Eduzan

Eduzan / MODULE 06 — Equities (renamed from Equity Investment)

EI 7 Relative Value Equity Valuation Approaches

Valuing equity with price and enterprise value multiples, both by comparison to peers and from forecasted fundamentals. Check-yourself items are study aids.

Relative valuation compares a market-based measure, such as share price or enterprise value, against an income statement, balance sheet, or cash flow figure to judge whether a company looks cheap or expensive versus its current price. Absolute approaches, such as a discounted cash flow (DCF) model, estimate a share price or firm value directly. Relative valuation instead leans on a ratio, a multiple, and the premise that assets which are alike ought to command comparable prices. Applying the principle of no arbitrage, an analyst expects a company’s multiple to gravitate toward those of close substitutes: a multiple far above the peer group hints at overvaluation, and one well below hints at undervaluation, on the view that the gap between price and estimated intrinsic value will eventually close. Multiples are quick to compute and easy to compare, but a disciplined process is needed before any confidence can be placed in the result.

A five-step process

The method of comparables draws conclusions about value by benchmarking a company against similar firms. A well-organized version of the process runs as follows.

Assemble a set of companies that resemble the target closely enough to serve as a benchmark.
Select an appropriate multiple.
Calculate, compare, and interpret the multiple for the company and its peers.
Judge, against those peers and across past, current, and expected future measures, whether the stock is rich, cheap, or fairly priced.
Use one or more multiples to support a DCF valuation, or to frame a relative value range against the firm’s actual trading range.

Choosing a peer group

The first step, selecting a peer group, is a benchmark set of comparable companies. The ideal peers share the target firm’s cash flow, risk, and growth characteristics. Analysts often start from firms in the same industry, since industry members typically face similar competitive forces, suppliers, customers, and value drivers. Standard classification frameworks help define an industry: the Refinitiv Business Classification (TRBC), the Global Industry Classification System (GICS), and the Industry Classification Benchmark (ICB) each sort companies from broad economic sectors down to narrow subindustries. Because peer construction is so consequential, a later section returns to it in depth.

Selecting a multiple

A multiple pairs a numerator that captures market value with a denominator that gauges company fundamentals. The numerator reflects value to a set of claimants: market capitalization represents value to shareholders, while enterprise value (EV) represents value to all providers of capital. The denominator must align with the same claimants. A share-price numerator belongs with an equity measure such as earnings, dividends, free cash flow to equity, or book value of equity; an EV numerator belongs with a whole-company measure such as revenue, EBIT, EBITDA, or free cash flow to the firm. A dividend-based multiple suits firms with stable dividends and a steady payout ratio, so stretching it across dividend payers and non-payers would be poor practice.

Commonly applied multiples by claimant and source

Source of fundamental	Shareholders	All capital providers
Income statement	P/E, P/Sales	EV/EBITDA, EV/EBIT, EV/Sales
Balance sheet	P/B	Firm value / book value of capital, EV / book value of capital less cash
Cash flow statement	Dividend yield, market cap / FCFE	EV / FCFF

Whatever multiple is chosen, it must be defined and computed the same way for every firm in the comparison. Inconsistencies creep in through differing accounting methods, reporting frequencies, one-time items, and timing differences. Consider three firms in one industry whose quarters end on 31 December, 30 November, and 31 October. Their share prices are struck at three different dates, so their price-to-book ratios (P/Bs) are not comparable until the prices are all restated to a common date, for example 31 December. Even then the book values sit at different dates, and a repurchase between an earlier reporting date and December can move book value in a way the analyst cannot always adjust for.

Reading the peer distribution

Once the multiple is defined, the analyst computes it across the peer set and locates the target within the distribution. A measure of central tendency, the mean or the median, is usually taken as the representative fair value for the set, treating extreme observations as candidates for mispricing or wrongful inclusion. A thorough analyst goes beyond the average to consider dispersion and skewness. A positively skewed distribution can have a mean that sits well above the median, in which case the median is the better gauge of the center. A related problem is the ratio that is not meaningful, such as a P/E when a firm reports a net loss.

Selected multiples of large European pharmaceutical firms, 2024

Company	Market cap (EUR mn)	EV (EUR mn)	EV/EBITDA	P/E
Median	196,701	222,631	9.60	22.17
Bayer AG	28,033	65,536	3.77	N/A
GSK plc	85,974	101,263	8.18	16.06
Roche Holding AG	196,701	222,631	9.60	16.48
Novartis AG	215,470	231,678	11.25	23.66
Sanofi	112,922	121,589	9.18	20.68
AstraZeneca PLC	219,376	244,034	16.45	37.61
Novo Nordisk A/S-B	540,534	542,916	34.36	45.24

Source: Bloomberg.

Bayer AG is an outlier on the low side for EV/EBITDA, and its P/E is not meaningful because of a net loss, so the analyst must decide whether to drop it. Novo Nordisk is an outlier on the high side and looks overvalued against these peers. Excluding either firm shifts the median or mean for the rest. Multiples are attractive because they are simple and need fewer assumptions than a DCF, yet each one carries implicit assumptions. Differences may signal mispricing, but they may equally reflect genuine differences in risk and expected return among firms that only appear to be in the same business.

