📖 权益模块终测（15 题）

Equity Investments

I. Lesson Focus

This final equity module consolidates all core Level I topics: equity valuation models (DDM, FCFE, multiples), industry life-cycle analysis, market efficiency forms, index construction methods, and alternative equity vehicles (private equity, hedge funds, REITs). Candidates must master formulas, assumptions, limitations, and interrelationships to solve integrated scenario-based questions.

II. The Problem

Investment analysts must simultaneously assess whether a market is efficient, determine a company’s stage in its industry life cycle, select the most appropriate valuation model (DDM, FCFE, P/E, EV/EBITDA), understand benchmark construction, and evaluate the role of illiquid alternative equity investments. This lesson tests comprehensive application through 15 high-quality questions while teaching the underlying theory, formulas, and common pitfalls.

III. Core Equity Valuation Framework

Equity valuation rests on the principle that intrinsic value equals the present value of expected future cash flows or a justified multiple. Key models include:

1. Dividend Discount Models (DDM)
   Gordon (constant) growth model:
   $P_0 = \frac{D_1}{r - g} = \frac{D_0(1+g)}{r - g}$
   Critical constraints: $g < r$ and $g$ must be sustainable.

2. Free Cash Flow to Equity (FCFE) Models
   $P_0 = \sum_{t=1}^{n}\frac{FCFE_t}{(1+r)^t} + \frac{P_n}{(1+r)^n}$
   Constant-growth version: $P_0 = \frac{FCFE_1}{r - g}$

3. Multiples Valuation

4. Trailing P/E = $P_0 / EPS_0$; Leading (forward) P/E = $P_0 / EPS_1$
5. Justified leading P/E (constant growth) = $\frac{(1-b)(1+g)}{r-g}$ where $b$ = retention ratio
6. EV/EBITDA is preferred when comparing firms with different capital structures because it is capital-structure neutral.

Key Linkages: ROE = Profit Margin × Asset Turnover × Equity Multiplier (DuPont). Sustainable growth rate $g = ROE × b$.

IV. Industry Analysis and Company Life Cycle

Industries progress through four stages—embryonic, growth, mature, and decline—each with distinct cash-flow patterns and suitable valuation approaches:

• Embryonic: high growth, negative FCFE → use P/S or EV/Sales
• Growth: high ROE, high reinvestment → multistage DDM or FCFE
• Mature: stable growth → Gordon model is most appropriate
• Decline: possible negative growth or liquidation value

Porter’s Five Forces help assess industry profitability and the sustainability of ROE and $g$.

V. Market Efficiency and Behavioral Finance

Efficient Market Hypothesis (EMH) has three forms:

• Weak form: prices reflect all past price and volume data → technical analysis should not work
• Semi-strong form: prices reflect all publicly available information → fundamental analysis should not generate consistent alpha
• Strong form: prices reflect all information, including private information → even insiders cannot earn abnormal returns

Behavioral biases (overconfidence, anchoring, herding, loss aversion) create mispricings that may allow skilled active managers to generate excess returns.

VI. Equity Index Construction Methods

• Price-weighted: e.g., Dow Jones; high-priced stocks dominate; suffers from split distortion.
• Equal-weighted: requires regular rebalancing; gives small-cap stocks more influence.
• Market-capitalization weighted: most common (S&P 500); automatically tilts toward growth stocks, creating a “growth bias.”
• Fundamental-weighted: weights by earnings, dividends, or book value to reduce valuation bias.

Passive investing offers low cost and transparency but cannot beat the market by definition. Active investing attempts to outperform through security selection or market timing.

VII. Alternative Equity Investments

• Private Equity (PE): includes venture capital, growth equity, and buyout funds. Characteristics: low liquidity, long lock-up periods, high target IRRs (>20%), and the classic “J-curve” of early negative returns followed by later gains.
• Hedge Funds: pursue absolute-return strategies with typical “2 and 20” fee structures. Common strategies: long/short equity, event-driven, global macro.
• REITs: must distribute ≥90% of taxable income; valued using FFO or AFFO multiples rather than traditional EPS.

Worked Cases

Case 1: Gordon Growth Model and Sensitivity

A stock pays $D_0 = 2.00$, with perpetual growth $g = 5\%$ and required return $r = 10\%$. Calculate today’s price. Then recompute if $g$ rises to 6% or $r$ falls to 9%.

