📖 WACC 综合计算练习

Corporate Finance

I. Lesson Focus

II. The Problem

A company is evaluating a new project and needs an appropriate discount rate to calculate its NPV. The firm’s capital structure includes debt, preferred equity, and common equity. Interest payments generate a tax shield, the cost of equity can be estimated by multiple methods, and weights should reflect the target capital structure rather than book values. Simply averaging the component costs without proper weighting or tax adjustment will produce a misleading discount rate, leading to incorrect capital budgeting decisions. This lesson builds mastery through three fully worked integrated cases and eight rigorous practice questions that test the complete WACC calculation process under realistic CFA-style scenarios.

III. Core WACC Formula and Calculation Logic

The Weighted Average Cost of Capital (WACC) represents the blended required return of all capital providers and is the appropriate discount rate for free cash flow to the firm (FCFF).

Core Formula: $$ \text{WACC} = w_d \cdot r_d (1 - t) + w_p \cdot r_p + w_e \cdot r_e $$

where: - $w_d$, $w_p$, $w_e$ = target weights of debt, preferred stock, and common equity based on market values - $r_d$ = pre-tax yield to maturity on debt - $t$ = marginal corporate tax rate - $r_p$ = cost of preferred stock (= annual preferred dividend / current market price) - $r_e$ = cost of common equity

Weight Selection Rule: 1. Use the firm’s explicitly stated target capital structure when available. 2. If no target is given, use current market-value weights. 3. Never use book-value weights.

IV. Three Common Methods to Estimate Cost of Equity $r_e$

1. Capital Asset Pricing Model (CAPM) $$ r_e = r_f + \beta (r_m - r_f) $$ where $r_f$ is the risk-free rate, $\beta$ is the stock’s beta, and $(r_m - r_f)$ is the market risk premium.

2. Dividend Discount Model (Gordon Growth Model) $$ r_e = \frac{D_1}{P_0} + g $$ Requires stable perpetual dividend growth with $g < r_e$.

3. Bond-Yield-plus-Risk-Premium Approach $$ r_e = r_d + \text{Equity Risk Premium} $$ The equity risk premium is typically given in the vignette (commonly 3%–5%).

V. Special Treatment of Preferred Stock and Debt Costs

• Preferred stock cost $r_p = \frac{\text{Annual preferred dividend}}{\text{Current market price of preferred}}$. Dividends are not tax-deductible.
• Debt cost must always be on an after-tax basis $r_d(1-t)$ because interest expense creates a tax shield.
• Convertible debt or debt with warrants is usually simplified to straight debt at Level I.

Worked Cases

Case 1: Basic Integrated Calculation (CAPM + Target Weights)

XYZ Corp.’s target capital structure is 40% debt, 10% preferred, 50% common equity. Marginal tax rate = 25%. Given data: - Debt YTM = 8% - Preferred annual dividend = $4, current price = $50 - Risk-free rate = 3%, market risk premium = 6%, β = 1.2

Solution: - After-tax cost of debt = 8% × (1 – 0.25) = 6% - Cost of preferred = 4 / 50 = 8% - Cost of equity (CAPM) = 3% + 1.2 × 6% = 10.2% - WACC = 0.4 × 6% + 0.1 × 8% + 0.5 × 10.2% = 2.4% + 0.8% + 5.1% = 8.3%

Case 2: DDM Equity Cost with Flotation Costs

ABC Corp. paid a $2.00 dividend last year; next year’s dividend is expected to be $2.16. Current share price = $36, perpetual growth rate = 4%. Target debt weight = 35%, pre-tax debt cost = 7%, tax rate = 30%, no preferred stock.

Solution: - $r_e = \frac{2.16}{36} + 4\% = 6\% + 4\% = 10\%$ - After-tax debt cost = 7% × (1 – 0.3) = 4.9% - WACC = 0.35 × 4.9% + 0.65 × 10% = 1.715% + 6.5% = 8.215%

If new equity flotation costs are 5%, net proceeds = 36 × (1 – 0.05) = $34.20, so revised $r_e = 2.16/34.2 + 4% ≈ 10.316% and WACC rises slightly.