Same industry, different businesses: Bayer and Novo Nordisk

Bayer AG earns nearly half its sales from Crop Sciences, and falling agricultural prices drove a net loss of close to EUR3 billion in 2023. Its 2016 acquisition of Monsanto led to more than USD10 billion in legal settlements over claims that a best-selling herbicide caused cancer, and within roughly five years the market capitalization had dropped below half of the USD63 billion Bayer paid for the business. Assumed liabilities and non-pharmaceutical profit drivers help explain the low multiples. Novo Nordisk, by contrast, is a pure pharmaceutical company concentrated in diabetes, obesity, and rare-disease care, with sales and profit roughly doubling over five years on soaring demand for Ozempic. Two firms in the same classification can therefore justify very different multiples.

Check yourself

When a distribution of P/E multiples is positively skewed, which is the better measure of central tendency, the mean or the median?

The median. A positively skewed distribution has a mean pulled above the median by very high multiples that may be outliers, so the median better reflects the center.

A share-price numerator should be paired with what kind of denominator, and why?

A denominator that reflects an equity claim, such as earnings, dividends, FCFE, or book value of equity, so that the parties with a claim on the numerator line up with those behind the denominator.

A justified multiple is an estimate of the fair value of a multiple, one that can be set against the actual multiple. With the method of comparables, that fair value is simply the peer mean or median. The method of forecasted fundamentals goes further: it derives the multiple from the drivers of value, namely profitability, growth, and reinvestment, by borrowing the logic of discounted cash flow valuation. A trailing multiple uses the prior 12 months; a forward multiple uses the next 12 months.

Deriving a justified price-to-book

Start from the constant growth dividend discount model, where the price is next period’s expected dividend divided by the spread of the required return over growth.

Divide both sides by book value of equity per share, then substitute two fundamental identities: the expected dividend equals expected earnings times the payout ratio, and earnings divided by book value equals return on equity (ROE). These steps express the justified P/B in terms of fundamentals.

Using the sustainable growth relationship, where growth equals the retention ratio times ROE, the payout term collapses out and the multiple simplifies further.

The compact form shows that the justified P/B rests on the spread between ROE and the cost of equity, since the same growth rate is subtracted from both. A company that earns more on its equity than investors require, and that grows, should trade above book.

Example 1 · Worked

An analyst gathers actual P/Bs together with ROE, an expected constant growth rate, and the cost of equity for three firms.

Inputs for three firms

Firm	P/B	ROE	g	Cost of equity
Ardfield	2.42	13%	2%	8.20%
Bantry	1.32	10%	3%	8.00%
Cloyne	4.56	18%	5%	8.30%

Which firm looks most likely to be undervalued on its P/B?

Solution. Apply the justified P/B, which equals the ROE-minus-g spread divided by the cost-of-equity-minus-g spread. For Bantry, 0.10 minus 0.03 is 0.07, and 0.08 minus 0.03 is 0.05, so the justified P/B is 1.40, above the actual 1.32: Bantry appears undervalued. For Ardfield, 0.11 over 0.062 gives 1.77, below the actual 2.42, so it appears overvalued. For Cloyne, 0.13 over 0.033 gives 3.94, below the actual 4.56, so it too appears overvalued. Only Bantry trades below its justified multiple.

Adjusting for one factor, or many

Peers rarely share identical fundamentals, so two techniques bring multiples closer to comparability. The adjustment approach modifies a multiple by a single fundamental variable. The regression approach estimates the multiple statistically after controlling for one or more characteristics. The best-known adjustment is the price/earnings-to-growth (PEG) ratio, which scales a P/E by the expected earnings growth rate to compare firms that grow at different speeds.

As with P/E, a higher PEG points toward overvaluation. When more than one fundamental matters, a cross-sectional regression is preferable. For P/B, an analyst can regress the multiple on ROE, growth, and cost of equity across the peer set; the residual for each firm is the gap between its actual multiple and the multiple predicted from fundamentals, and large residuals flag likely mispricing.

Example 2 · Worked

For a set of comparable firms, an analyst regresses P/B on ROE and growth (the cost-of-equity coefficient was not significant and was dropped). The fitted relationship has an intercept of minus 2.58, an ROE coefficient of 29.02, and a growth coefficient of 46.53. Firm 3 has ROE of 18%, growth of 5%, cost of equity of 8.3%, and an actual P/B of 4.56.

1. Find Firm 3’s justified P/B from a constant growth model.

Solution. The spread 0.18 minus 0.05 is 0.13, and 0.083 minus 0.05 is 0.033, so the constant growth justified P/B is 3.94.

2. Find Firm 3’s justified P/B predicted by the regression, and judge the valuation.

Solution. The prediction is minus 2.58 plus 29.02 times 0.18 plus 46.53 times 0.05, which is minus 2.58 plus 5.2236 plus 2.3265, or 4.97. Because the actual P/B of 4.56 sits below the regression estimate of 4.97, Firm 3 may be undervalued. The regression already blends in peer information, so it combines the method of comparables with fundamentals without relying on the constant growth assumption alone.

From a multiple to an intrinsic value

The last step of relative valuation is to apply a multiple to reach an intrinsic value per share, either directly (multiply a peer multiple by the matching fundamental to infer a fair price) or indirectly, as the terminal value inside a present value model. Recall that a present value model discounts a forecast of cash flows plus a terminal value that captures everything beyond the horizon.

The terminal value in the second term can be estimated with an appropriate multiple applied to a forecasted fundamental at the end of the horizon.

Example 3 · Worked

In late February, an analyst values Calastra Group as of the prior December. The median trailing P/E among Calastra’s listed competitors is 16.0.

