Market-Based Valuation (Multiples)

Table of Contents
1. READING 22
2. MARKET-BASED VALUATION: PRICE AND ENTERPRISE VALUE MULTIPLES
3. EXAM FOCUS
4. MODULE 22.1: P/E MULTIPLE
5. MODULE 22.2: P/B MULTIPLE
6. MODULE 22.3: P/S AND P/CF MULTIPLE
7. MODULE 22.4: EV AND OTHER ASPECTS
8. MODULE QUIZ 22.2, 22.3, 22.4
9. KEY CONCEPTS
10. ANSWER KEY FOR MODULE QUIZZES
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READING 22

MARKET-BASED VALUATION: PRICE AND ENTERPRISE VALUE MULTIPLES

EXAM FOCUS

This topic review covers the estimation of P/E, P/B, PEG, P/S, P/CF, and enterprise value/EBITDA ratios. The justified price multiple models draw heavily on valuation concepts from dividend-discount models and free-cash-flow models. You should be able to estimate justified price multiples for individual firms and to apply the method of comparables to estimate relative value.

MODULE 22.1: P/E MULTIPLE

PROFESSOR'S NOTE

The module videos for this topic review do not exactly correspond to the module content, for the ease of exposition and flow of material.

Video covering this content is available online.

Warm-Up: Multiples

Price multiples are among the most widely used tools for equity valuation. Comparing stocks' price multiples helps an investor judge whether a particular stock is overvalued, undervalued, or fairly valued in terms of measures such as earnings, sales, cash flow, or book value per share. Enterprise value multiples relate the total value of a company (the market value of its capital from all sources) to a measure of operating earnings such as EBITDA. Momentum indicators compare a stock's price or a company's earnings to their values in earlier periods.

LOS 22.a

Contrast the method of comparables and the method based on forecasted fundamentals as approaches to using price multiples in valuation and explain economic rationales for each approach.

The method of comparables values a stock using the average price multiple of stocks of similar companies. Its economic rationale is the Law of One Price: two similar assets should sell at comparable price multiples (for example, price-to-earnings). This is a relative valuation method: it indicates whether a stock is over- or undervalued relative to a benchmark but does not produce an absolute intrinsic value.

The method based on forecasted fundamentals (also called the method of forecasted fundamentals) values a stock using the ratio of its intrinsic value (from a discounted cash flow model) to some fundamental variable (for example, earnings per share). The economic rationale is valuation theory: intrinsic value equals the present value of expected future cash flows discounted at the appropriate risk-adjusted rate of return. The justified price multiple uses that intrinsic value in the numerator.

EXAMPLE: Method of comparables

MK Technologies shares are selling for $50. Earnings for the last 12 months were $2 per share. The average trailing P/E ratio for firms in MK's industry is 32×. Determine whether MK is over- or undervalued using the method of comparables.

Answer:

MK's trailing P/E is:

MK is relatively undervalued because its observed trailing P/E ratio (25×) is less than the industry average trailing P/E ratio (32×).

EXAMPLE: Method of forecasted fundamentals

Shares of Comtronics, Inc., are selling for $30. The mean analyst earnings per share forecast for next year is $4.00, and the long-run growth rate is 5%. Comtronics has a dividend payout ratio of 60%. The required return is 14%. Calculate the fundamental value of Comtronics using the Gordon growth model and determine whether Comtronics shares are over- or undervalued using the method of forecasted fundamentals.

Answer:

The Gordon growth model (constant-growth dividend discount model) is: P0 = D1 / (r - g), where D1 is the dividend expected in year 1, r is the required return, and g is the growth rate.

Expressing D0 in terms of earnings per share E0 and the payout ratio, and noting that D1 = D0 (1 + g) and E1 = E0 (1 + g), we can calculate intrinsic value and the justified P/E.

The fundamental value according to the Gordon growth model is: P0 = (E1 × payout ratio) / (r - g).

The fair value P/E ratio based on forecasted fundamentals is: P0 / E1 = payout ratio / (r - g).

The observed leading P/E ratio based on the current market price is: P0 / E1 (observed) = 30 / 4 = 7.5.

Comtronics is overvalued because the observed P/E multiple of 7.5 is greater than the fair value P/E ratio of 6.67. Notice that we would have come to the same conclusion by comparing market price ($30.00) to intrinsic value ($26.67).

LOS 22.b - 22.d (Summary)

Price multiples are ratios of a stock's market price to a fundamental variable. The most common example is the price-to-earnings (P/E) ratio. A justified price multiple is the multiple that would prevail if the stock were fairly valued. If the actual multiple is greater than the justified multiple, the stock is overvalued; if it is less, the stock is undervalued (all else equal).

P/E Ratio

Rationales for using the P/E ratio in valuation:

• Earnings power, as measured by earnings per share (EPS), is a primary determinant of investment value.
• P/E ratio is popular among investors and analysts.
• Empirical research shows that differences in P/E are significantly related to long-run average stock returns.

Shortcomings of the P/E ratio include:

• Earnings can be negative, which produces a meaningless P/E.
• The volatile, transitory portion of earnings complicates interpretation of P/Es.
• Accounting choices and managerial discretion can distort reported earnings, reducing comparability across firms.

