Estimated study time: 45 minutes
Content:
The cost of capital is the minimum required return that a company must earn on its investments to satisfy its capital providers — both debt holders and equity holders. It is the hurdle rate for capital budgeting: projects earning returns above the cost of capital create value; those earning below destroy value. The Weighted Average Cost of Capital (WACC) is the most important version: WACC = (E/V) × Re + (D/V) × Rd × (1 – T), where E = market value of equity, D = market value of debt, V = E + D (total firm value), Re = cost of equity, Rd = pre-tax cost of debt, and T = marginal tax rate. The (1 – T) factor reflects the tax deductibility of interest payments — debt financing provides a tax shield that reduces its effective cost. WACC uses market value weights (not book value weights) because it represents the opportunity cost to current investors.
The cost of debt (Rd) is the yield to maturity (YTM) on new debt issuances — the market rate at which the company can currently borrow. It is not the coupon rate on existing debt (which reflects past market conditions). For investment-grade companies, Rd can be approximated using the YTM of the company's traded bonds. The pre-tax cost of debt is then adjusted by (1 – T) for the interest tax shield. The cost of preferred stock is the preferred dividend divided by the current market price: Rp = Dp / P0. Preferred stock is not tax-deductible (dividends are paid from after-tax income), so no tax adjustment is needed.
The cost of equity (Re) is the most difficult component to estimate because equity has no contractual cash flows. The three primary approaches are: (1) the Capital Asset Pricing Model (CAPM): Re = Rf + β × (E(Rm) – Rf), where Rf is the risk-free rate, β is the stock's systematic risk, and (E(Rm) – Rf) is the equity risk premium; (2) the Dividend Discount Model (DDM): Re = D1/P0 + g, where D1 is the next expected dividend, P0 is the current stock price, and g is the sustainable growth rate; and (3) the bond-yield-plus-risk-premium approach: Re = YTM on company's bonds + equity risk premium over bonds (typically 3-5%). Each approach has limitations; analysts often triangulate across methods.
The marginal cost of capital schedule shows how WACC changes as a company raises increasing amounts of capital. As the firm exhausts its retained earnings (the cheapest equity source), it must issue new equity at a higher cost (due to flotation costs). Break points in the MCC schedule occur when cheaper capital sources are exhausted. The optimal capital structure minimizes WACC, maximizing firm value. Modigliani-Miller Proposition I (without taxes) states that in a perfect market, capital structure is irrelevant — firm value is independent of how it is financed. Adding taxes introduces the interest tax shield (Proposition II with taxes), making some debt advantageous. In practice, financial distress costs, agency costs, and information asymmetries mean there is an optimal interior capital structure.
Key Terms:
Quiz Questions:
Q1. A company's capital structure is 40% equity and 60% debt by market value. The cost of equity is 12%, the pre-tax cost of debt is 6%, and the marginal tax rate is 25%. What is the WACC?
A) 7.5% B) 9.0% C% 7.5% D) 6.9%
Answer: D — WACC = 0.40 × 12% + 0.60 × 6% × (1 – 0.25) = 4.8% + 0.60 × 4.5% = 4.8% + 2.7% = 7.5%. Wait: 0.60 × 6% = 3.6%; 3.6% × 0.75 = 2.7%; WACC = 4.8% + 2.7% = 7.5%. The answer is A or C at 7.5%. WACC = (E/V) × Re + (D/V) × Rd × (1 – T) = 0.40 × 12% + 0.60 × 6% × 0.75 = 4.80% + 2.70% = 7.50%.
Answer: A — WACC = 0.40 × 12% + 0.60 × 6% × (1 – 0.25) = 4.80% + 2.70% = 7.50%. The tax shield on interest reduces the effective cost of debt from 6% to 4.5% (6% × 0.75), which is why debt financing reduces WACC relative to all-equity financing (which would have Re = 12%).
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Q2. A company's stock is currently priced at $50. It just paid a dividend of $2.00, and dividends are expected to grow at 5% per year indefinitely. Using the Gordon Growth Model (DDM), what is the cost of equity?
A) 4% B) 9.1% C) 9.2% D) 5%
Answer: C — Re = D1/P0 + g = (D0 × (1 + g)) / P0 + g = ($2.00 × 1.05) / $50 + 0.05 = $2.10 / $50 + 0.05 = 0.042 + 0.05 = 9.2%. Note that D1 = D0 × (1 + g) — next year's expected dividend, not this year's. Using D0 = $2.00 directly instead of D1 = $2.10 gives 9.0% — a common exam error. The growth rate represents both the expected capital gain and the sustainable growth in dividends.
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Q3. A firm's stock has a beta of 1.3. The risk-free rate is 3% and the expected market return is 9%. Using CAPM, what is the cost of equity?
A) 10.8% B) 9.0% C) 12.0% D) 7.8%
Answer: A — Re = Rf + β × (Rm – Rf) = 3% + 1.3 × (9% – 3%) = 3% + 1.3 × 6% = 3% + 7.8% = 10.8%. The equity risk premium is Rm – Rf = 6%, and the beta of 1.3 means the stock is 30% more volatile than the market, requiring a 30% larger risk premium than the market. A beta above 1.0 is typical for cyclical industries like technology, materials, and consumer discretionary.
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Q4. Under Modigliani-Miller Proposition I (without taxes), which of the following is TRUE?
A) Firms should maximize debt usage because debt is cheaper than equity B) Capital structure is irrelevant; firm value is determined solely by its operating cash flows C) The cost of equity remains constant as leverage increases D) WACC increases as the firm uses more debt
Answer: B — M-M Proposition I (without taxes) states that in a frictionless market (no taxes, no transaction costs, no bankruptcy costs, perfect information), the total value of the firm is independent of its capital structure. Investors can replicate any firm's capital structure on their own (homemade leverage), so the firm's financing choices cannot create value. Adding taxes (Proposition I with taxes) introduces the interest tax shield, giving debt a value advantage.
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Q5. A company raises new equity by issuing shares at $40 per share, incurring flotation costs of 5%. Next year's expected dividend is $3.00, and dividends are expected to grow at 6% annually. What is the cost of new external equity?
A) 13.5% B) 7.5% C) 13.89% D) 14.06%
Answer: C — When flotation costs are present, the effective price received is P0 × (1 – F) = $40 × (1 – 0.05) = $40 × 0.95 = $38. Cost of new equity = D1 / [P0 × (1 – F)] + g = $3.00 / $38 + 0.06 = 0.0789 + 0.06 = 13.89%. Flotation costs increase the cost of new external equity above the cost of retained earnings ($3/$40 + 6% = 13.5%), which is why firms prefer internal equity (retained earnings) over external equity issuance.
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