1. Calastra earned USD700 million over the prior four quarters. Estimate the market capitalization by applying the peer P/E directly.

Solution. Multiply trailing earnings by the peer multiple: 700 million times 16.0 is USD11,200 million.

2. Alternatively, the analyst forecasts five years of net income together with free cash flow to equity (FCFE), sets a Year 5 terminal value from the same 16.0 multiple, and uses a 10% cost of equity. Revise the market-cap estimate.

Calastra forecast (USD millions)

Year	1	2	3	4	5
Net income	779	857	934	1009	1080
FCFE	580	661	745	830	920

Solution. Discount the five FCFE figures at 10%: 580 over 1.10, 661 over 1.10 squared, and so on, summing to USD2,771 million. The terminal value is Year 5 net income times the multiple, 1,080 times 16.0, or 17,280, discounted five years at 10% to 17,280 over 1.10 to the fifth power, which is USD10,730 million. The revised market-cap estimate is 2,771 plus 10,730, or USD13,501 million. This mixes a present value approach with a relative value terminal value.

Check yourself

Ferrillton has a stable ROE of 12%, a cost of equity of 8%, and expected dividend growth of 2%. What is its justified P/B?

The spread 12% minus 2% is 10%, and 8% minus 2% is 6%, so the justified P/B is 1.67.

A regression predicts a stock’s P/B to be higher than its actual P/B. What does that imply?

The stock may be undervalued: its fundamentals (ROE and growth) suggest the multiple should be higher than the market is assigning.

Income statement measures are the most frequently used denominators because earnings drive firm value. Net income is the broadest shareholder-return measure and reflects every cost. Sales sit at the top of the statement and ignore cost structure entirely. EBIT and EBITDA are operating measures available to both debt and equity providers, EBIT after depreciation and amortization and EBITDA before them.

Price-to-earnings and the earnings yield

The price-to-earnings ratio (P/E) is the share price divided by earnings per share (EPS). A trailing P/E uses the last four quarters of EPS; a forward P/E uses consensus estimates for the next 12 months. The inverse, E/P, is the earnings yield, a common measure of equity return. Forward earnings yield also reveals how much of a price reflects growth. A firm with no growth opportunities should pay out all earnings, so its price is next period’s EPS divided by the cost of equity. Any value above that represents the present value of growth opportunities (PVGO).

Dividing through by price and rearranging links the forward earnings yield to the cost of equity and the share of price attributable to growth.

Example 4 · Worked

An analyst compiles price, cost of equity, and a forward EPS estimate for four firms.

Inputs for four firms

	Firm 1	Firm 2	Firm 3	Firm 4
Price	50.00	120.00	35.00	80.00
Cost of equity	10%	9%	12%	8%
Forward EPS	3.00	8.75	0.84	7.20

1. What is Firm 1’s earnings yield, and what proportion of its price is PVGO?

Solution. The earnings yield is 3.00 over 50.00, or 6%. The PVGO share is 1 minus 0.06 divided by 0.10, which is 1 minus 0.60, or 40%. So 40% of the 50 price, that is 20 per share, reflects future opportunities, and the other 30 per share is the present value of forward earnings (3.00 divided by 0.10).

2. Which firm has the lowest ratio of PVGO to price?

Solution. Firm 4. Its PVGO share is 1 minus (7.20 over 80) divided by 0.08, which is 1 minus 1.125, or minus 12.5%. Firm 2 is at 19.0% and Firm 3 at 80.0%, so Firm 4 is lowest. A negative PVGO suggests that reinvestment would destroy value, so earnings should be returned to shareholders instead.

Justified P/E from fundamentals

Dividing the constant growth model by EPS and using the fact that the payout ratio equals dividends per share over EPS gives the justified trailing P/E.

Higher growth and a higher payout ratio lift the multiple; a higher cost of equity lowers it. Growth and payout are linked, though, because faster growth usually requires retaining more earnings, so a firm cannot mechanically raise its P/E by paying out more.

Example 5 · Worked

An analyst builds a sensitivity table of justified trailing P/E multiples, holding the dividend payout ratio at 80% while varying growth and the cost of equity.

1. Find the justified trailing P/E for 3% growth and an 8% cost of equity.

Solution. The numerator is 0.8 times 1.03, or 0.824; the denominator is 0.08 minus 0.03, or 0.05. The justified P/E is 16.48.

2. Raise the cost of equity to 12%, keeping growth at 3%. What happens?

Solution. The denominator becomes 0.12 minus 0.03, or 0.09, and 0.824 over 0.09 is 9.16. A higher cost of equity cuts the multiple from 16.48 to 9.16.

3. Instead raise growth to 5%, keeping the cost of equity at 8%. What happens?

Solution. The numerator becomes 0.8 times 1.05, or 0.84, and 0.84 over 0.05 is 28.00. Higher growth raises the multiple from 16.48 to 28.00.

Justified trailing P/E multiples at an 80% payout ratio

Cost of equity \ g	0%	1%	2%	3%	4%	5%
8%	10.00	11.54	13.60	16.48	20.80	28.00
9%	8.89	10.10	11.66	13.73	16.64	21.00
10%	8.00	8.98	10.20	11.77	13.87	16.80
11%	7.27	8.08	9.07	10.30	11.89	14.00
12%	6.67	7.35	8.16	9.16	10.40	12.00

Figure 1: Justified trailing P/E rising with growth

At a fixed 80% payout, the justified P/E climbs as growth rises and sits lower for the higher cost of equity. The marked point is 16.48 at 3% growth and an 8% cost of equity.

