📖 公司金融综合复习

Corporate Finance

I. Lesson Focus

This integrated review consolidates capital budgeting, cost of capital, capital structure, dividend policy, corporate governance, and mergers and acquisitions. Candidates must master how changes in one area (e.g., increasing leverage) affect WACC, NPV, sustainable growth, and shareholder value. The focus is on applying formulas across modules in complex scenarios typical of the CFA Level I exam.

II. The Problem

A manufacturing firm must simultaneously decide whether to invest in a new production line (capital budgeting), adjust its debt-to-equity mix (capital structure), change its dividend payout ratio (dividend policy), and potentially acquire a competitor (M&A). These decisions interact: higher leverage lowers WACC but raises financial risk; a higher dividend payout reduces retained earnings, lowering the sustainable growth rate and potentially requiring external financing that alters the target capital structure. The ultimate goal is to maximize firm value. CFA exams frequently combine these topics into a single large vignette requiring simultaneous calculation of NPV, adjustment of WACC, evaluation of agency conflicts, and assessment of whether an acquisition creates value. This lesson systematically reviews and integrates all core concepts with fully worked cases.

III. Core Framework of Capital Budgeting Decisions

The primary objective of capital budgeting is to accept projects that increase shareholder wealth. The dominant decision rule is Net Present Value (NPV):
$$ \text{NPV} = \sum_{t=0}^{n} \frac{\text{CF}_t}{(1+r)^t} - \text{Initial Investment} $$
Accept if NPV > 0. Internal Rate of Return (IRR) is the discount rate that sets NPV = 0; accept if IRR > required return (r). However, IRR suffers from multiple-IRR and ranking problems (scale and timing differences). When NPV and IRR conflict, NPV is always preferred.

Incremental cash flows are critical—only cash flows that change because of the decision are included:
- Initial outlay = cost of fixed assets + increase in net working capital – after-tax proceeds from sale of old assets
- Operating cash flow = (Revenue – Costs – Depreciation) × (1 – tax rate) + Depreciation
- Terminal cash flow = after-tax salvage value + recovery of net working capital

Key caution: sunk costs are ignored; taxes on salvage value and changes in net working capital must be included.

IV. Integration of Capital Structure and WACC

Under MM Proposition I without taxes, capital structure is irrelevant to firm value. With corporate taxes, the interest tax shield increases firm value:
$$ V_L = V_U + t_c \times D $$
In reality, financial distress costs and agency costs create an optimal capital structure where the marginal benefit of the tax shield equals the marginal cost of distress.

The Weighted Average Cost of Capital (WACC) is the key project discount rate:
$$ \text{WACC} = w_e \times r_e + w_d \times r_d \times (1-t_c) $$
Weights must reflect the target capital structure using market values. Increasing leverage raises the cost of equity ($r_e = r_0 + (r_0 - r_d)\times\frac{D}{E}$) and eventually the cost of debt, producing a U-shaped WACC curve.

In capital budgeting, the WACC used must match the project’s risk. Projects with above-average risk require an upward adjustment to the discount rate.

V. Dividend Policy and Sustainable Growth Rate Linkage

MM dividend irrelevance holds in perfect markets, but taxes, signaling, agency costs, and clientele effects matter in practice.
Retention ratio (b) = 1 – dividend payout ratio
Sustainable growth rate g = ROE × b

Raising the dividend payout lowers b, reduces g, and decreases internally generated funds. In integrated questions, a change in dividend policy directly affects reinvestment capacity, external financing needs, and the target capital structure.

VI. Corporate Governance, Agency Problems, and Mergers

Primary agency conflicts are manager–shareholder and shareholder–creditor. Common governance mechanisms include independent boards, equity-based compensation, managerial ownership, threat of hostile takeover, and protective covenants.

Value creation in M&A comes from synergy:
Synergy value = Value of combined firm post-merger – (Value of acquirer + Value of target)
Common valuation approaches: comparable company multiples, discounted cash flow (DCF), and premium paid.
Acquisition premium = (Offer price – Target’s current market price) / Target’s current market price
An acquisition creates value for the acquirer’s shareholders only if the present value of synergies exceeds the premium paid.

In comprehensive scenarios, an acquisition may alter capital structure (via new debt), change WACC, affect growth rates, and influence dividend policy; all effects must be considered simultaneously.

Worked Cases

Case 1: Capital Budgeting and WACC Integration

XYZ Corp. is evaluating a new production line requiring an initial investment of CNY 8 million. The project lasts 5 years and generates annual pre-tax operating cash flow of CNY 2.6 million. Tax rate is 25%. Project risk matches the firm’s average risk. Target D/E = 0.6, cost of equity = 12%, pre-tax cost of debt = 7%. Calculate NPV and decide whether to accept.

