📖 估值倍数：P/B, P/S, EV/EBITDA

Equity Investments

I. Lesson Focus

This lesson examines three key relative valuation multiples: Price-to-Book (P/B), Price-to-Sales (P/S), and Enterprise Value to EBITDA (EV/EBITDA). Candidates must master their definitions, theoretical derivations, advantages, limitations, and appropriate industry applications. The focus is on calculating justified multiples, adjusting for differences in growth, profitability, and leverage among comparable companies, and recognizing when to switch multiples when earnings are negative or highly volatile.

II. The Problem

You are valuing a mature manufacturing firm and a high-growth software company. Both trade at a P/E of 35×, yet one has an ROE of only 8% while the other has an ROE of 28%. A single multiple cannot determine which stock is cheaper. You need P/B, P/S, and EV/EBITDA to cross-validate relative value, understand their behavior in cyclical, loss-making, or asset-heavy businesses, and select the most appropriate metric for each situation. This lesson solves exactly that practical and exam-critical problem.

III. Fundamental Principles of Valuation Multiples

Valuation multiples express market price as a ratio of a fundamental metric (earnings, book value, sales, EBITDA). The central idea is comparable company analysis: firms with similar risk, growth, and profitability profiles should trade at similar multiples.

Multiples are divided into equity multiples (numerator is equity value, denominator is an equity metric) and enterprise-value multiples (numerator is total firm value, denominator is a metric available to all capital providers).

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

Definition:
$$ P/B = \frac{\text{Current Share Price}}{\text{Book Value per Share (BVPS)}} $$

Theoretical Foundation: Derived from the residual income model. When ROE > cost of equity (r), P/B > 1; when ROE = r, P/B = 1; when ROE < r, P/B < 1.

Justified P/B Formula (constant growth):
$$ P/B = \frac{ROE - g}{r - g} $$

where $g =$ sustainable growth rate $=$ ROE × retention ratio.

Advantages: - Book value is more stable and less easily manipulated than earnings. - Especially useful for banks, insurance, real estate, and other asset-based industries. - Works for loss-making firms when EPS is negative.

Limitations: - Accounting standards (IFRS vs. US GAAP) create comparability issues. - Intangible assets are often understated in light-asset, technology, or brand-heavy companies, making P/B appear artificially high. - Share repurchases can distort BVPS.

Best Used For: Financial institutions, cyclical industrials, and any firm with positive net assets.

V. Price-to-Sales Ratio (P/S)

Definition:
$$ P/S = \frac{\text{Current Share Price}}{\text{Sales per Share}} $$

or on an aggregate basis: Market Cap / Total Revenue.

Theoretical Formula (derived from Gordon growth model):
$$ \frac{P_0}{S_0} = \frac{(1 - b) \times PM_0 \times (1 + g)}{r - g} $$

where $b =$ retention ratio, $PM_0 =$ net profit margin, $g =$ expected growth rate.

Advantages: - Sales revenue is the hardest fundamental to manipulate. - Remains valid even when net income is zero or negative. - Highly effective for cyclical troughs, start-ups, loss-making retailers, and early-stage SaaS companies.

Limitations: - Ignores differences in cost structure and profitability margins. - High fixed-cost businesses cannot be directly compared with low fixed-cost peers. - Does not distinguish between profitable and unprofitable firms with identical sales.

Best Used For: Loss-making companies and revenue-driven businesses (e-commerce, early-stage software).

VI. Enterprise Value to EBITDA (EV/EBITDA)

Definition:
$$ EV/EBITDA = \frac{\text{Enterprise Value}}{\text{EBITDA}} $$

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

Advantages: - Neutral to capital structure; eliminates the distorting effect of different debt levels. - EBITDA removes the impact of depreciation and amortization policies, improving international comparability. - Excellent for capital-intensive industries (manufacturing, telecom, airlines, utilities). - Usable as long as EBITDA is positive.

Limitations: - EBITDA is not true cash flow; it ignores capital expenditure differences. - Still sensitive to differences in asset lives and depreciation methods. - Does not capture working-capital management efficiency.

Best Used For: Capital-intensive sectors, firms with widely differing leverage, and in M&A valuation.

VII. Selecting Multiples and Adjusting Comparables

When selecting peers, adjust for differences in size, expected growth, ROE, leverage, business-cycle stage, and industry sub-segment. Common techniques include: - Industry median or mean. - Regression-based adjustments (e.g., P/B regressed on ROE). - Fundamental adjustments for growth and margin differentials.