When earnings need cleaning up

P/E has drawbacks. EPS can be zero, negative, or tiny relative to price, which makes the ratio misleading or meaningless. GameStop illustrates the trap: in fiscal 2024 it reported a USD34.5 million operating loss but USD49.5 million of interest income on its large cash balances, giving net income of USD6.7 million (USD0.02 per share). At a price near USD14, the P/E was roughly 700, yet the economic meaning was murky because the profit came from cash, not operations. Non-recurring items, such as asset-sale gains, write-downs, goodwill impairment, and discontinued operations, should be stripped out so the denominator targets core earnings.

For cyclical firms, trailing EPS is low or negative at the trough and unusually high at the peak, so analysts use normalized EPS, an estimate of mid-cycle earnings. Two methods are common: the mean EPS across the latest complete cycle, or that cycle’s mean ROE applied to the current book value per share.

Example 6 · Worked

Zensia SA, a European chemical company, faces demand that tracks the economic cycle. Its price is EUR18.21. Recent per-share data follow.

Zensia per-share history

	Yr −7	Yr −6	Yr −5	Yr −4	Yr −3	Yr −2	Yr −1
EPS	0.62	0.53	0.24	0.63	1.49	1.02	0.89
BVPS	3.00	3.43	3.57	4.10	5.49	6.41	7.20
ROE	20.7%	15.5%	6.7%	15.4%	27.1%	15.9%	12.4%

The current-EPS P/E is 18.21 divided by 0.89, or 20.46, but the analyst worries this is distorted by cyclicality.

1. Recompute the P/E using average EPS.

Solution. The seven EPS figures sum to 5.42, so average EPS is 0.7743. The P/E is 18.21 over 0.7743, or 23.52.

2. Recompute the P/E using average ROE.

Solution. Average ROE over the seven years is 16.2%. Implied normalized EPS is the latest book value times that ROE, 7.20 times 16.2%, or 1.1664. The P/E is 18.21 over 1.1664, or 15.6. When company size changes materially, the average-ROE method is preferred, because the average-EPS method does not control for the change in scale.

Price-to-sales

Revenue is the broadest income statement measure. Because sales fluctuate less than earnings and stay positive even when profit is negative, price-to-sales (P/S) suits mature, cyclical, and loss-making firms. Dividing the constant growth model by sales, and noting that dividends over sales equals the net profit margin times the payout ratio, gives the justified P/S, which is the justified P/E scaled by the net profit margin.

Example 7 · Worked

A firm has an 80% payout ratio, 3% expected growth, an 8% cost of equity, and a stable 15% net profit margin.

1. Find the justified P/S, then confirm the justified P/E.

Solution. The numerator is 0.15 times 0.80 times 1.03, or 0.1236, and the denominator is 0.05, so the justified P/S is 2.472. Dividing by the net profit margin, 2.472 over 0.15, returns the justified P/E of 16.48, matching the earlier P/E result.

2. A second firm shares the same inputs but has a 20% net profit margin. By how much does its justified P/S differ?

Solution. Only the margin differs, so the percentage difference is 0.2 over 0.15 minus 1, which is 33.33%.

3. The first firm cuts its payout from 80% to 70% and lifts growth from 3% to 3.5%. Find the new justified P/S.

Solution. The numerator is 0.15 times 0.70 times 1.035, or 0.108675, and the denominator is 0.08 minus 0.035, or 0.045, giving 2.415. The multiple slips from 2.472 to 2.415, because the lower payout hurt the ratio more than the faster growth helped.

P/S has a logical flaw: the numerator is an equity claim while sales are available to all capital providers, so many analysts prefer an EV-to-sales multiple for leveraged firms. Comparisons also require adjusting for cost-structure and revenue-recognition differences. The PEG ratio offers a related caution across high-growth names.

Magnificent Seven P/E and PEG ratios as of 2024

Company	Trailing P/E	Implied growth (%)	PEG	P/E rank	PEG rank
Nvidia	77.50	30.9	2.51	1	2
Amazon.com	51.87	25.3	2.05	2	5
Tesla	45.35	7.3	6.21	3	1
Microsoft	36.41	16.3	2.23	4	4
Meta	29.53	12.1	2.44	5	3
Apple	27.19	17.7	1.54	6	6
Alphabet	27.11	23.1	1.17	7	7

Source: FactSet.

Scaling P/E by growth reshuffles the ranking. Amazon.com has the second-highest P/E, but its PEG becomes more moderate once growth is accounted for, showing that a high P/E alone does not prove a stock is expensive.

Check yourself

A firm’s justified trailing P/E is 13.0625 from a 75% payout, 4.5% growth, and a 10.5% cost of equity. Show the setup.

0.75 times 1.045 divided by (0.105 minus 0.045) equals 0.78375 over 0.06, which is about 13.06.

Why is P/S considered mismatched for a highly leveraged firm?

The price numerator is an equity claim, but sales are available to both debt and equity holders, so an EV-to-sales multiple is usually preferred when leverage is significant.

When the fundamental in the denominator belongs to all capital providers, the numerator should be a whole-firm value. Enterprise value (EV) measures value to every claimant.

Book values of debt and preferred often proxy for their market values, and cash and short-term investments come off because they do not support operations. Firm value adds the market values of debt and equity together, and enterprise value then removes cash on top of that.

