📖 薄弱点强化：WACC

Corporate Finance

I. Lesson Focus

II. The Problem

A manufacturing firm is evaluating a new project. Management needs to know the true blended cost of financing the project. Using an incorrect discount rate will lead to over- or under-valuing the project and poor capital allocation decisions. WACC represents the firm’s overall required return to all capital providers (equity and debt), adjusted for the tax deductibility of interest. Calculation errors in WACC remain one of the most frequent reasons candidates lose points in the Corporate Finance section. This lesson systematically strengthens this critical weak area with precise formulas, numerical applications, and common traps.

III. Core Concept and Formula 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, weighted by the market proportions of each source. It is the most commonly used discount rate in project valuation.

Core Formula: $$ WACC = w_e \times r_e + w_d \times r_d \times (1 - t) $$ where: - $w_e = E / V$, $w_d = D / V$, $V = E + D$ (all at market values) - $r_e$: cost of equity (typically from CAPM) - $r_d$: pre-tax cost of debt (usually YTM) - $t$: marginal corporate tax rate

Key Principles: - Weights must reflect the target capital structure at market values, not book values. - Only interest-bearing debt that generates a tax shield receives the (1-t) adjustment. - If preferred stock exists, add the term $w_p \times r_p$ (no tax shield).

IV. Calculating Each Component of Capital Cost

1. Cost of Equity $r_e$

Most frequently calculated with CAPM: $$ r_e = r_f + \beta_e \times (r_m - r_f) $$ - $\beta_e$ must be the levered beta consistent with the capital structure used. - If an unlevered beta (asset beta) is provided, relevering is required.

Hamada Formula (Levering Beta): $$ \beta_L = \beta_U \times \left[1 + (1 - t) \times \frac{D}{E}\right] $$

2. Cost of Debt $r_d$

• Use the yield to maturity (YTM) on existing or new debt.
• If bonds trade at par, $r_d$ ≈ coupon rate.
• Flotation costs are generally not used to adjust $r_d$; instead, they increase the project’s initial outlay.

3. Tax Rate $t$

• Always apply the marginal tax rate, never the effective (average) tax rate.
• When multiple tax jurisdictions are given, use the marginal rate applicable to the incremental project cash flows.

V. Choosing Capital Structure Weights

The most common exam trap involves weight selection: - Correct: Target capital structure using market-value weights. - Incorrect: Book-value weights, current actual weights (if different from target), or historical weights. - When the question states a “target debt-to-equity ratio,” weights must be derived from that target.

If the target is not explicitly given, current market-value weights may be used as a proxy, but always check whether the vignette implies a target structure.

VI. Special Situations

1. Preferred Stock: Dividends are not tax-deductible. The formula expands to: $$ WACC = w_e r_e + w_p r_p + w_d r_d (1-t) $$
2. Project Risk Differs from Firm Risk: Adjust beta using the pure-play method (find comparable firms, unlever their betas, then relever at the project’s target D/E).
3. Convertible Bonds or Warrants: Treat as debt until conversion; do not adjust unless the vignette provides specific probabilities.
4. Leases: Finance leases (and operating leases under IFRS 16) are capitalized and treated as debt in WACC calculations.

Worked Cases

Case 1: Basic WACC Calculation

ABC Company has market value of equity E = CNY 80 million and debt D = CNY 20 million. Its target capital structure is 70% equity and 30% debt. Levered equity beta = 1.2, risk-free rate = 4%, equity risk premium = 6%, pre-tax cost of debt = 7%, tax rate = 25%.

Calculate WACC.

Solution: - $r_e = 4\% + 1.2 \times 6\% = 11.2\%$ - $w_e = 0.70$, $w_d = 0.30$ - $WACC = 0.7 \times 11.2\% + 0.3 \times 7\% \times (1-0.25) = 7.84\% + 1.575\% = 9.415\%$

Case 2: Unlevered Beta and Relevering

XYZ Company has an unlevered beta ($\beta_U$) = 0.9, target D/E = 0.6, tax rate = 30%, risk-free rate = 3.5%, equity risk premium = 5.5%, pre-tax cost of debt = 6.5%.

