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

### Core Idea

In a perfect capital market with no transaction costs and no taxes, the value of the firm and its cost of capital remain unchanged irrespective of changes in capital structure.

This is also called the capital structure irrelevance proposition.

### Assumptions of MM Theory

1. Capital markets are perfect — all information is freely available; no transaction costs.

2. All investors are rational.

3. Firms can be grouped into 'equivalent risk classes' on the basis of their business risk.

4. No corporate taxes (in the no-tax version).

### Three Propositions of MM (Without Tax)

#### Proposition I — Value of the Firm

The total market value of a firm equals its expected Net Operating Income (NOI) divided by the discount rate appropriate to its risk class (decided by the market).

V_L = V_U = \frac{NOI}{K_o}

Where:

$V_L$ = Value of levered firm
$V_U$ = Value of unlevered firm
$K_o$ = Overall cost of capital (WACC)

> Implication: Two firms identical in all respects except capital structure must have the same total value.

#### Proposition II — Cost of Equity

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

K_{eg} = K_{eu} + (K_{eu} - K_d) \times \frac{D}{E}

#### Proposition III — Overall Cost of Capital is Constant

The capital structure (financial leverage) does NOT affect the overall cost of capital ($K_o$). $K_o$ is determined only by the business risk of the firm — it is independent of the debt-equity mix.

### Arbitrage Process

MM uses the arbitrage mechanism to support this theory. If two identical firms have different values due to different capital structures, investors will exploit the arbitrage opportunity — selling shares of the overvalued firm and buying the undervalued — until prices equalise.

Worked example

### Example 1

Q (PM): Explain briefly Modigliani and Miller approach (without tax).

A: In a perfect capital market with no taxes/transaction costs, MM argued that the value and cost of capital of a firm are independent of its capital structure. Assumptions: perfect markets, rational investors, equivalent risk classes, no corporate taxes. Three propositions: (i) V_L = V_U = NOI/K_o; (ii) K_eg = K_eu + (K_eu − K_d)(D/E) — cost of equity rises with leverage to reflect financial risk; (iii) K_o is constant — depends only on business risk, not on the financing mix.

### Example 2

Q (May 07 — 2 Marks): Explain in brief the assumptions of MM theory.

A: (a) Perfect capital markets — free information, no transaction cost; (b) All investors are rational; (c) No corporate taxes; (d) Firms can be grouped into equivalent risk classes on the basis of business risk.

⚠️ Common exam mistakes

Forgetting the 'no taxes' assumption — this distinguishes MM (without tax) from MM (with tax).
Stating that cost of equity stays constant — actually, cost of equity RISES with leverage in MM theory to offset the cheaper debt.
Confusing MM with the Net Income approach — in NI approach, capital structure DOES matter; in MM (no tax), it doesn't.
Omitting the 'equivalent risk class' assumption (often required for full marks).

Reference:

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Modigliani-Miller (MM) Approach Without Tax

Worked example

⚠️ Common exam mistakes