Example 8 · Worked

An analyst estimates enterprise value for Scarola S.p.A., an Italian company that reports semiannually, five months after fiscal year-end. At year-end Scarola had 2.5 billion shares closing at EUR30, EUR25 billion of debt, and EUR8 billion of cash (all in EUR billions below).

1. Compute EV at fiscal year-end.

Solution. EV is debt plus market value of equity minus cash: 25 plus (2.5 times 30) minus 8, which is 25 plus 75 minus 8, or 92. Book value of debt of 25 stands in for market value.

2. During the next five months, Scarola issued EUR10 billion of debt to fund buybacks (the price did not react), and the share price then rose from EUR30 to EUR33. Estimate a mid-year EV.

Solution. The debt issue lifts debt to 35 and, because proceeds bought back stock, cuts equity by 10 to 65 before the price move. Equity then rose 10% (33 over 30 minus 1), to 65 times 1.10. So EV is 35 plus (65 times 1.10) minus 8, which is 35 plus 71.5 minus 8, or 98.5.

3. Suppose instead the debt funded new operating assets. Recompute.

Solution. Now the buyback does not shrink equity, so equity starts at 75. EV is 35 plus (75 times 1.10) minus 8, which is 109.5.

EV/EBITDA and its drivers

Operating earnings belong to debt and equity holders, so they pair naturally with EV. Starting from the constant growth model for the firm, EV equals next period’s free cash flow to the firm (FCFF) over the spread of the weighted average cost of capital (WACC) above growth.

Substituting FCFF and dividing by EBITDA disaggregates the EV/EBITDA multiple into four terms, revealing the sign of each driver.

With everything else fixed, the multiple rises when the cost of capital falls, spending on capital drops, growth quickens, or taxes ease. EV/EBITDA also neutralizes differences in depreciation and amortization policy, which is why it is favored for capital-intensive firms. EBITA (excluding amortization only) or EBIT can replace EBITDA when amortization or neither charge is material.

Example 9 · Worked

Drayton Company trades at an observed EV/EBITDA of 3.52. Its WACC is 7.1%, long-run FCFF growth is 2.0%, base-year EBITDA is EUR300 million, depreciation is EUR150 million, capital expenditure is EUR190 million, net working capital change is zero, and the tax rate is 30%.

1. Compute the justified EV/EBITDA.

Solution. The spread WACC minus g is 0.051. The first term is (1 minus 0.30) over 0.051, or 13.73. The depreciation term is (150 times 0.3 over 300), that is 0.15, over 0.051, or 2.94. The capital expenditure term is (190 over 300), that is 0.6333, over 0.051, or 12.42, and it is subtracted. Working capital is zero. The justified multiple is 13.73 plus 2.94 minus 12.42, which is 4.25.

2. The analyst now assumes a 25% tax rate, 2.5% growth, capital expenditure of EUR230 million, and depreciation of EUR180 million. Recompute.

Solution. The spread is now 0.046. The first term is 0.75 over 0.046, or 16.30; the depreciation term is (180 times 0.25 over 300), that is 0.15, over 0.046, or 3.26; the capital expenditure term is (230 over 300), that is 0.7667, over 0.046, or 16.67, subtracted. The multiple falls to 16.30 plus 3.26 minus 16.67, which is 2.90.

3. Which single change drove the multiple down, despite the analyst expecting each change to help?

Solution. Capital expenditure. It carries a negative sign in the disaggregation, so the jump from 190 to 230 lowered the multiple. Lower taxes helped the first term but slightly hurt the depreciation term, an ambiguous net effect, while higher depreciation helped its own term.

Ryanair vs. EasyJet: key data and multiples as of 2024

Company	Market cap (EUR bn)	EV (EUR bn)	EV/EBITDA	P/E
Ryanair	20.53	19.27	6.18	10.75
EasyJet	4.13	3.93	2.93	10.89

Source: Bloomberg.

The two airlines look nearly identical on P/E, yet their EV/EBITDA multiples diverge sharply (6.18 versus 2.93). Ryanair earns EBITDA margins of 23.2% against EasyJet’s 14.0%, and operating and profit margins roughly triple those of EasyJet. Equity investors gain from EasyJet’s higher leverage and larger cash balances (helped by prepaid vacation sales), which flatter the P/E, but the EV-based measure exposes the weaker operating profitability once cash is netted and operating earnings are the focus.

Book value multiples

Balance sheet multiples set a value on each unit of the assets a company puts to work earning returns. The most common is price-to-book (P/B), the market value of equity over the book value of equity. A higher P/B goes with a higher ROE relative to the cost of equity and a larger payout. Book value comparisons can be distorted by intangible-asset treatment, historical-cost and depreciation choices, and heavy share buybacks. P/B, along with price-to-tangible-book, which strips goodwill and other intangibles out, are staples in banking, where firms carry few fixed assets, hold similar balance sheet positions, and run high regulated leverage.

Price-to-book multiples for global banks, 2024

Company	Market cap (USD bn)	Price to tangible book	P/B
J.P. Morgan	561.64	2.24	1.83
Bank of America	303.59	1.57	1.15
Deutsche Bank AG	33.77	0.54	0.48
Barclays PLC	41.20	0.65	0.56

Source: Bloomberg.

J.P. Morgan and Bank of America carry higher P/Bs than their European peers, but that gap may be justified by their larger presence in high-margin, less balance-sheet-intensive fee businesses such as investment banking and wealth management.

