📖 估值倍数综合练习

Equity Investments

I. Lesson Focus

This lesson consolidates all major valuation multiples (P/E, P/B, EV/EBITDA, P/S) introduced in the Equity Investments curriculum. Candidates will master when to select each multiple, how to calculate justified multiples using the dividend discount model, perform cross-company and cross-border comparisons, and avoid the most frequent calculation and interpretation traps tested at Level I.

II. The Problem

You are a sell-side analyst required to produce a two-week valuation report covering three consumer electronics companies listed in mainland China, Hong Kong, and the United States. The client demands both DCF absolute valuations and relative valuations using multiples. The three firms exhibit dramatically different earnings growth rates, ROE, capital structures, and accounting policies. Naively applying the same P/E multiple produces valuation errors of up to 40%. This lesson uses realistic cases to systematically practice the selection, adjustment, calculation, and combined use of P/E, P/B, EV/EBITDA, and P/S multiples so that candidates can rapidly decide “which multiple is most appropriate” and avoid common pitfalls on exam day.

III. Fundamental Principles and Selection Framework for Valuation Multiples

The core logic of relative valuation is comparable company analysis: firms with similar risk, growth, and cash-flow characteristics should trade at similar multiples.

Common Equity Multiples versus Enterprise Value Multiples
- Equity multiples (P/E, P/B, P/S, P/CF): numerator is share price, denominator is a per-share metric.
- Enterprise value multiples (EV/EBITDA, EV/EBIT, EV/Sales): numerator is enterprise value (EV = market cap + net debt + minority interest + preferred stock).

Three Golden Rules for Choosing a Multiple
1. Numerator and denominator must match (equity vs. enterprise).
2. Denominator must be positive and economically meaningful (never use P/E on loss-making firms).
3. The multiple must be highly correlated with the company’s fundamental drivers (growth, ROE, risk, accounting policies).

Leading versus Trailing Multiples
- Trailing P/E = current price / last 12 months EPS
- Leading P/E = current price / expected next-year EPS

IV. In-Depth Analysis and Adjustments for the P/E Ratio

P/E is the most frequently tested multiple. Its theoretical foundation comes from the Gordon growth model:

$$P_0 = \frac{D_1}{r-g}=\frac{E_1\times(1-b)}{r-g}$$

Therefore:

$$ \text{Justified Leading P/E} = \frac{1-b}{r-g} $$

$$ \text{Justified Trailing P/E} = \frac{(1-b)(1+g)}{r-g} $$

where $b$ = retention ratio and $g = b \times \text{ROE}$.

Key Adjustments
- Remove non-recurring items (one-time gains/losses).
- Adjust for differences in accounting standards (R&D capitalization, depreciation policies).
- For cyclical firms, use normalized EPS rather than reported EPS.

V. Appropriate Use and Limitations of P/B

P/B is especially useful for financial institutions and asset-heavy companies. Its justified form is:

$$ \text{Justified P/B} = \frac{\text{ROE}-g}{r-g} $$

Advantages: book value is relatively stable and harder to manipulate; can be used for loss-making firms.
Disadvantages: severely undervalues light-asset, high-R&D companies (e.g., technology); heavily influenced by accounting choices (inventory methods, depreciation lives).

VI. Advantages and Calculation of EV/EBITDA

EV/EBITDA is the preferred multiple for cross-border comparisons and firms with dissimilar capital structures because it is unaffected by interest, taxes, and depreciation policies.

$$ \text{EV} = \text{Market Cap} + \text{Net Debt} + \text{Minority Interest} + \text{Preferred Stock} - \text{Cash \& Equivalents} $$

EBITDA = EBIT + Depreciation & Amortization.

Best Used For: capital-intensive industries (manufacturing, telecom, energy), M&A valuation, and comparing companies facing different tax regimes.

VII. Brief Notes on Other Multiples

• P/S is suitable when earnings are negative but revenues are stable (e.g., early-stage firms). It is positively related to net profit margin and growth.
• Dividend yield is useful for stable high-payout companies but ignores growth potential.

Worked Cases

Case 1: Justified P/E Calculation and Comparison

Company A: expected EPS growth $g=6\%$, retention ratio $b=0.4$, required return $r=10\%$, current leading P/E = 18×.

