📖 权益综合复习（下）

Equity Investments

I. Lesson Focus

This lesson integrates dividend discount models, free cash flow models, relative valuation multiples, industry life-cycle analysis, Porter’s Five Forces, and behavioral finance biases into a unified equity valuation and investment decision framework. Candidates must be able to select the appropriate model for a given company’s life-cycle stage, adjust multiples for differences in growth, risk and accounting policies, and identify when market prices deviate from intrinsic value due to behavioral biases.

II. The Problem

A portfolio manager is simultaneously analyzing three stocks. Company A is in a high-growth phase with an extremely high current P/E. Company B is the market leader in a mature industry, generating stable free cash flow but appearing undervalued by the market. Company C has aggressive earnings management and operates in a highly cyclical industry. The task is to combine DDM, FCFF/FCFE, relative valuation, industry analysis, and behavioral finance concepts to determine which security truly offers investment value. This lesson reviews and synthesizes all major equity investment tools to build a coherent analytical process.

III. Integrated Equity Valuation Framework

Equity valuation is divided into absolute and relative approaches. Absolute valuation relies primarily on dividend discount models (DDM) and discounted free-cash-flow models (FCFF/FCFE). Relative valuation uses multiples such as P/E, P/B, and EV/EBITDA.

Dividend Discount Models (DDM)
The Gordon (constant) growth model is:
$$P_0 = \frac{D_1}{r - g} = \frac{D_0(1+g)}{r - g}$$
where r is the required rate of return and g is the perpetual growth rate (typically capped at nominal GDP growth).

Multi-stage DDMs forecast dividends individually during high-growth periods, apply the H-model for transitional growth, and revert to the Gordon model in the stable phase.

Free Cash Flow Models
FCFE = NI − Net Investment + Net Borrowing − Preferred Dividends
FCFF = EBIT(1−t) + Depreciation − FCInv − WCInv

Stable-growth FCFE valuation:
$$P_0 = \frac{FCFE_1}{r_e - g}$$

IV. Industry Analysis and Company Life Cycle

Industries progress through four stages: embryonic, growth, maturity, and decline. Profitability, competitive structure, and appropriate valuation multiples differ markedly across stages.

• Embryonic: high risk, high growth, usually zero dividends → use P/S or EV/Sales
• Growth: rapid revenue increase, expanding margins → PEG ratio often useful
• Maturity: stable cash flows → DDM and P/E are preferred
• Decline: possible negative growth → liquidation value or P/B

Porter’s Five Forces (rivalry among existing competitors, threat of new entrants, threat of substitutes, supplier bargaining power, buyer bargaining power) determine industry attractiveness.

V. Pitfalls and Adjustments in Relative Valuation

P/E can be trailing or leading (forward). The justified leading P/E for constant growth is:
$$\frac{(1-b)(1+g)}{r-g}$$
where b is the retention ratio.

When using relative valuation, adjustments are required for: 1. Differences in expected growth rates 2. Differences in risk (beta) 3. Differences in financial leverage 4. Accounting differences (goodwill impairment, R&D expensing vs. capitalization)

VI. Behavioral Finance in Equity Investing

Common investor biases include: - Overconfidence: leads to high turnover and under-diversification - Representativeness: equating a good company with a good investment - Anchoring: using recent price peaks as valuation reference points - Herding: amplifies bubbles and crashes

The Efficient Market Hypothesis (EMH) has three forms: weak, semi-strong, and strong. Behavioral finance argues markets are not perfectly efficient, allowing prices to deviate from fundamentals for extended periods and creating opportunities for active managers.

Worked Cases

Case 1: Two-Stage DDM Valuation

ABC Corp pays a current dividend D0 = 2.00. Dividends are expected to grow at 25% for the next three years, then at a perpetual rate of 6%. The required return is 12%. Calculate the current intrinsic value.

