📖 WACC（加权平均资本成本）导论

Corporate Finance

I. Lesson Focus

This lesson introduces the Weighted Average Cost of Capital (WACC), its calculation using market-value or target weights, the after-tax adjustment for debt, and its critical role as the discount rate in corporate valuation and capital budgeting. Candidates must master the formula, component costs, weighting methods, and common pitfalls involving tax shields, target versus current weights, and project risk adjustments.

II. The Problem

A company is evaluating a new factory expected to generate stable free cash flows. It can finance the project with new equity, bonds, or retained earnings. Each source has a different cost: equity is usually much more expensive than debt, but debt introduces financial risk and provides a tax shield. Managers need a single “average” cost of financing to serve as the hurdle rate. This blended rate is the Weighted Average Cost of Capital (WACC). If a project’s IRR exceeds WACC, it creates shareholder value; otherwise, it destroys value. In the CFA exam, WACC is the essential bridge connecting capital structure, cost of capital, and firm valuation and appears almost every year.

III. Core Concept and Calculation Logic of WACC

The Weighted Average Cost of Capital (WACC) is the average rate of return a company must pay to satisfy all its capital providers (debt holders and equity investors), weighted by the proportion of each source in the firm’s target capital structure. It represents the marginal cost of capital from all financing sources.

The fundamental WACC formula is: $$ \text{WACC} = w_d \cdot r_d \cdot (1 - t) + w_p \cdot r_p + w_e \cdot r_e $$ where: - $w_d$, $w_p$, $w_e$ = target or market-value weights of debt, preferred stock, and common equity - $r_d$ = before-tax cost of debt (yield to maturity on bonds) - $t$ = marginal corporate tax rate - $r_p$ = cost of preferred stock - $r_e$ = cost of common equity

Why market-value weights instead of book-value weights?
Market values reflect what investors currently require and represent the true marginal cost of raising new capital. Book values are historical and often diverge from economic reality. In exam questions that supply both, market-value or target weights must be used.

Tax Shield Effect: Interest expense is tax-deductible, so the effective after-tax cost of debt is reduced by the tax rate. This is why the debt component is multiplied by $(1-t)$.

IV. Determining Capital Weights

1. Target Capital Structure Weights: The proportions management intends to maintain over the long term; these are conceptually preferred for WACC used as a long-term discount rate.
2. Current Market-Value Weights: Calculated from today’s security prices; appropriate for short-term project evaluation.
3. Book-Value Weights: Used only when the question explicitly requires them or data are insufficient; generally not preferred.

When the vignette does not specify, default to target weights. If only current market values are given, use those.

V. Estimating the Cost of Each Capital Component

• Cost of Debt ($r_d$): Usually the yield to maturity (YTM) on the company’s bonds. For non-traded debt, use the yield of similarly rated bonds plus a risk premium.
• Cost of Preferred Stock ($r_p$): $r_p = \frac{D_p}{P_p}$, where $D_p$ is the annual preferred dividend and $P_p$ is the current market price of preferred shares.
• Cost of Common Equity ($r_e$): Three common approaches:
• CAPM: $r_e = r_f + \beta (r_m - r_f)$
• Dividend Discount Model (DDM): $r_e = \frac{D_1}{P_0} + g$
• Bond-yield-plus-risk-premium: $r_e = r_d + \text{equity risk premium}$

CAPM is the most frequently tested method on the CFA Level I exam.

VI. Applications and Assumptions of WACC

WACC is primarily used to: 1. Discount Free Cash Flow to the Firm (FCFF) to obtain enterprise value. 2. Serve as the hurdle rate in capital budgeting. 3. Evaluate the value of synergies in mergers and acquisitions.

Key Assumptions: - The capital structure (weights) remains constant. - The project has the same business risk as the firm’s existing operations. - The firm can raise unlimited capital at the current marginal cost (flotation costs ignored).

If a project’s risk differs materially from the firm’s average risk, an adjusted WACC or unlevered cost of capital should be used.

Worked Cases

Case 1: Basic WACC with Market-Value Weights

XYZ Company has equity market value of CNY 80 million and debt market value of CNY 20 million. Before-tax cost of debt is 8%, tax rate 25%, cost of equity 12%. Current weights match target weights.