Worked Cases

Case 1: P/B Valuation of a Bank

A bank trades at $12 per share with BVPS of $10, ROE = 14%, cost of equity $r = 10\%$, and sustainable growth $g = 5\%$. Calculate the justified P/B and determine if the stock is undervalued.

Solution:
Justified P/B = (0.14 − 0.05) / (0.10 − 0.05) = 0.09 / 0.05 = 1.80.
Actual P/B = 12 / 10 = 1.20.
Since actual P/B < justified P/B, the bank appears undervalued.

Case 2: P/S for a Loss-Making E-commerce Firm

A loss-making online retailer trades at $25 with sales per share of $40 (current net margin = −5%). Expected long-term net margin = 8%, retention ratio $b = 60\%$, $g = 12\%$, $r = 13.5\%$.

Solution:
Justified P/S = [(1−0.6) × 0.08 × (1+0.12)] / (0.135 − 0.12) = (0.4 × 0.08 × 1.12) / 0.015 ≈ 2.39.
Actual P/S = 25 / 40 = 0.625.
The large discount suggests the market is extremely pessimistic about future profitability; further due diligence is warranted.

Case 3: EV/EBITDA Comparison in Capital-Intensive Industry

Firm X: EV = $8.0 billion, EBITDA = $1.2 billion → EV/EBITDA = 6.67×.
Comparable Firm Y trades at 8.5× with 3% higher expected growth but lower CapEx/Depreciation ratio (X = 1.4, Y = 1.1).

Analysis: Although X appears cheaper, its heavier reinvestment burden must be adjusted for. After adjustment, X may be undervalued by approximately 15–20% and could be an attractive acquisition target.

Traps

Key Formulas

• $P/B = \frac{P_0}{BV_0} = \frac{ROE - g}{r - g}$
• $P/S = \frac{(1-b) \times PM_0 \times (1+g)}{r-g}$
• $EV = \text{Market Cap} + \text{Net Debt} + \text{Minority Interest} + \text{Preferred Stock} - \text{Cash}$
• Justified $P/B = \frac{ROE - g}{r - g}$
• When ROE = r, justified P/B = 1
• P/B increases with ROE and g, decreases with r
• EV/EBITDA is preferred when capital structures differ significantly

Practice Questions

Q1. If a company consistently earns an ROE above its cost of equity, its P/B ratio is most likely:
A. Less than 1
B. Greater than 1
C. Equal to 1
D. Unrelated to ROE

Q2. Which situation is most appropriate for applying the P/S multiple?
A. A consistently profitable bank
B. A biotech firm with three years of losses
C. A capital-intensive manufacturer
D. A high-dividend utility

Q3. The primary advantage of EV/EBITDA over P/E is that it:
A. Is easier for management to manipulate
B. Eliminates the effect of different capital structures
C. Requires no growth-rate adjustment
D. Works when EBITDA is negative

Q4. A stock trades at $20 with BVPS of $15, ROE = 12%, r = 10%, g = 4%. Its justified P/B is closest to:
A. 1.33
B. 1.60
C. 2.00
D. 0.80

Q5. When comparing two airlines with markedly different leverage, the least appropriate multiple is:
A. P/B
B. P/S
C. EV/EBITDA
D. P/E

Q6. According to the residual income model, when ROE equals the required return on equity, the justified P/B should equal:
A. 0
B. 1
C. ROE/r
D. (ROE−g)/(r−g)

Q7. Which statement about the P/S ratio is incorrect?
A. Sales are difficult to manipulate
B. It can be used for loss-making firms
C. It fully reflects differences in cost structures
D. It is suitable for revenue-driven internet companies

Q8. A firm has EV = $120 million and EBITDA = $20 million. The median EV/EBITDA for peers is 7.0×. The subject firm’s growth rate is 2% below the peer average. The most reasonable conclusion is:
A. The firm is significantly overvalued
B. The firm is significantly undervalued
C. Further adjustments are required before concluding
D. The 7.0× median can be applied directly

Answers

Takeaways

• ROE relative to cost of equity is the primary driver of justified P/B.
• P/S is the preferred multiple for loss-making and revenue-focused companies, but its inability to capture profitability differences is a frequent exam trap.
• EV/EBITDA is capital-structure neutral and best suited for capital-intensive or highly leveraged industries.
• All multiples require adjustment for growth, ROE, margins, and business-cycle stage.
• When earnings are negative, default to P/B, P/S, or EV/EBITDA before considering P/E.
• Light-asset businesses often show elevated P/B; cross-check with P/S and EV/Sales for a complete picture.