3.3 Capital Structure & Leverage

Modigliani-Miller Propositions

The Modigliani-Miller (MM) theorem is the foundation of capital structure theory.

MM Proposition I (no taxes): In a frictionless world with no taxes and no bankruptcy costs, a firm's value is determined by its assets and cash flows, not by how it is financed. Capital structure is irrelevant because investors can replicate any leverage themselves (homemade leverage).

MM Proposition II (no taxes): The cost of equity rises linearly with leverage, exactly offsetting the benefit of cheaper debt, so WACC stays constant.

MM with corporate taxes: Because interest is tax-deductible, the interest tax shield adds value. Firm value rises with leverage, and in the extreme the theory implies a capital structure that is nearly all debt.

Trade-Off Theory

The pure tax conclusion is unrealistic. The trade-off theory balances the tax shield benefits of debt against the rising costs of financial distress (bankruptcy, lost customers, fire-sale asset values) and agency costs. The optimal capital structure is the point where the marginal tax benefit of one more dollar of debt equals the marginal distress cost.

Pecking-Order Theory

A competing view, the pecking-order theory, says firms prefer financing in a set order: internal funds (retained earnings) first, then debt, and new equity only as a last resort. The logic is information asymmetry: managers issue equity when they believe shares are overvalued, so the market reads a new equity issue as bad news. Unlike the trade-off theory, the pecking order implies no single target debt ratio.

Optimal Capital Structure and WACC

The optimal capital structure is the debt-equity mix that minimizes WACC, which is equivalent to maximizing firm value. Adding cheap, tax-shielded debt lowers WACC at first. But as leverage climbs, lenders demand higher rates (rising Rd) and shareholders demand more for the added risk (rising Re). Beyond the optimum, these rising costs overwhelm the tax benefit and WACC turns back up, forming a U-shaped curve.

Business Risk vs. Financial Risk

• Business risk is the inherent variability of operating income (EBIT), independent of how the firm is financed. It stems from demand volatility, cost structure, and competition, and is amplified by fixed operating costs.
• Financial risk is the additional risk borne by equity holders from using debt. The more fixed interest a firm must pay, the more volatile its EPS becomes and the higher the chance of distress.

A firm with high business risk should generally use less debt to keep total risk manageable, while a stable-cash-flow firm (e.g., a utility) can support more debt.

Leverage Measures

Three elasticity measures quantify how fixed costs magnify volatility.

Degree of Operating Leverage (DOL)

DOL = % Change in EBIT / % Change in Sales = Contribution Margin / EBIT

DOL rises with fixed operating costs. A firm with contribution margin of $400,000 and EBIT of $100,000 has DOL = 400,000 / 100,000 = 4.0, so a 10% rise in sales produces a 40% rise in EBIT.

Degree of Financial Leverage (DFL)

DFL = % Change in EPS / % Change in EBIT = EBIT / (EBIT - Interest)

DFL rises with fixed interest costs. With EBIT of $100,000 and interest of $20,000, DFL = 100,000 / (100,000 - 20,000) = 100,000 / 80,000 = 1.25, so a 40% rise in EBIT produces a 50% rise in EPS.

Degree of Total Leverage (DTL)

DTL = DOL x DFL = % Change in EPS / % Change in Sales

Using the figures above, DTL = 4.0 x 1.25 = 5.0. A 10% increase in sales magnifies all the way to a 50% increase in EPS. DTL captures the firm's total leverage, combining operating (business) and financial risk into one multiplier.

Interpreting the Leverage Numbers

The key insight is that leverage is a double-edged sword: the same multiplier that magnifies gains in good years magnifies losses in bad ones. A DTL of 5.0 means a 10% sales decline cuts EPS by 50%. Firms with high operating leverage (heavy fixed costs, like airlines or software) should be cautious about layering on high financial leverage, because the combined DTL can produce extreme EPS swings and a real risk of insolvency in a downturn.

Operating Leverage Near Break-Even

DOL is highest just above the break-even point, where EBIT is small relative to contribution margin, and falls as sales rise well above break-even. This is why a young firm operating near break-even feels enormous earnings volatility from small sales changes, while a mature, high-volume firm with the same cost structure has a much lower DOL.

Putting It Together

Management chooses the operating cost structure (driving DOL) based on the business model, then sets the financing mix (driving DFL) to keep total risk, the DTL, within acceptable bounds. A capital-intensive firm with high business risk should deliberately hold less debt; a stable-cash-flow firm can substitute cheaper debt for equity to lower WACC and lift shareholder returns, as long as the rising distress costs stay below the tax-shield benefit. This is the practical link between the leverage measures and the optimal-capital-structure decision.