📖 公司金融测试讲评

Corporate Finance

I. Lesson Focus

This lesson provides a comprehensive review of all major Corporate Finance topics tested at CFA Level I. It integrates capital budgeting decision rules, cost of capital calculation, capital structure theory, dividend policy, and corporate governance mechanisms. Emphasis is placed on formula application, numerical accuracy, conceptual distinctions, and the exact traps that repeatedly appear in the actual exam.

II. The Problem

A candidate in a mock exam faced contradictory signals when both NPV and IRR were calculated for the same project, forgot the tax shield when computing WACC, confused residual dividend policy with stable dividend policy, and misidentified agency problems in a corporate governance scenario. These errors are extremely common. This lesson revisits the underlying theory with precise formulas, works through three detailed numerical cases, highlights eight classic traps, and supplies eight targeted practice questions with full explanations so that candidates can eliminate these recurring mistakes.

III. Capital Budgeting Review

Capital budgeting evaluates long-term investment projects. The two primary methods are Net Present Value (NPV) and Internal Rate of Return (IRR).

NPV formula: $$ NPV = \sum_{t=0}^{n} \frac{CF_t}{(1+r)^t} - C_0 $$ where $r$ is the required rate of return (typically WACC), $CF_t$ is the cash flow at time $t$, and $C_0$ is the initial outlay.

Decision rule: Accept if NPV > 0; reject if NPV < 0. NPV measures the direct increase in shareholder wealth and is the theoretically superior criterion.

IRR is the discount rate that sets NPV equal to zero. Decision rule: Accept if IRR exceeds the required return.

Conflicts: NPV and IRR can give opposite recommendations when projects differ in size or have unconventional cash-flow patterns. In all conflicts, NPV is the correct decision tool.

Payback period and discounted payback are supplementary tools. Their advantages are simplicity; disadvantages are that they ignore cash flows beyond the payback period and (in the case of simple payback) ignore the time value of money.

IV. Cost of Capital and Capital Structure

The Weighted Average Cost of Capital (WACC) is the appropriate discount rate for projects with the same risk as the firm: $$ WACC = w_d \cdot r_d \cdot (1 - t) + w_e \cdot r_e $$ Weights $w_d$ and $w_e$ must be based on market values at the target capital structure. $r_d$ is pre-tax cost of debt, $t$ is the marginal tax rate (the tax shield appears here), and $r_e$ is cost of equity.

Cost of equity is most commonly estimated with CAPM: $$ r_e = r_f + \beta (E(R_m) - r_f) $$ Alternative approaches are the dividend discount model $r_e = D_1/P_0 + g$ and the bond-yield-plus-risk-premium method.

Modigliani-Miller (MM) Propositions: - Without taxes, capital structure is irrelevant to firm value (MM Proposition I). - With corporate taxes, value of a levered firm is $V_L = V_U + tD$. Debt provides a tax shield. - In reality, financial distress costs and agency costs create a trade-off; an optimal capital structure balances the tax advantage of debt against these costs.

V. Dividend Policy and Corporate Governance

Under perfect capital markets, MM dividend irrelevance theory states that dividend policy does not affect firm value; shareholders can create homemade dividends.

Real-world influences include: - Signaling theory: dividend increases convey positive information about future earnings. - Agency theory: higher dividends reduce free cash flow available to managers, lowering agency costs. - Tax considerations: dividends are often taxed at higher rates than capital gains.

Common dividend policies: - Residual dividend policy: fund all positive-NPV projects first, then pay out whatever earnings remain. This produces volatile dividends. - Stable dividend policy: maintain a steady or steadily growing dividend per share; more popular with investors. - Target payout ratio policy: aim for a long-run payout ratio but allow short-term flexibility.

Corporate governance addresses the principal-agent problem between shareholders and managers. Key mechanisms include independent boards, equity-based compensation, threat of hostile takeovers, monitoring by institutional investors, and mandatory disclosure. ESG considerations are increasingly recognized as factors that can lower the cost of capital and enhance long-term firm value.

Worked Cases

Case 1: NPV-IRR Conflict

Project A requires an initial investment of CNY 1,000,000 and generates cash flows of CNY 800,000 in Year 1 and CNY 600,000 in Year 2. The required return is 10%. Compute NPV and IRR and decide acceptance.