Two common versions of P/E:

• Trailing P/E uses earnings over the most recent 12 months (last four quarters).
• Leading (forward) P/E uses expected earnings for the next 12 months (next four quarters or next fiscal year).

Trailing P/E is less useful for forecasting/valuation if the firm's business has materially changed. Leading P/E may be unreliable when earnings are highly volatile and next-year forecasts are poor.

EXAMPLE: Calculating P/E ratio

Byron Investments, Inc., reported €32 million in earnings during the current fiscal year. An analyst forecasts an EPS over the next 12 months of €1.00. Byron has 40 million shares outstanding at a market price of €18.00 per share. Calculate Byron's trailing and leading P/E ratios.

Answer:

(Preserve the calculation steps as given in the source material when provided.)

MODULE QUIZ 22.1

1. Consumer Products, Inc., has a trailing P/E of 27.52, while the median peer group P/E is 33.25. Assuming that there are no differences in the fundamentals among the peer firms and Consumer Products, it is most likely that the firm's stock:

• A. should be sold short.
• B. appears to be overvalued.
• C. appears to be undervalued.

2. A firm has a justified price-to-sales ratio of 2.0×, a net profit margin of 5%, and a long-term growth rate of 4%. The justified leading P/E (based on the Gordon growth model) is closest to:

• A. 34.8.
• B. 38.5.
• C. 40.0.

3. At the end of 2023, an analyst estimates the value of Copyright, Inc., common stock to be $84 per share using a two-stage, dividend discount H-model and forecasts earnings for 2024 to be $4.20 per share. Copyright is most likely:

• A. underpriced if its actual leading P/E is 15.0×.
• B. underpriced if its actual leading P/E is 23.0×.
• C. overpriced if its actual leading P/E is 16.6×.

MODULE 22.2: P/B MULTIPLE

P/B Ratio

Video covering this content is available online.

Advantages of the price-to-book (P/B) ratio include:

• Book value is cumulative and usually positive, even when EPS is negative, so P/B can be used where P/E cannot.
• Book value is more stable than EPS; useful when EPS is very volatile.
• P/B is appropriate for firms whose value is driven by net asset value (for example, finance, investment, insurance, and banking firms).
• P/B can be useful when valuing companies expected to wind down operations.
• Empirical research indicates P/B helps explain differences in long-run average returns.

Disadvantages of P/B include:

• P/B does not capture the value of intangible economic assets (human capital, internally generated goodwill).
• P/B can be misleading across firms with different asset sizes or business models (for example, outsourcing reduces asset base and raises P/B relative to a non-outsourcing peer).
• Different accounting conventions (e.g., expensing versus capitalising R&D; FIFO vs LIFO inventory) reduce comparability of book values across firms and countries.
• Inflation and technological change can make book values diverge from market values.

The price-to-book ratio is defined as market price per share / book value per share.

Analysts often adjust book value to improve comparability. Common adjustments include:

• Using tangible book value = book value of equity - intangible assets (e.g., goodwill).
• Adjusting balance sheets for off-balance-sheet items and differences between recorded and fair values.
• Restating book values to a common inventory accounting method (FIFO/LIFO) where necessary.

EXAMPLE: Calculating P/B ratio

Based on the information in the following figure, calculate the P/B for Crisco Systems, Inc., and Soothsayer Corp. as of the end of 2023.

Data for Crisco Systems, Inc., and Soothsayer Corp.

Answer:

Crisco Systems, Inc.:

Soothsayer Corp.:

MODULE 22.3: P/S AND P/CF MULTIPLE

P/S Ratio

Advantages of the price-to-sales (P/S) ratio include:

• P/S is meaningful even for distressed firms because sales revenue is generally positive.
• Sales are harder to manipulate than EPS or book value.
• P/S ratios are typically less volatile than P/E multiples, making them useful when earnings are unusually high or low.
• P/S is appropriate for valuing mature, cyclical industries and start-ups with no earnings history; also used for investment partnerships and management companies.
• Empirical research finds differences in P/S relate to differences in long-run average returns.

Disadvantages of P/S include:

• High sales growth does not necessarily imply high operating profits or cash flow.
• P/S does not capture differences in cost structure across firms.
• Revenue recognition practices can still distort sales (for example, bill-and-hold sales accelerate revenue recognition).

P/S multiples are computed as: price per share / sales per share or market value of equity / total sales.

EXAMPLE: Calculating P/S ratio

Based on the information in the following figure, calculate the current P/S for Crisco Systems, Inc., and Soothsayer Corp.

Answer:

Crisco Systems, Inc.:

Soothsayer Corp.:

P/CF Ratio

Advantages of the price-to-cash flow (P/CF) ratio include:

• Cash flow is harder for managers to manipulate than earnings.
• P/CF is more stable than P/E.
• Using cash flow reduces problems arising from low quality of reported earnings.
• Empirical evidence indicates P/CF differences relate to differences in long-run returns.

