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 (WACC) blends what a firm pays each capital provider, weighted by the market-value share of each. You interpret it as the return an average-risk project must earn to satisfy all providers at once, so it is the hurdle rate for projects that look like the firm itself.

$$\text{WACC} = \frac{E}{V} r_e + \frac{D}{V} r_d (1-t) + \frac{P}{V} r_p$$

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 (YTM) on new debt the firm would issue today, not the coupon on existing bonds. Multiply by (1−t) because interest is tax-deductible.

Common mistakes

• Using book values for WACC weights. Book equity includes retained earnings, but it is never remeasured to the stock's market value. 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%.
• Dividing the last dividend. The model divides next year's dividend by price. Example 3's cost of equity is $1.04 / $20 + 4% = 9.2%. Trap: 9.0%, from $1.00 / $20 + 4%.

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, and debt is weighted at market value
• Preferred dividends take no (1−t) adjustment because they are paid from after-tax income
• Cost of equity three ways: CAPM $r_f + \beta \cdot \text{ERP}$, DDM $D_1/P_0 + g$, and pre-tax bond yield plus a 3% to 5% premium

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. For cost of equity, grow the dividend one year before dividing by price, and add the premium to the pre-tax bond yield.

The full lesson (about 4,344 words, 29 min read) adds 9 worked examples, all 8 common mistakes, a self-check, free in the app.

Learning objectives

• capital structure

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