Value-to-book and enterprise-value-to-book

When peers differ in leverage, or where a firm carries negative equity, a wider value-to-book measure serves better than P/B. Value-to-book compares the market value of debt and equity to the book value of both; the EV version subtracts cash from numerator and denominator.

Expressing FCFF as after-tax EBIT times one minus the reinvestment rate, then dividing the firm value by the book value of capital, produces the fundamental form. Return on capital (ROC) is after-tax EBIT over the book value of capital.

Example 10 · Worked

StevCo trades at a value-to-book of 1.60. Its WACC is 7.5%, long-run FCFF growth is 3.0%, book value of equity is EUR400 million, book value of debt is EUR900 million, base-year EBITDA is EUR300 million, depreciation is EUR150 million, capital expenditure is EUR190 million, net working capital change is zero, and the tax rate is 30%.

Estimate StevCo’s justified value-to-book under constant growth.

Solution. After-tax EBIT is (300 minus 150) times (1 minus 0.30), or 105. Return on capital is 105 over (400 plus 900), which is 8.077%. Reinvestment combines depreciation and capital expenditure: (190 minus 150) over 105, or about 0.381. The justified value-to-book is 0.08077 times (1 minus 0.381) over (0.075 minus 0.03), which is 0.08077 times 0.619 over 0.045, or about 1.11. The stock’s observed 1.60 sits above this justified level.

Check yourself

Two airlines have nearly equal P/Es but very different EV/EBITDA multiples. What could explain the difference?

Differences in leverage and cash balances (which affect the equity-based P/E) and differences in operating profitability. The EV-based measure nets out cash and focuses on operating earnings, so it can diverge even when P/Es align.

Why choose enterprise-value-to-book over price-to-book?

To handle differences in or changes to leverage across peers, and to value firms that may have negative book value of equity.

Cash flow measures feed DCF valuation directly, so cash-flow multiples link cleanly to value drivers and tend to resist the manipulation and quality issues of earnings. Denominators in common use include dividends, operating cash flow (CFO), FCFE, and FCFF.

Dividend yield

Cash dividends are the narrowest cash flow measure. The price-to-dividend multiple has an inverse, the dividend yield, which is the preferred presentation because it is often a more predictable slice of total return than price appreciation. A trailing dividend yield uses the annualized most recent dividend (the dividend rate) over the current price; a leading dividend yield uses the forecast for the next year. Dividend yield can be written as the payout ratio times the earnings yield, or derived from the constant growth model.

The drivers are the required return and the growth rate. If the numerator were the expected future dividend, the justified leading dividend yield would simply be the cost of equity minus growth. A firm with a steeper cost of equity carries a higher yield, and a faster-growing firm a lower one.

Example 11 · Worked

A company has an 80% payout ratio, an 8% cost of equity, and 3% growth, which earlier gave a justified trailing P/E of 16.48.

1. Find the justified trailing dividend yield.

Solution. Using the payout-times-earnings-yield route, 80% times 1 over 16.48 is 4.85%. Using the growth-model route, (0.08 minus 0.03) over 1.03 is also 4.85%.

2. The firm has a 15% ROE and cuts its payout from 80% to 70%. Find the updated yield.

Solution. First update growth with the sustainable growth rate: g equals (1 minus 0.70) times 15%, or 4.5%. Then the yield is (0.08 minus 0.045) over 1.045, which is 3.35%.

Dividend yield reflects only one component of total return, is zero for non-payers, and is low for firms that pay out little free cash flow, so it works best among comparable firms with clear, consistent dividend policies.

Free cash flow multiples

Data vendors sometimes approximate cash flow crudely as net income plus depreciation and amortization, labeled simply CF. More precise measures include CFO from the statement of cash flows (which captures working capital changes), FCFE (closely tied to equity value but sensitive to capital expenditure timing and debt changes), and FCFF (which adds back after-tax interest to capture returns to debtholders). Dividing firm value by FCFF, or equity value by FCFE, isolates the cost of capital and growth as drivers.

Both multiples fall with the required return and rise with growth. Their weakness is dependence on short-term or cyclical swings in capital expenditure, working capital, and, for FCFE, debt usage.

Industry-specific measures

Analysts often use sector-specific denominators built on physical assets, reserves, output, or operating metrics rather than standardized financial statement figures. These link directly to sector value drivers and sidestep accounting distortions. They are common both in capital-intensive industries (mineral extraction, transportation) and in asset-light ones (technology). For oil producers, multiples such as EV per unit of production or EV per unit of developed reserves capture value tied to the commodity.

Selected multiples for European oil producers, 2024

Company	Market cap (EUR bn)	P/E	EV/Production	EV/Developed reserves
Median	42.29	7.7	58.65	26.81
Shell plc	208.99	8.6	85	36.86
TotalEnergies SE	158.49	7.87	74.46	26.81
BP p.l.c.	96.16	7.7	58.65	33.19
Equinor ASA	79.28	8.5	31.68	19.82
Eni SpA	47.91	6.69	39.3	17.12
Repsol SA	18.11	4.72	47.36	25.47
OMV AG	15.74	6.88	75.88	34.18

Source: Bloomberg. Production and reserves are measured in barrel-of-oil equivalents.

The rankings across P/E and the reserve or production multiples line up closely despite some deviations, with Shell topping the group on P/E and on the EV-based measures alike. The downside of sector measures is that they do not compare across industries, can misprice a whole sector versus the market, and are hard to connect to fundamentals. The table below summarizes the main multiples, their drivers, and where they fit.

