📖 估值比率（P/E, P/B, EV/EBITDA）

Financial Statement Analysis

I. Lesson Focus

This lesson examines the three most widely used valuation multiples—price-to-earnings (P/E), price-to-book (P/B), and enterprise value-to-EBITDA (EV/EBITDA). Candidates must be able to calculate each ratio, derive justified (theoretical) values using dividend discount and residual income models, select the most appropriate multiple for a given industry or situation, and identify common calculation and interpretation pitfalls.

II. The Problem

Equity analysts must quickly determine whether a stock is cheap or expensive relative to its peers or its own fundamentals. Market price can be compared with earnings, book value, or cash-flow proxies, but each ratio has different numerators, denominators, sensitivities to accounting choices, leverage, and growth. Using the wrong multiple or failing to adjust for non-recurring items, differing depreciation policies, or capital structure can lead to misclassification of growth stocks as value traps or highly leveraged firms as bargains. This lesson solves the practical problem of how to correctly compute, justify, compare, and interpret these ratios in real-world and exam settings.

III. Core Logic of Valuation Ratios

Valuation ratios express price (per-share or enterprise) relative to a fundamental driver of value. The “right” level of a multiple depends on expected growth, risk (required return), return on equity, capital structure, and industry characteristics. CFA Level I emphasizes three core multiples: trailing and leading P/E, P/B, and EV/EBITDA. Each has theoretical justifications derived from the Gordon growth model or residual-income model.

IV. Price-to-Earnings (P/E) Ratio

4.1 Definitions

• Trailing P/E = Current share price / EPS over the past 12 months
• Leading (Forward) P/E = Current share price / Expected EPS over the next 12 months

EPS should be based on continuing operations, excluding non-recurring items.

Formulas:
$$ \text{Trailing P/E} = \frac{P_0}{\text{EPS}_0}, \quad \text{Leading P/E} = \frac{P_0}{\text{EPS}_1} $$

4.2 Theoretical Justification (Gordon Growth Model)

$$ \text{Justified Leading P/E} = \frac{1-b}{r-g} $$ where $b$ = retention ratio, $r$ = required rate of return, $g$ = perpetual growth rate. Higher growth or lower risk produces a higher justified P/E.

4.3 Advantages and Disadvantages

Advantages: Intuitive, widely used by market participants, strongly related to earnings growth.
Disadvantages:
- Useless for loss-making companies;
- Distorted by accounting differences (depreciation, R&D expensing);
- Highly volatile for cyclical firms—high trailing P/E may simply reflect temporarily depressed earnings.

V. Price-to-Book (P/B) Ratio

5.1 Definition

$$ \text{P/B} = \frac{\text{Current Share Price}}{\text{Book Value per Share}} $$ Book value is usually common shareholders’ equity minus preferred stock; analysts often use tangible book value (excluding goodwill and intangibles).

5.2 Theoretical Justification (Residual Income Model)

$$ \text{Justified P/B} = 1 + \frac{\text{ROE}-r}{r-g} $$ When ROE > r, justified P/B > 1.

5.3 When to Use and Limitations

Best suited for banks, insurance, and real-estate companies where assets drive value.
Poor for technology or brand-heavy firms whose intangible assets are understated on the balance sheet.
Limitations: accounting differences (revaluation, goodwill impairment, R&D capitalization) impair comparability; meaningless when book value is negative.

VI. Enterprise Value to EBITDA (EV/EBITDA)

6.1 Definition

$$ \text{EV/EBITDA} = \frac{\text{Enterprise Value}}{\text{EBITDA}} $$ EV = Market capitalization + Net debt + Minority interest + Preferred stock – Cash and cash equivalents.
EBITDA = Operating income before interest, taxes, depreciation, and amortization.

6.2 Key Advantages

• Independent of capital structure (no leverage bias);
• Independent of depreciation and tax policies;
• Usable for companies with negative net income (provided EBITDA > 0);
• Excellent for cross-border and cross-industry comparisons, especially capital-intensive sectors.

6.3 Limitations

• Ignores capital expenditures—growth companies may appear cheaper than they are;
• Does not reflect changes in working capital;
• Still affected by revenue-recognition and expense-capitalization choices.

Worked Cases

Case 1: Trailing vs. Leading P/E and Growth

Company A trades at ¥45. Reported 2023 EPS = ¥3.0 (includes ¥0.5 one-time gain). Expected 2024 EPS = ¥3.8. Perpetual growth = 4 %, required return = 10 %, payout = 40 %.