Solution steps:
1. WACC = (0.6/1.6)×12% + (1/1.6)×7%×(1–0.25) = 4.5% + 3.28125% = 7.78125% ≈ 7.78%
2. Annual depreciation = 8 / 5 = 1.6 million (straight-line, zero salvage)
3. Annual after-tax operating cash flow = (2.6 – 1.6)×(1–0.25) + 1.6 = 0.75 + 1.6 = 2.35 million
4. NPV = –8 + 2.35 × PVIFA(7.78%, 5)
PVIFA(7.78%, 5) ≈ 4.152
NPV ≈ –8 + 9.7572 = +1.7572 million > 0 → Accept the project.

Case 2: Sustainable Growth Rate, Dividend Policy, and Financing Needs

ABC Corp. has ROE = 18%, current dividend payout = 40%, asset turnover = 1.2, profit margin = 12%. Target D/E = 0.5. Calculate its sustainable growth rate. If the firm wants to grow at 15%, to what level must the dividend payout be adjusted?

Solution steps:
1. Current retention ratio b = 1 – 0.4 = 0.6
2. Sustainable growth g = ROE × b = 18% × 0.6 = 10.8%
3. Required b for 15% growth = 15% / 18% ≈ 0.8333
4. New dividend payout = 1 – 0.8333 ≈ 16.67%
Conclusion: The firm must sharply reduce its dividend payout to support the higher growth rate internally; otherwise, external equity issuance will be needed, diluting existing shareholders and potentially shifting the capital structure.

Case 3: Integrated Merger Analysis

Target Co. has a current market value of CNY 250 million; Acquirer Co. is valued at CNY 600 million. Post-merger, annual after-tax synergy cash flows of CNY 4.5 million are expected in perpetuity with 3% growth. Acquirer’s WACC is 9%. The cash offer is CNY 310 million. Calculate the value creation for Acquirer’s shareholders.

Solution steps:
1. PV of synergies = 4.5 / (0.09 – 0.03) = 4.5 / 0.06 = 75 million
2. Premium paid = 310 – 250 = 60 million
3. Net value creation = 75 – 60 = 15 million > 0
Conclusion: The acquisition creates CNY 15 million of value for Acquirer shareholders. Note that additional debt financing could further lower WACC and increase synergy PV; agency conflicts must also be evaluated.

Traps

Key Formulas

• NPV = $\sum \frac{\text{CF}_t}{(1+r)^t}$ – Initial outlay
• WACC = $w_e r_e + w_d r_d (1-t_c)$
• Cost of equity (MM no tax): $r_e = r_0 + (r_0 - r_d)\frac{D}{E}$
• Levered firm value (MM with tax): $V_L = V_U + t_c D$
• Sustainable growth: g = ROE × b = ROE × (1 – dividend payout ratio)
• Merger value creation = PV(synergies) – premium paid
• Economic profit = NOPAT – (WACC × Total capital)
• Free cash flow: FCF = NOPAT + Depreciation – Capex – ΔNWC

Practice Questions

Q1. Which of the following should not be included when calculating incremental project cash flows?
A. Sunk costs
B. Opportunity costs
C. Increase in net working capital
D. After-tax proceeds from sale of old equipment

Q2. A project has an IRR of 14% while the firm’s WACC is 11%. The project’s risk is significantly higher than the firm average. The correct decision is to:
A. Accept because IRR > WACC
B. Reject or adjust the discount rate upward
C. Use the APV method instead of WACC
D. Cannot be determined

Q3. According to MM theory with corporate taxes, firm value is maximized at:
A. 100% equity
B. 100% debt (theoretically)
C. An interior optimal debt ratio once distress costs are considered
D. The same structure as in the no-tax case

Q4. Given ROE = 20% and a target growth rate of 12%, the maximum sustainable dividend payout ratio is closest to:
A. 40%
B. 60%
C. 8%
D. 32%

Q5. Value creation for the acquirer’s shareholders in an M&A transaction equals:
A. The premium paid
B. PV of synergies minus the premium paid
C. The target’s current market value
D. The post-merger combined firm value

Q6. Which action simultaneously lowers both WACC and the sustainable growth rate?
A. Increasing the dividend payout ratio
B. Increasing debt in the region left of optimal capital structure
C. Reducing project risk
D. Increasing the retention ratio

Q7. Two mutually exclusive projects: Project A has higher NPV but lower IRR than Project B. Which should be chosen?
A. Project B
B. Project A
C. Both
D. Insufficient information

Q8. The most common error when calculating WACC is:
A. Using the pre-tax cost of debt
B. Using target capital structure market-value weights
C. Forgetting to multiply debt cost by (1 – t)
D. Using historical equity risk premium only

Answers

Takeaways

• Capital budgeting decisions are always driven by NPV; IRR is supplementary only
• WACC must use target market-value weights and match project risk
• Sustainable growth g = ROE × retention ratio directly links dividend policy to financing needs and capital structure
• M&A creates value only when the present value of synergies exceeds the control premium paid
• Agency conflicts are central to corporate governance; equity incentives and independent boards are primary remedies
• All corporate-finance topics are interconnected: capital structure affects WACC, WACC affects NPV, dividends affect growth, and acquisitions change every variable simultaneously