Key price and value multiples

Multiple	Fundamental drivers	Applications
Price/Earnings	Dividend payout ratio, growth rate	Firms with positive, recurring EPS
Dividend Yield	Dividend size and growth	Mature, dividend-paying firms
Price/Sales	Net profit margin	Zero- or low-leverage firms; cyclical profitability
Value/EBITDA	Tax rate, depreciation, investment	Capital-intensive firms
Price/Book Value of Equity	Return on equity	Firms with similar leverage and asset profiles
Enterprise Value/Book Value of Capital	Return on capital	Firms with differing leverage or negative book equity
Price/FCFE	FCFE growth rate	Firms with stable FCFE
Value/FCFF	FCFF growth rate	Firms with stable FCFF

Check yourself

Which two variables are enough to estimate PVGO as a share of price?

The forward P/E (its inverse is the forward earnings yield) and the cost of equity. No dividend assumption is needed.

For which firms is dividend yield the least useful valuation indicator?

Non-dividend payers, where the yield is zero, and firms that pay out only a small share of their free cash flow, since the yield captures just one part of total return.

Deciding which companies form the benchmark is often the hardest and most important choice in relative valuation. Ideal peers share the target’s fundamental characteristics: growth, risk (gauged by return on equity or on capital), and a cash flow or earnings gauge such as the net profit margin. Since no two firms are identical, analysts pick peers in one of two ways: firms with the same principal business activity, or firms grouped by statistical factors that explain equity risk and return.

Industry-based peer groups

Firms that supply comparable goods or services inside one branch of manufacturing or trade belong to the same industry and usually face similar competitive forces, so investors treat them as substitutes. Consider Enel SpA, an electricity and gas utility active in 30 countries with revenue concentrated in Italy, Spain, and Portugal. An initial screen of European utility peers can be refined by dropping smaller, less geographically diversified firms, for example those below EUR10 billion of market capitalization.

Revised information and multiples for Enel SpA and peers

Company	Market cap (EUR mn)	EV (EUR mn)	EV/EBITDA	P/E
Median	24,632	33,753	6.38	15.00
Enel SpA	63,033	144,005	6.60	16.41
EnBW Energie Baden-Württemberg	18,311	33,237	5.13	11.65
Fortum Oyj	11,090	12,487	6.38	7.23
Iberdrola SA	74,864	139,222	8.93	15.00
Engie SA	39,573	73,779	5.58	17.65
VERBUND AG	24,632	27,475	6.14	10.87
SSE plc	21,471	33,753	184.27	31.40

Source: Bloomberg.

After the screen, Enel’s apparent P/E overvaluation nearly disappears. SSE plc remains an outlier because an extraordinary loss in the prior year cut its EBITDA and earnings, inflating both multiples; the analyst should consider excluding it, favoring the median over the mean, or adjusting for the non-recurring item. Even within utilities, firms differ in their mix of generation, transmission, and trading, and in their energy sources (coal and gas versus wind and solar), all of which affect multiples. Peer selection must weigh market structure, cyclicality, and life-cycle stage.

Industry peer groups face recurring challenges: unique firms or concentrated industries offer too few comparables; some industries mix firms at very different life-cycle stages; cross-border peers face different regulation and taxes; and multi-industry firms blend segments with different risk, growth, and cash flow profiles. Amazon.com is a good example, part retailer, part cloud provider. Its AWS segment grew from 4% to nearly 16% of revenue between 2013 and 2023 at a 40% compound rate, and it runs operating margins of 25% to 30%, far above the sub-5% margins of the North America and International segments.

Three fixes apply. In a concentrated industry, place little weight on relative valuation and lean on DCF. Where comparables span life-cycle stages, drop those in a different stage, without narrowing the group too far. For a multi-industry firm, build a peer group per segment and blend the multiples using revenue, operating income, or asset weights.

Example 12 · Worked

eXinc Labs Limited, an Indian pharmaceutical company, earns 35% of sales from patented drugs and 65% from active ingredients for generics. Segment peer medians are shown below.

eXinc segment multiples

Segment	Median EV/EBITDA
Generic	10.5
Patented	18.3

Compute a blended peer EV/EBITDA multiple to apply to eXinc.

Solution. Weight each segment multiple by its share of sales: 0.65 times 10.5 plus 0.35 times 18.3, which is 6.825 plus 6.405, or 13.2. This blended 13.2 becomes the EV/EBITDA the analyst applies to the company’s EBITDA.

Factor-based peer groups

Factor investing groups companies by statistical characteristics tied to risk and return, traits that have historically delivered a long-run premium as payment for bearing systematic risk. Systematic risk is the unavoidable market risk affecting all equities; non-systematic (idiosyncratic) risk affects a single firm or industry. The best-known single-factor model, the capital asset pricing model (CAPM), ties expected return to how closely a security tracks the market, captured by its beta.

A beta above 1 implies an expected return above the market, and below 1 implies below. Grouping firms with similar betas gathers companies with similar systematic risk and therefore similar costs of equity and expected returns, while still allowing different cash flow and growth profiles. This helps overcome the limits of industry grouping, since high-beta constituents can span many industries and a wide range of P/Es. The drawback is model misspecification: a factor relationship fitted over one period and sample may not predict well elsewhere, and many factors underperform over long stretches and show cyclicality.

Check yourself

What is the preferred way to set a peer multiple for a firm spread across several industries?

Blend the industry peer multiples by weighting each with the firm’s share of revenue, income, or assets in that industry.