Calculation:
Justified Leading P/E = $(1-0.4)/(0.10-0.06)=0.6/0.04=15×$

Conclusion: the stock appears 20% overvalued at 18×. The implied sustainable growth rate using ROE = 15% is $g=0.4×15\%=6\%$, consistent with the assumption.

Case 2: Using EV/EBITDA When Capital Structures Differ

Company X: market cap = 8 bn, net debt = 2 bn, EBITDA = 1.5 bn → EV/EBITDA = $(8+2)/1.5=6.67×$
Company Y: market cap = 12 bn, net cash = 1 bn, EBITDA = 1.8 bn → EV/EBITDA = $(12-1)/1.8=6.11×$

Although Y’s P/E looks more expensive because it has no leverage, EV/EBITDA shows the valuations are similar once capital structure is neutralized.

Case 3: Comprehensive P/B Application to a Bank

Bank: ROE = 14%, $g=4\%$, $r=11\%$, current P/B = 1.8×.

Justified P/B = $(0.14-0.04)/(0.11-0.04)=0.10/0.07≈1.43×$

The stock appears 26% overvalued. If the bank has understated loan-loss provisions, true ROE may be only 10%, lowering justified P/B to 0.86× and indicating severe overvaluation.

Traps

Key Formulas

• Justified Leading P/E = $(1-b)/(r-g)$
• Justified Trailing P/E = $(1-b)(1+g)/(r-g)$
• Justified P/B = $(\text{ROE}-g)/(r-g)$
• Sustainable growth $g=b\times\text{ROE}$
• $\text{EV}=\text{Market Cap}+\text{Net Debt}+\text{Minority Interest}+\text{Preferred Stock}-\text{Cash}$
• PEG = (P/E) / growth rate (in percent); PEG < 1 may indicate undervaluation (use with caution)
• EV/EBITDA is independent of interest, tax, and depreciation policy differences

Practice Questions

Q1. Using the Gordon model, if retention ratio $b=0.35$, $r=9\%$, $g=5.25\%$, the justified leading P/E is closest to:
A. 7.22　B. 8.08　C. 11.43　D. 12.14

Q2. In which situation is EV/EBITDA most appropriate?
A. Two loss-making high-tech start-ups
B. Two capital-intensive manufacturers with very different leverage ratios
C. Two high-dividend banks
D. Two cyclical firms with highly volatile revenue

Q3. A stock trades at $45. Last year’s EPS was $2.80; next year’s expected EPS is $3.20. The trailing and leading P/E ratios are respectively:
A. 16.07 and 14.06
B. 14.06 and 16.07
C. 16.07 and 12.50
D. 12.50 and 14.06

Q4. Given ROE = 16%, $g=6\%$, $r=11\%$, the justified P/B is closest to:
A. 1.00　B. 1.45　C. 1.82　D. 2.00

Q5. When valuing a loss-making biotech company, the least appropriate multiple is:
A. P/S　B. EV/Sales　C. P/E　D. EV/EBITDA

Q6. Which statement about P/B is incorrect?
A. It is useful for valuing financial institutions.
B. It can severely undervalue firms with large intangible assets.
C. Book value is unaffected by accounting policies.
D. It can be used for loss-making companies.

Q7. A firm has EV = $250 m, EBITDA = $40 m, net debt = $60 m. If its P/E is 18× and market cap = $180 m, the implied interest and tax amount embedded in the EBITDA multiple is closest to:
A. $10 m　B. $20 m　C. $30 m　D. Cannot be calculated

Q8. Analyst notes Country A firms trade at average trailing P/E of 22× while Country B trades at 15×. The most likely explanation is:
A. Country A firms have higher average growth rates
B. Country A firms have lower ROE
C. Country A firms have significantly higher leverage
D. Country A firms use more aggressive depreciation policies

Answers

Takeaways

• The key to multiple selection is “consistency”: numerator-denominator match and alignment with fundamental drivers.
• Both justified P/E and P/B derive directly from the Gordon model; memorize $(1-b)/(r-g)$ and $(\text{ROE}-g)/(r-g)$.
• EV/EBITDA is the best tool when capital structures or tax regimes differ.
• Never use P/E on loss-making companies; prefer P/S or EV/Sales instead.
• Every multiple requires adjustment for non-recurring items, accounting differences, and cyclical normalization.
• On exam day, when asked “most appropriate multiple,” first ask: Is the firm profitable? Are leverage levels different? Is the business asset-light?