📖 权益综合复习（上）

Equity Investments

I. Lesson Focus

This cumulative review integrates industry analysis, company analysis, equity valuation models (DDM, FCFE, multiples), and index construction methods. The focus is on applying these tools together to determine intrinsic value, compare it with market price, and reach an investment decision. Candidates must master when to use each model, how to adjust for growth stages, and common calculation pitfalls.

II. The Problem

An investor holds a portfolio of equities and needs to decide whether a particular stock is overvalued or undervalued. The analyst is given macroeconomic conditions, industry structure (Porter’s Five Forces), company financials (ROE, payout, growth), and multiple valuation outputs. The task is to select the most appropriate model, compute intrinsic value using the correct inputs, compare it to the current market price, and recommend a buy/hold/sell decision. Exam questions frequently combine these elements in a single vignette.

III. Equity Investment Analysis Framework Review

Equity analysis uses either a top-down or bottom-up approach. Top-down begins with macroeconomics (GDP growth, interest rates, inflation), moves to industry selection, then to individual securities. Bottom-up starts directly with company-specific competitive advantages and financial quality.

Macro variables affect equities through changes in expected cash flows and the equity risk premium. Rising interest rates typically increase the required return (r), lowering valuations. Economic expansion benefits cyclical industries (autos, industrials) while defensive (non-cyclical) industries such as utilities and staples show more stable earnings.

IV. Core Elements of Industry Analysis

Industry analysis relies on Porter’s Five Forces and the industry life-cycle model.

Porter’s Five Forces
- Threat of new entrants
- Threat of substitutes
- Bargaining power of buyers
- Bargaining power of suppliers
- Rivalry among existing competitors

High rivalry in mature industries usually exerts the strongest downward pressure on profitability.

Industry Life Cycle
- Embryonic: high growth, high risk, negative or low profits
- Growth: rapid revenue increase, improving margins, heavy capex
- Mature: stable growth, high free cash flow, higher payout ratios
- Decline: falling demand, excess capacity, low or negative ROE

Cyclical industries have earnings that move strongly with the economic cycle; defensive industries maintain relatively stable demand across cycles.

V. Company Analysis and Financial Ratios

Company analysis evaluates profitability, efficiency, leverage, and sustainable growth.

Key ratios:
- ROE = Net Income / Average Shareholders’ Equity
- DuPont decomposition: ROE = (Net Profit Margin) × (Asset Turnover) × (Financial Leverage)
- Sustainable growth rate g = ROE × Retention ratio (b), where b = 1 – Dividend payout ratio

A company with ROE persistently above its cost of equity and a sustainable growth rate aligned with actual growth possesses an economic moat. Analysts must check whether the assumed long-term growth rate is realistic (typically cannot exceed nominal GDP growth in perpetuity).

VI. Equity Valuation Model Framework

1. Dividend Discount Models (DDM)

Best suited for firms with stable, predictable dividend policies.

Gordon (Constant) Growth Model
$$P_0 = \frac{D_1}{r - g}$$
where $D_1 = D_0(1+g)$, $r$ is the required return, and $g$ must be less than $r$ and sustainable indefinitely.

Multi-stage DDM
Forecast dividends explicitly during the high-growth phase, then apply the Gordon model for the terminal value at the start of stable growth.

2. Free Cash Flow Models

FCFE = CFO – Capital expenditures + Net borrowing

The intrinsic value is the present value of expected future FCFE discounted at the required equity return, plus the discounted terminal value. Terminal value is often calculated with the Gordon formula applied to the first stable FCFE.

FCFE is especially useful for non-dividend-paying growth companies because it measures cash available to equity holders after all operating and investment needs.

3. Multiples Valuation

• Price-to-Earnings (P/E): leading (forward) or trailing
• Justified (fundamental) leading P/E = $\frac{(1-b)(1+g)}{r-g}$ (derived from Gordon model)
• EV/EBITDA is preferred when comparing firms with different capital structures

When using relative valuation, comparable companies must be similar in industry, size, growth prospects, and risk. Justified multiples link absolute and relative approaches.

VII. Security Market Indices and Performance Evaluation

• Price-weighted index (e.g., DJIA): weights proportional to share price; high-priced stocks dominate.
• Market-capitalization-weighted index (e.g., S&P 500): weights proportional to total market value; creates “winner-take-most” bias.
• Equal-weighted index: requires periodic rebalancing; captures small-firm effect.

Indices serve as benchmarks. Active return = Portfolio return – Benchmark return. Understanding construction method is essential for interpreting index performance and tracking error.

