firms in the same risk class, each with NOI = Rs. 10 lakh. K0 = 10%. Firm A is unlevered; Firm B has 50% debt. Under MM (no tax), both firms have value = 10,00,000 / 0.10 = Rs. 1 crore. Firm B's equity cost will be higher than A's to compensate for financial risk, but WACC remains 10%.

⚠️ Common exam mistakes

Applying MM (no-tax) conclusions when corporate tax exists — the with-tax version gives a different result
Forgetting that cost of equity rises with leverage even when WACC stays constant
Ignoring the arbitrage mechanism that underpins MM Proposition I

Reference:

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