What defines a factor-based final peer group?

Firms with similar beta coefficients regardless of industry classification, since similar betas imply similar systematic risk and expected return.

A warning frames this final step: the peer group itself may not be fairly valued. A firm can look expensive against its peers yet still land near the bottom of the multiples on offer in a market that is inflated across the board, in which case the whole industry may be mispriced. Because of this, conclusions drawn from multiples alone deserve caution, and relative valuation works best alongside present value methods. Analysts can also draw on past and projected future multiples, not only current ones.

Current, past, and future multiples

Current multiples use the most recent period in the denominator, so they are exposed to non-recurring items, accounting differences, and cyclicality, much like the base-year problem in present value models. Past multiples are used two ways: a company against its own history, which highlights deterioration or improvement likely to persist, and a company against peer historical averages, which gauges relative performance under similar conditions over time.

As an illustration, an analyst comparing Ford Motor Company found current P/E and EV/EBITDA of 6.47 and 3.38 against 10-year averages of 8.06 and 3.92, suggesting undervaluation (the P/E average omits the loss years 2019 and 2020). Extending the comparison to Honda and Volkswagen over the same decade showed Honda’s EV/EBITDA at roughly double Ford’s, which was in turn about twice Volkswagen’s; Ford began the period valued more like Honda but drifted toward Volkswagen’s lower multiple. Historical comparisons can be shaped by strategy or business changes at the firm or its peers, so the method of forecasted fundamentals helps interpret the shifts.

Future multiples put projections in the denominator, such as a forward P/E built on the coming year’s earnings. For the European pharmaceutical peers, forward P/Es reveal detail the trailing figures hide.

Selected multiples of European pharmaceutical firms, 2024

Company	Trailing P/E	P/E FY 1	P/E FY 2
Median	22.17	13.25	12.04
Bayer AG	N/A	5.56	5.19
GSK plc	16.06	11.21	10.00
Roche Holding AG	16.48	13.25	12.04
Novartis AG	23.66	14.23	13.05
Sanofi	20.68	11.63	10.22
AstraZeneca PLC	37.61	18.92	16.83
Novo Nordisk A/S-B	45.24	38.44	31.35

Source: Bloomberg.

Bayer’s trailing P/E is not meaningful because of a loss, but its forward P/E of 5.56 is economically sensible as earnings recover. Novo Nordisk’s forward P/E declines in line with peers.

Multiples for terminal value

A projected multiple is often used to fix the terminal value that closes a forecast, the second term in the present value expression, by applying the multiple to a forecasted fundamental. The peer group must fit the firm’s expected future state rather than its current one.

Example 13 · Worked

Swisserv AG, a Swiss consultancy, has a base-year FCFE of CHF3,120,000, expected FCFE growth of 12% a year for three years, and a 10% required return on equity. Rather than assume stable growth for the terminal value, the analyst applies a price-to-FCFE multiple of 15 (seen among more established consultancies) at the close of Year 3.

Estimate Swisserv’s intrinsic value.

Solution. Grow the base FCFE at 12%: Year 1 is 3,494,400, Year 2 is 3,913,728, and Year 3 is 4,383,375. The Year 3 terminal value is that year’s FCFE times 15, which is 65,750,630. Discounting it three years at 10%, 65,750,630 over 1.10 cubed, gives 49,399,422. The present values of the three FCFE amounts at 10% are 3,176,727, 3,234,486, and 3,293,295. Adding all four present values gives an intrinsic value of 59,103,930, about CHF59.1 million.

Choosing the right peer group for a terminal-value multiple

Suppose a technology firm enjoys seven years of high growth before settling to a sustainable pace, and an analyst wants a peer P/E to set the terminal value at Year 7. The best choice is a peer group of larger, slower-growth technology firms, because those companies mirror the firm’s expected future characteristics. A current high-growth peer group would carry P/E multiples too rich for the mature stage, and the firm’s own historical multiples reflect very different past fundamentals, so neither fits the terminal point.

Check yourself

Why can comparing a company’s current multiple only to its own history not, by itself, prove misvaluation?

Historical multiples reflect the company’s past fundamentals, which may have changed, and the comparison brings in no peer information, so a conclusion of over- or undervaluation would also require comparables.

A firm is undervalued relative to its peers. Why might it still be overvalued in absolute terms?

The peer group itself may be overvalued. Relative valuation only ranks a stock against its peers, so a present value model is needed to judge absolute value.

End of lesson.

Back to MODULE 06 — Equities (renamed from Equity Investment)

EI 7 Relative Value Equity Valuation Approaches

Overview

Relative Valuation and the Method of Comparables

A five-step process

Choosing a peer group

Selecting a multiple

Reading the peer distribution

The Method of Forecasted Fundamentals

Deriving a justified price-to-book

Adjusting for one factor, or many

From a multiple to an intrinsic value

Earnings and Sales Multiples

Price-to-earnings and the earnings yield

Justified P/E from fundamentals

When earnings need cleaning up

Price-to-sales

Enterprise Value and Book Value Multiples

EV/EBITDA and its drivers

Book value multiples

Value-to-book and enterprise-value-to-book

Cash Flow and Industry-Specific Multiples

Dividend yield

Free cash flow multiples

Industry-specific measures

Selecting a Peer Group

Industry-based peer groups

Factor-based peer groups

Multiples Across Time and Terminal Value

Current, past, and future multiples

Multiples for terminal value