Case 3: Complex Scenario — Target vs. Market Weights

DEF Corp. has book values of $60 m debt and $90 m equity; market values are $58 m debt and $142 m equity. Management’s target debt weight is 35%. Debt YTM = 6.5%, tax rate = 25%, β = 1.1, risk-free rate = 2.5%, market risk premium = 5.5%, no preferred stock.

Solution (using target weights): - Target weights: debt 35%, equity 65% - After-tax debt cost = 6.5% × (1 – 0.25) = 4.875% - $r_e = 2.5\% + 1.1 × 5.5\% = 8.55\%$ - WACC = 0.35 × 4.875% + 0.65 × 8.55% = 1.706% + 5.5575% = 7.2635% ≈ 7.26%

Using current market weights (debt ≈ 29%) would produce a lower WACC.

Traps

Key Formulas

• WACC = $w_d r_d(1-t) + w_p r_p + w_e r_e$
• $r_e$ (CAPM) = $r_f + \beta (E(R_m) - r_f)$
• $r_e$ (DDM) = $D_1 / P_0 + g$
• $r_e$ (BYPRP) = $r_d +$ equity risk premium
• Cost of preferred = Annual dividend / Current market price (no tax adjustment)
• Weight priority: Target structure > Current market values > Never book values
• Flotation cost adjustment applies only to the denominator when issuing new shares

Practice Questions

Q1. A company’s target capital structure is 30% debt and 70% equity. The tax rate is 25%, pre-tax cost of debt is 8%, and cost of equity is 12%. The firm’s WACC is closest to:
A. 9.3%　B. 10.2%　C. 10.5%　D. 11.1%

Q2. When using the Gordon growth model to estimate cost of equity, an analyst should use:
A. Last year’s paid dividend (D0)
B. Next year’s expected dividend (D1)
C. The reciprocal of current share price
D. Historical average dividend yield

Q3. Which of the following weights is least appropriate for WACC calculation?
A. Target capital structure weights
B. Current market-value weights
C. Current book-value weights
D. Management’s planned weights for the next three years

Q4. A preferred stock has a par value of $100, pays an annual dividend of $6, and currently trades at $75. Its cost is closest to:
A. 6%　B. 8%　C. 8.33%　D. 6.67%

Q5. Given β = 1.25, risk-free rate = 3.5%, and market risk premium = 5%, the cost of equity using CAPM is:
A. 9.75%　B. 10.0%　C. 10.75%　D. 11.25%

Q6. A firm has current debt market value of $40 million and equity market value of $60 million. Management’s target debt ratio is 45%. For WACC calculation the debt weight should be:
A. 40%　B. 45%　C. 50%　D. Based on book value

Q7. Which statement about the debt tax shield is most accurate?
A. Preferred stock receives an identical tax shield
B. After-tax cost of debt is needed only when discounting FCFF
C. Interest tax shields reduce the effective cost of debt
D. Higher tax rates increase WACC

Q8. Pre-tax debt cost = 7%, tax rate = 30%, preferred cost = 9%, equity cost = 13%. Target weights are 25% debt, 10% preferred, 65% equity. WACC is closest to:
A. 10.08%　B. 10.45%　C. 10.75%　D. 11.05%

Answers

Takeaways

• WACC must be calculated using target or current market-value weights; book values are never acceptable.
• Debt cost is always after-tax; preferred stock and common equity have no tax shield.
• Cost of equity may be estimated by any of the three methods (CAPM, DDM, bond-yield-plus-risk-premium); vignettes often mix them.
• When management states a target capital structure, that structure governs the weights.
• Flotation costs affect only the net proceeds in the denominator of the cost of new equity.
• If project risk differs materially from the firm’s average risk, the company WACC is inappropriate; adjust beta or use a pure-play approach.