Worked Cases

Case 1: Gordon Growth Model

A company pays a current dividend $D_0 = \$2.00$. Expected perpetual growth $g = 5\%$, required return $r = 11\%$. Calculate the intrinsic value.

Solution:
$D_1 = 2.00 \times 1.05 = \$2.10$
$$P_0 = \frac{2.10}{0.11 - 0.05} = \frac{2.10}{0.06} = \$35.00$$

At a market price of $32, the stock is undervalued and should be purchased.

Case 2: Two-Stage DDM

Current dividend $D_0 = \$1.50$. Supernormal growth of 20% for three years, then perpetual growth of 5%. Required return $r = 12\%$. Compute today’s value.

Solution:
$D_1 = 1.50 \times 1.20 = \$1.80$
$D_2 = 1.80 \times 1.20 = \$2.16$
$D_3 = 2.16 \times 1.20 = \$2.592$
$D_4 = 2.592 \times 1.05 = \$2.7216$
Terminal value at t=3: $TV_3 = \frac{2.7216}{0.12-0.05} = \$38.88$

$$P_0 = \frac{1.80}{1.12} + \frac{2.16}{1.12^2} + \frac{2.592 + 38.88}{1.12^3} \approx 1.607 + 1.723 + 32.85 = \$36.18$$

Case 3: Multiples versus Absolute Valuation

EPS = $3.20$, expected growth $g = 8\%$, retention ratio $b = 0.4$, $r = 10\%$.

Justified leading P/E = $\frac{(1-0.4)(1+0.08)}{0.10-0.08} = \frac{0.6 \times 1.08}{0.02} = 32.4$
Fair value = $32.4 \times 3.20 = \$103.68$

If the current market price is $95 and peer average trailing P/E is 28, the stock appears undervalued on both absolute and relative bases.

Traps

Key Formulas

• Gordon Growth: $P_0 = \frac{D_1}{r-g}$
• Justified leading P/E = $\frac{(1-b)(1+g)}{r-g}$
• Sustainable growth: $g = \text{ROE} \times b$
• FCFE = CFO – FCInv + Net Borrowing
• DuPont: ROE = (NI/Sales) × (Sales/Assets) × (Assets/Equity)
• Active return = Portfolio return – Benchmark return
• Terminal value (Gordon): $TV_n = \frac{FCFE_{n+1}}{r-g}$

Practice Questions

Q1. According to Porter’s Five Forces, which factor typically exerts the greatest pressure on profitability in a mature industry?
A. Threat of new entrants
B. Rivalry among existing competitors
C. Threat of substitutes
D. Buyer bargaining power

Q2. A firm has ROE = 18%, retention ratio b = 0.6, and nominal GDP growth = 6%. Its sustainable growth rate is closest to:
A. 6.0%
B. 10.8%
C. 18.0%
D. 30.0%

Q3. In the Gordon model, if the expected growth rate increases from 4% to 6% while the required return stays constant, the intrinsic value will:
A. Decrease
B. Remain unchanged
C. Increase
D. Cannot be determined

Q4. Which index construction method is most prone to a “winner-take-most” bias?
A. Price-weighted
B. Equal-weighted
C. Market-capitalization-weighted
D. Fundamental-weighted

Q5. A stock trades at $42. Next year’s expected dividend is $2.10, perpetual growth is 5%, and required return is 9%. According to the DDM, the stock is:
A. Overvalued
B. Undervalued
C. Fairly valued
D. Insufficient information

Q6. When calculating FCFE, which item is added back?
A. Capital expenditures
B. Depreciation
C. Net borrowing
D. Increase in working capital

Q7. The relationship between justified trailing P/E and leading P/E is usually:
A. Trailing P/E is higher
B. Leading P/E is higher
C. They are equal
D. Depends on growth only

Q8. A defensive industry in the mature stage is most likely to exhibit:
A. High capex and high growth
B. Stable margins and high dividend payout
C. Intense price competition and negative ROE
D. High R&D and low asset turnover

Answers

Takeaways

• Combine top-down and bottom-up perspectives: macro and industry context must support company-level assumptions.
• The Gordon model requires a stable growth rate lower than the required return; high-growth firms need multi-stage models.
• Justified P/E bridges absolute and relative valuation and is directly derived from retention, growth, and cost of equity.
• FCFE is superior to dividends for firms that do not pay dividends or have volatile payout policies.
• Market-cap-weighted indices are the most common benchmarks but embed concentration risk.
• Industry life-cycle stage heavily influences appropriate valuation multiples; declining firms rarely deserve premium multiples.