Calculate the target WACC.

Solution: - $\beta_L = 0.9 \times [1 + (1-0.3)\times 0.6] = 0.9 \times 1.42 = 1.278$ - $r_e = 3.5\% + 1.278 \times 5.5\% = 10.529\%$ - $w_e = 1/(1+0.6) = 0.625$, $w_d = 0.375$ - $WACC = 0.625 \times 10.529\% + 0.375 \times 6.5\% \times (1-0.3)$ $= 6.5806\% + 1.70625\% = 8.28685\% \approx 8.29\%$

Case 3: Preferred Stock and Market Weights

MNO Company: common equity market value = CNY 120 million, preferred stock = CNY 30 million, debt = CNY 50 million. Cost of common equity = 13%, preferred dividend yield = 8%, pre-tax cost of debt = 7.5%, tax rate = 25%. Current market weights are to be used.

Calculate WACC.

Solution: - Total V = 120 + 30 + 50 = 200 million - $w_e = 120/200 = 0.60$, $w_p = 0.15$, $w_d = 0.25$ - $WACC = 0.6 \times 13\% + 0.15 \times 8\% + 0.25 \times 7.5\% \times (1-0.25)$ $= 7.8\% + 1.2\% + 1.40625\% = 10.40625\% \approx 10.41\%$

Traps

Key Formulas

• $WACC = w_e r_e + w_d r_d (1-t) + w_p r_p$ (if preferred stock exists)
• $r_e = r_f + \beta_L \times ERP$
• $\beta_L = \beta_U [1 + (1-t)(D/E)]$
• $w_e = E / (E + D)$, $w_d = D / (E + D)$ (market values)
• Target capital structure weights take precedence over current weights
• Only interest-bearing debt receives the (1-t) adjustment

Practice Questions

Q1. When calculating WACC, the most appropriate weights are:
A. Book-value weights
B. Target capital structure market-value weights
C. Current actual book-value weights
D. Historical average weights

Q2. A firm has an unlevered beta of 0.85, a tax rate of 25%, and a target D/E ratio of 0.8. The levered beta is closest to:
A. 0.85
B. 1.36
C. 1.19
D. 1.51

Q3. Which of the following is NOT multiplied by (1-t) in the WACC formula?
A. Bank loan interest rate
B. Preferred stock dividend rate
C. Corporate bond YTM
D. Implicit rate on finance leases

Q4. If a company permanently increases its target debt ratio, the new WACC will most likely:
A. Increase
B. Decrease
C. Remain unchanged
D. Cannot be determined

Q5. For a project, equity weight = 60%, $r_e$ = 12%, debt weight = 40%, $r_d$ = 8%, tax rate = 30%. The WACC is:
A. 9.44%
B. 10.08%
C. 9.92%
D. 8.96%

Q6. The primary reason for using the pure-play method to adjust beta is to:
A. Remove differences in financial leverage
B. Remove differences in operating leverage
C. Adjust the market risk premium
D. Adjust the risk-free rate

Q7. The most accurate measure of the cost of debt is usually the:
A. Coupon rate
B. Historical average borrowing rate
C. Yield to maturity (YTM)
D. Benchmark bank rate

Q8. When a company has convertible bonds outstanding, in the WACC calculation they are usually treated as:
A. Ignored completely
B. Debt until conversion
C. Equity
D. Weighted by conversion probability

Answers

Takeaways

• WACC must be calculated using target capital structure at market values — the single most important rule.
• Only debt receives the (1-t) tax shield; neither common nor preferred equity qualifies.
• Always relever an unlevered beta with the Hamada formula before inserting into CAPM.
• Use marginal tax rate and YTM; avoid effective tax rates and coupon rates.
• When project risk differs from the firm, apply the pure-play method to adjust beta.
• Flotation costs adjust the initial cash outflow, not the WACC itself.