Solution:
$P_0 = \frac{2.00 × 1.05}{0.10 - 0.05} = 42.00$
At $g = 6\%$: $P_0 = \frac{2.00 × 1.06}{0.10 - 0.06} = 53.00$ (+26.2%)
At $r = 9\%$: $P_0 = \frac{2.10}{0.09 - 0.05} = 52.50$ (+25.0%)
Conclusion: Price is extremely sensitive to small changes in growth or discount rate assumptions.

Case 2: Two-Stage FCFE Valuation

A firm’s 2024 FCFE is 150 million. FCFE grows at 15% annually for 2025–2028, then settles into perpetual 4% growth. Required return $r = 11\%$. Terminal value at end-2028 uses the Gordon model. Compute current equity value (in millions).

Solution:
FCFE stream: 2025 = 172.5, 2026 ≈ 198.4, 2027 ≈ 228.1, 2028 ≈ 262.3
Terminal value (2028) = $\frac{262.3 × 1.04}{0.11 - 0.04} ≈ 38.97$
PV of FCFE (4 periods) ≈ 6.12
PV of terminal value ≈ 25.78
Total equity value ≈ 31.90 million

Case 3: Life-Cycle Stage and P/E Selection

A high-growth firm has ROE = 22%, retention ratio $b = 0.75$, current EPS = 4.00, and $r = 12\%$. Calculate sustainable growth and justified forward P/E. If the firm later matures with $g = 5\%$ and $b = 0.4$, recompute P/E and recommend valuation approach.

Solution:
Sustainable $g = 0.22 × 0.75 = 16.5\%$ (multistage model required while $g > r$).
Mature stage: payout = 0.6, justified leading P/E = $\frac{0.6 × 1.05}{0.12 - 0.05} = 9.0$
Conclusion: Use multistage DDM/FCFE in growth phase; switch to single-stage Gordon or stable multiples once mature.

Traps

Key Formulas

• $P_0 = \frac{D_1}{r-g}$
• $g = ROE × b$
• Justified leading P/E = $\frac{(1-b)(1+g)}{r-g}$
• Sustainable growth (internal) = $\frac{ROE×b}{1-ROE×b}$
• FCFE = FCFF – Int(1-t) + Net Borrowing
• DuPont: ROE = PM × AT × EM
• Sharpe ratio = (Rp – Rf) / σp
• Information ratio = (Rp – Rb) / Tracking Error

Practice Questions

Q1. In a semi-strong efficient market, which of the following is most likely to still produce excess returns?
A. Technical analysis
B. Fundamental analysis
C. Material non-public information
D. Machine-learning models using only public filings

Q2. A stock has $D_0 = 1.80$, $g = 6\%$, $r = 11\%$. Its intrinsic value is closest to:
A. 36.00
B. 38.16
C. 42.00
D. 45.00

Q3. Which statement about market-capitalization-weighted indexes is correct?
A. They automatically buy low and sell high
B. They tend to create a growth bias
C. They overweight small-cap stocks
D. They require no rebalancing

Q4. A firm has ROE = 18%, retention ratio = 60%, and required return = 10%. Its sustainable growth rate is closest to:
A. 6.8%
B. 10.8%
C. 18.0%
D. 30.0%

Q5. The primary advantage of using EV/EBITDA is that it:
A. Is independent of capital structure
B. Only works for mature firms
C. Ignores depreciation policy
D. Directly values equity

Q6. Early negative cash flows in private equity funds are primarily caused by:
A. The J-curve effect
B. Up-front management fees
C. Long investment holding periods
D. All of the above

Q7. If markets are strong-form efficient, then:
A. Fundamental analysis still adds value
B. Technical analysis can generate alpha
C. Even insider information cannot produce abnormal returns
D. Active managers will always beat benchmarks

Q8. A company reports current EPS = 5, expected next-year EPS = 5.5, payout ratio = 40%, $g = 8\%$, $r = 12\%$. Its justified leading P/E is closest to:
A. 8.0
B. 10.0
C. 13.2
D. 16.5

Answers

Takeaways

• Valuation ultimately depends on cash flows, discount rate, and sustainable growth; Gordon model is highly sensitive to $g$ and $r$
• Industry life-cycle stage dictates model choice: multistage for growth, single-stage Gordon for maturity
• Semi-strong efficiency is the most tested form; if public information is reflected, fundamental analysis should not consistently outperform
• Index weighting methodology directly determines risk exposures and biases (price, equal, cap, fundamental)
• Private equity and hedge funds are illiquid, high-fee alternative equity investments characterized by the J-curve and absolute-return objectives
• DuPont analysis plus sustainable growth rate link financial statement analysis to valuation models and must be mastered