Solution:
D1 = 2.00 × 1.25 = 2.50
D2 = 2.50 × 1.25 = 3.125
D3 = 3.125 × 1.25 = 3.90625

Terminal value at t=3: $P_3 = \frac{3.90625×1.06}{0.12-0.06} = 69.01$

Present value:
$P_0 = \frac{2.50}{1.12} + \frac{3.125}{1.12^2} + \frac{3.90625+69.01}{1.12^3} = 58.47$

Case 2: Relative Valuation with Industry Adjustment

Company X reports EPS = 3.2 and trades at P/E = 18. Peer Company Y has a 12% growth rate while X grows at 18%. Both have β = 1.1. Risk-free rate = 5%, equity risk premium = 6%. Using the PEG approach and fundamental P/E, determine whether X is overvalued.

PEG_X = 18 / 18 = 1.0
PEG_Y (assuming P/E = 15) = 15 / 12 = 1.25

X appears cheaper on PEG. However, justified P/E = (1−0.4)(1+0.18) / (0.05 + 1.1×0.06 − 0.18) ≈ 14.0.
Since actual P/E (18) > justified P/E (14), Company X is overvalued.

Case 3: Behavioral Finance and Valuation Bias

A technology stock has delivered 80% annualized returns for three years. Analysts are raising targets and retail investors are piling in. The manager notes declining ROE, negative free cash flow, yet the stock trades at 30× forward earnings.

Analysis: The market exhibits representativeness bias (extrapolating past high growth) and herding. Using an FCFF model, the manager estimates intrinsic value is approximately 35% below current market price and recommends selling.

Traps

Key Formulas

• Gordon DDM: $P_0 = \frac{D_1}{r-g}$
• Sustainable growth rate: g = ROE × b (retention ratio)
• Justified leading P/E: $\frac{(1-b)(1+g)}{r-g}$
• FCFE = NI − (FCInv − Dep) − WCInv + Net Borrowing
• PEG = (P/E) / g (in percent)
• DuPont: ROE = Profit Margin × Asset Turnover × Equity Multiplier
• Levered beta: $\beta_L = \beta_U[1+(1-t)(D/E)]$
• Equity risk premium = Expected market return − risk-free rate

Practice Questions

Q1. In the Gordon growth model, if the expected growth rate increases from 4% to 6% while all else remains constant, the stock price will:
A. Decrease
B. Increase by less than 50%
C. Increase by more than 50%
D. Change cannot be determined

Q2. Which of the following is least likely a valid reason to use the price-to-book (P/B) ratio?
A. The firm has stable ROE
B. The firm has significant intangible assets
C. The firm is a financial services company
D. Book value is close to liquidation value

Q3. A stock trades at $40. Next year’s expected EPS is $4, payout ratio is 40%, perpetual growth is 5%, and required return is 12%. The justified leading P/E is closest to:
A. 8.0
B. 10.0
C. 12.0
D. 15.0

Q4. In behavioral finance, the tendency of investors to extrapolate recent strong performance into the future is known as:
A. Anchoring bias
B. Representativeness bias
C. Mental accounting
D. Loss aversion

Q5. Which statement about FCFF and FCFE is most accurate?
A. FCFE is always greater than FCFF
B. When net borrowing is positive, FCFE can exceed FCFF
C. FCFF ignores the effect of interest expense
D. FCFE is discounted at WACC

Q6. For a firm in the mature stage of its industry life cycle, the most appropriate valuation approach is typically:
A. High PEG and high P/S
B. DDM combined with justified P/E
C. EV/Sales and replacement cost of assets
D. Pure technical analysis

Q7. A company has ROE = 18%, retention ratio = 60%, and required return = 12%. Using the sustainable growth model, its justified P/B ratio is closest to:
A. 1.8
B. 2.7
C. 3.0
D. 4.5

Q8. In a semi-strong form efficient market, which information cannot be used to earn abnormal returns?
A. Technical chart patterns
B. Recently released quarterly earnings
C. Material non-public information
D. All of the above

Answers

Takeaways

• Always cross-validate absolute (DDM/FCFE) and relative (P/E, P/B) valuations.
• Perpetual growth rate g must be less than the required return r; otherwise the model is invalid.
• Industry life-cycle stage dictates the choice of valuation method and multiple.
• Behavioral biases frequently cause prices to deviate from intrinsic value and represent exploitable opportunities for active managers.
• Every multiple must be adjusted for differences in growth, risk, and accounting policies before comparison.
• Sustainable growth rate g = ROE × retention ratio links DuPont analysis directly to valuation models.