Capital Structure

Every firm finances itself with some mix of debt and equity. Capital structure asks two questions: what mix minimizes the cost of capital, and does the mix even affect firm value? Modigliani and Miller built the foundation, taxes and bankruptcy costs built the rest.

The weighted-average cost of capital blends what a firm pays each capital provider, weighted by the market-value share of each.

$$\text{WACC}=\frac{E}{V}{r}_e+\frac{D}{V}{r}_d(1-t)+\frac{P}{V}{r}_p$$

KEY: Use market values of debt and equity, not book values. Equity market value is share price times shares outstanding. Debt market value is the present value of remaining cash flows at current yield.

Cost of debt (r_d) is the yield to maturity on new debt the firm would issue today, not the coupon on existing bonds. Multiply by (1−t) because interest is tax-deductible. The tax shield is the reason debt is cheaper than equity at first.

Cost of equity (r_e) is typically estimated with CAPM: r_e = r_f + β(r_m − r_f). Alternatives include the dividend discount model and bond-yield-plus-risk-premium.

Common mistakes

• Using book values for WACC weights. Book equity ignores retained earnings dynamics and share-price changes. Trap: a firm with $100M book equity but $500M market cap should weight equity at $500M.
• Using the coupon as the cost of debt. WACC uses current YTM on new debt. A firm with a 4% coupon bond now yielding 7% has cost of debt of 7%, not 4%.
• Forgetting the (1−t) adjustment on debt. Pre-tax debt cost of 6% with a 25% tax rate becomes 4.5% after tax. Skipping the adjustment inflates WACC.

Bottom line

• $\text{WACC}=(E/V)\cdot r_e+(D/V)\cdot r_d\cdot (1-t)+(P/V)\cdot r_p$, using market values and the after-tax cost of debt
• Cost of debt uses the current YTM on new debt, not the coupon on legacy bonds
• Preferred dividends take no (1−t) adjustment because they are paid from after-tax income
• MM I no taxes: structure is irrelevant. MM II no taxes: $r_e$ rises linearly with D/E, WACC stays flat

Exam shortcut

Memorize the WACC formula and always use market-value weights with after-tax cost of debt. For MM with taxes, V_L = V_U + t·D and the shortcut WACC = r_0 × (1 − t·D/V) usually beats the long form. When the question asks about "optimal," answer minimum WACC and maximum firm value; when it asks about "target," answer long-run desired mix that the firm trends toward over time.

The full lesson (about 2,473 words, 16 min read) adds 2 worked examples, all 6 common mistakes, a self-check, free in the app.

Learning objectives

• capital structure

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