Calculations:
Adjusted trailing EPS = 3.0 – 0.5 = 2.5 → Trailing P/E = 45 / 2.5 = 18.0
Leading P/E = 45 / 3.8 ≈ 11.84
Justified leading P/E = (1 – 0.6) / (0.10 – 0.04) = 0.4 / 0.06 ≈ 6.67

Conclusion: The leading P/E of 11.84 exceeds the justified multiple; the stock appears overvalued.

Case 2: P/B and ROE Analysis (Bank)

Bank B trades at ¥12.80 with book value per share ¥10.00. ROE = 18 %, required return = 11 %, growth = 5 %.

Justified P/B = 1 + (0.18 – 0.11) / (0.11 – 0.05) = 1 + 0.07 / 0.06 ≈ 2.17
Actual P/B = 12.80 / 10.00 = 1.28 < 2.17, suggesting the market doubts the sustainability of the bank’s ROE or perceives hidden risks.

Case 3: EV/EBITDA Cross-Industry Comparison

Company C (manufacturing) has EV = ¥8.5 billion and EBITDA = ¥1.2 billion → EV/EBITDA = 7.08.
Industry average = 8.5. Company C uses more aggressive (shorter-life) depreciation, understating EBITDA by approximately 10 %. Adjusted comparable EV/EBITDA ≈ 7.87. After adjustment the stock still appears cheap relative to peers.

Traps

Key Formulas

• Trailing P/E = $P_0$ / EPS₀ (adjusted for non-recurring items)
• Leading P/E = $P_0$ / EPS₁
• Justified Leading P/E = $(1-b)/(r-g)$
• Justified P/B = $1 + (\text{ROE} - r)/(r - g)$
• Enterprise Value = Market Cap + Net Debt + Minority Interest + Preferred Stock – Cash
• EV/EBITDA (removes effects of leverage and depreciation policy)
• PEG = (P/E) / expected growth rate (in percent); values < 1 often considered attractive (supplementary only)

Practice Questions

Q1. Which of the following is least likely a disadvantage of using trailing P/E?
A. Cannot be used for loss-making firms
B. Affected by differences in accounting policies
C. Completely unaffected by capital structure
D. High volatility for cyclical companies

Q2. Using the residual-income model, if ROE = 15 %, r = 10 %, and g = 4 %, the justified P/B is closest to:
A. 0.83
B. 1.83
C. 2.17
D. 1.00

Q3. The primary advantage of EV/EBITDA over P/E is that it:
A. Is simpler to calculate
B. Is unaffected by capital structure and depreciation policies
C. Can be used for all firms with negative earnings
D. Fully captures changes in working capital

Q4. A stock has a P/E of 25× and expected earnings growth of 30 %. Its PEG ratio is 0.83. This most likely indicates the stock is:
A. Significantly overvalued
B. Significantly undervalued
C. Fairly valued
D. Impossible to judge

Q5. When comparing two commercial banks, the most appropriate valuation multiple is usually:
A. EV/EBITDA
B. P/B
C. P/E
D. EV/Sales

Q6. A firm with large construction-in-progress assets and accelerated depreciation will most likely show an EV/EBITDA that, relative to industry peers, appears:
A. Overstated
B. Understated
C. Unaffected
D. Indeterminate

Q7. Leading P/E is more reliable than trailing P/E when a company has just reported:
A. A large non-recurring loss
B. Stable mature-phase earnings
C. Steady year-over-year EPS growth
D. Peak cyclical earnings

Q8. Which statement about justified (leading) P/E is incorrect?
A. Positively related to growth rate g
B. Negatively related to required return r
C. Positively related to retention ratio b
D. Approaches infinity as g approaches r

Answers

Takeaways

• Distinguish trailing and leading P/E; always adjust for non-recurring items and avoid P/E with loss-making firms.
• P/B is most useful for asset-heavy industries; justified P/B > 1 when ROE exceeds the cost of equity.
• EV/EBITDA is the most robust multiple because it neutralizes capital-structure and depreciation differences—ideal for cross-industry and international comparisons.
• For cyclical companies, normalized or forward-looking earnings prevent misleadingly high or low multiples.
• Theoretical multiples are driven by growth, risk, and profitability (ROE); always compare actual vs. justified values.
• Accounting policy, leverage, growth stage, and non-operating items must be adjusted before drawing valuation conclusions.