Weights: $w_e = 80/100 = 0.8$, $w_d = 0.2$
WACC = $0.2 \times 8\% \times (1-0.25) + 0.8 \times 12\% = 0.2 \times 6\% + 9.6\% = 1.2\% + 9.6\% = 10.8\%$

Case 2: WACC Including Preferred Stock

ABC Company’s target capital structure (by market value): debt 30%, preferred 10%, common equity 60%.
$r_d = 9\%$, $t = 30\%$, preferred dividend yield 7.5%, $r_e = 14\%$.
WACC = $0.3 \times 9\% \times (1-0.3) + 0.1 \times 7.5\% + 0.6 \times 14\%$
= $0.3 \times 6.3\% + 0.75\% + 8.4\% = 1.89\% + 0.75\% + 8.4\% = 11.04\%$

Case 3: Target versus Current Weights Decision

Company A currently has a 40% debt-to-total-capital ratio (market value) but a target of 25%. Current $r_d = 7.5\%$, $r_e = 13\%$, $t = 25\%$.
Current WACC = $0.4 \times 7.5\% \times 0.75 + 0.6 \times 13\% = 2.25\% + 7.8\% = 10.05\%$
Target WACC = $0.25 \times 7.5\% \times 0.75 + 0.75 \times 13\% = 1.406\% + 9.75\% = 11.156\%$

Conclusion: If the firm plans to move toward its target structure, the new project should be evaluated at 11.156%, not the currently lower 10.05%.

Traps

Key Formulas

• $WACC = w_d \cdot r_d (1-t) + w_p \cdot r_p + w_e \cdot r_e$
• Component weight $w_i = \frac{\text{Market Value of Component } i}{\text{Total Firm Market Value}}$
• Preferred stock cost: $r_p = \frac{\text{Preferred Dividend}}{\text{Market Price of Preferred}}$
• After-tax cost of debt = $r_d (1-t)$
• When capital structure changes, WACC typically declines then rises (optimal capital structure exists)

Practice Questions

Q1. A company’s target capital structure is 40% debt and 60% equity. Before-tax cost of debt is 7%, tax rate 30%, cost of equity 13%. The firm’s WACC is closest to:
A. 9.76%　B. 10.36%　C. 10.60%　D. 11.20%

Q2. The main disadvantage of using book-value weights to calculate WACC is that they:
A. Ignore the tax shield　B. Do not reflect current investor-required returns　C. Are too complex to compute　D. Cannot be used to discount FCFF

Q3. Which component does NOT require multiplication by $(1-t)$?
A. Debt cost　B. Preferred stock cost　C. Equity cost　D. Both B and C

Q4. A firm’s current market-value debt weight is 35% while its target weight is 25%. Using the target weights will most likely produce a WACC that is:
A. Lower than the current-weight WACC　B. Higher than the current-weight WACC　C. The same　D. Impossible to determine

Q5. A preferred stock has a par value of $100, annual dividend of $8, and current market price of $92. Its cost is closest to:
A. 7.8%　B. 8.0%　C. 8.7%　D. 9.2%

Q6. The most appropriate method to estimate cost of equity for WACC is usually:
A. Historical average stock return　B. CAPM　C. Past dividend growth rate　D. Bond yield plus 5%

Q7. If a new project has significantly higher systematic risk than the firm’s existing operations, the appropriate action is to:
A. Use the existing WACC directly　B. Increase beta and recalculate WACC　C. Use the unlevered cost of equity　D. Both B and C are acceptable

Q8. A firm’s WACC is 10.5% with a 25% tax rate. If the firm were financed entirely with equity, its cost of equity would most likely be:
A. Equal to 10.5%　B. Higher than 10.5%　C. Lower than 10.5%　D. Impossible to determine

Answers

Takeaways

• WACC is the market-value-weighted, after-tax average cost of financing.
• Debt must be adjusted for the tax shield; preferred and common equity are not.
• Use target capital structure weights whenever stated; otherwise use current market values.
• WACC is appropriate only for projects with risk similar to the firm’s existing business.
• Never forget the $(1-t)$ adjustment and always distinguish book from market values.
• When project risk differs, adjust beta or use a project-specific discount rate rather than the firm WACC.