Solution: $$ NPV = -1,000,000 + \frac{800,000}{1.10} + \frac{600,000}{1.10^2} = -1,000,000 + 727,273 + 495,868 = 223,141 > 0 $$ Accept the project.

IRR solves $-1,000,000 + 800,000/(1+IRR) + 600,000/(1+IRR)^2 = 0$. IRR ≈ 35.7% > 10%, so both metrics agree.

If a second larger project had a higher NPV but lower IRR, the NPV rule prevails.

Case 2: WACC Calculation and the Tax Shield

A firm targets a capital structure of 40% debt and 60% equity. Pre-tax cost of debt is 8%, cost of equity is 14%, and the tax rate is 25%. Calculate WACC.

$$ WACC = 0.4 \times 0.08 \times (1-0.25) + 0.6 \times 0.14 = 0.4 \times 0.06 + 0.084 = 0.024 + 0.084 = 0.108 = 10.8\% $$

Forgetting the (1-t) term produces an incorrect WACC of 11.6%. This overstates the hurdle rate and systematically understates project NPVs.

Case 3: Residual versus Stable Dividend Policy

Net income is CNY 8 million. Capital budget requires CNY 5 million of equity financing. Under a residual dividend policy, dividends = 8m – 5m = CNY 3 million. If the firm instead follows a stable dividend policy of CNY 2 per share (1 million shares outstanding), it pays CNY 2 million in dividends and must raise CNY 1 million of new equity. Candidates frequently reverse the priority: residual policy does not stabilize dividends; stable policy does.

Traps

Key Formulas

• $NPV = \sum \frac{CF_t}{(1+r)^t} - C_0$
• $WACC = w_d r_d (1-t) + w_e r_e$
• $r_e = r_f + \beta (E(R_m)-r_f)$
• $V_L = V_U + tD$ (MM with taxes)
• Sustainable growth rate = ROE × (1 – payout ratio)
• $r_e = D_1/P_0 + g$
• Decision hierarchy: NPV > IRR > Payback
• Corporate governance goal: minimize agency costs

Practice Questions

Q1. Which capital budgeting metric is theoretically the best?
A. Internal rate of return (IRR)
B. Net present value (NPV)
C. Payback period
D. Profitability index

Q2. The most appropriate weights for WACC are based on:
A. Book values
B. Target capital structure using market values
C. Historical average book values
D. Next year’s forecasted book values

Q3. According to MM theory with taxes, as debt increases, firm value will:
A. Remain unchanged
B. Increase linearly
C. Increase then eventually decline due to financial distress costs
D. Increase without limit

Q4. A project has cash flows of –200, +300, –150. Which statement is correct?
A. The project has a unique IRR
B. The project may have multiple IRRs
C. NPV is necessarily positive
D. NPV cannot be used for decision making

Q5. A firm following a residual dividend policy is most likely to experience:
A. A stable dividend payout ratio
B. Highly volatile dividend amounts
C. Constant dividend per share growth
D. Priority given to stable dividends per share

Q6. When using the CAPM to calculate cost of equity, which beta is required?
A. Asset (unlevered) beta
B. Equity (levered) beta
C. Industry-average beta
D. Risk-free beta

Q7. Which of the following most effectively mitigates the agency conflict between shareholders and managers?
A. Increasing fixed managerial salary
B. Granting stock options to management
C. Reducing the frequency of disclosure
D. Lowering board independence

Q8. If a firm’s WACC is 10% and an independent project’s IRR is 9%, the project’s NPV is most likely:
A. Positive
B. Zero
C. Negative
D. Indeterminate

Answers

Takeaways

• NPV is the gold-standard capital budgeting rule; IRR is followed only when it agrees with NPV.
• WACC must use market-value target weights and always incorporates the debt tax shield (1-t).
• Residual dividend policy produces volatile dividends; stable dividend policy prioritizes steady dividends per share.
• MM with taxes shows debt increases firm value, but real-world costs create a trade-off and an optimal capital structure.
• Corporate governance exists to reduce agency costs; equity compensation is a primary tool.
• Exam traps repeatedly involve forgetting the tax shield, reversing NPV/IRR priority, confusing residual versus stable dividends, and misapplying beta. Spot these patterns immediately.