Drawbacks relate to the definition of cash flow:

• The earnings-plus-noncash-charges proxy ignores items affecting actual operating cash flow (for example, noncash revenue and changes in working capital).
• Theoretically, free cash flow to equity (FCFE) is preferable, but FCFE is more volatile than operating cash flow and not necessarily more informative for ratio comparisons.

MODULE 22.4: EV AND OTHER ASPECTS

Dividend Yield

Video covering this content is available online.

Dividend yield (D/P) is the ratio of the common dividend to the market price. It is often used for valuing indices.

Advantages of the dividend yield approach:

• Dividend yield contributes directly to total investment return.
• Dividends are often viewed as less risky than capital appreciation.

Disadvantages:

• Dividend yield ignores capital appreciation, which is the other component of total return.
• The dividend displacement of earnings concept states that dividends paid now reduce future earnings and growth, creating a trade-off.

Total return = dividend yield + capital appreciation.

Dividend yield (trailing or leading) = dividend over last/future 12 months / current price.

EXAMPLE: Calculating dividend yield

OnePrice, Inc., just paid a dividend of $0.50 per share. The consensus forecasted dividends for OnePrice over the next four quarters are $0.50, $0.55, $0.60, and $0.65. The current market price is $47.50. Calculate the leading and trailing dividend yield.

Answer:

LOS 22.e

Calculate and interpret underlying earnings, explain methods of normalizing earnings per share (EPS), and calculate normalized EPS.

Underlying earnings (also called persistent, continuing, or core earnings) exclude nonrecurring components such as gains/losses from asset sales, writedowns, provisions for future losses, and changes in accounting estimates. For comparability, analysts generally use diluted EPS to account for the effect of potentially dilutive securities.

PROFESSOR'S NOTE

Analysts must link valuation inputs to financial statement analysis. Management has discretion in labeling items as nonrecurring; the analyst's task is to identify recurring components that reflect the firm's true earnings power.

EXAMPLE: Calculating underlying earnings

Using the data in the following figure, calculate the trailing P/E for Magnolia Enterprises as of September 2022 using underlying earnings.

Data for Magnolia Enterprises [amounts in Canadian dollars (C$)].

Answer:

Earnings can contain a transitory portion due to cyclicality. Business cycles are expected to repeat: the tendency for high P/Es at cyclical troughs (due to low EPS) and low P/Es at cyclical peaks (due to high EPS) is known as the Molodovsky effect.

Normalized earnings adjust earnings for cyclicality. Two methods:

• Historical average EPS: normalized EPS is the average EPS over some recent period (often the most recent business cycle).
• Average ROE method: normalized EPS = average ROE × current book value per share (BVPS); average ROE is often measured over the most recent business cycle. This method adjusts for firm size via current BVPS and is generally preferred over the historical average EPS method.

EXAMPLE: Calculating normalized earnings

Using data in the following figure, calculate normalized earnings using the method of historical average EPS and the method of average ROE for Magnolia Enterprises.

Data for Magnolia Enterprises [amounts in C$]

Answer:

Normalized earnings are C$4.25 based on the historical average EPS method and C$4.52 using the average ROE method.

LOS 22.f

Explain and justify the use of earnings yield (E/P).

When earnings are negative, P/E becomes meaningless. Analysts therefore may use normalized EPS and/or express valuation as the earnings yield (E/P), because price is never negative. A high E/P suggests a cheap security; a low E/P suggests an expensive security. Securities can be ranked from cheap to expensive on the basis of their E/P ratios.

LOS 22.g, 22.i

Describe fundamental factors that influence alternative price multiples and dividend yield; calculate and interpret the justified P/E, P/B, and P/S based on forecasted fundamentals.

We derive the fundamentals that affect multiples using valuation models (for example, the single-stage Gordon growth model). Knowing the formula for the justified price multiple reveals the fundamental determinants.

Justified P/E Multiple

Start with the Gordon growth formula for stock value:

P0 = D1 / (r - g), where D1 = dividend next period, r = required return, g = expected growth rate.

Express D0 as E0 × (D0 / E0) (i.e., EPS × payout ratio) and retention rate as b. Then the trailing P/E can be written in terms of payout ratio, retention, growth, and required return. Recognizing that E1 = E0 (1 + g) and D1 = D0 (1 + g), the leading P/E is:

P0 / E1 = (payout ratio) / (r - g).

PROFESSOR'S NOTE

If earnings are expected to grow (g > 0), then E1 > E0 and the justified leading P/E (P0 / E1) will be smaller than the justified trailing P/E (P0 / E0) because the denominator is larger when using E1. In fact, justified trailing P/E = justified leading P/E × (1 + g).

From the justified P/E formulas, fundamental determinants are:

• Growth rate (g): P/E is positively related to expected growth.
• Required return (r): P/E is inversely related to r (higher required return → lower P/E).
• Inflation pass-through capability: firms that can pass inflation to customers tend to have higher P/Es, all else equal.

EXAMPLE: Calculating justified P/E ratio for Comtronics again

Shares of Comtronics are selling for $30. The mean analyst E1 forecast is $4, long-run growth is 5%, payout ratio is 60%, required return 14%. Calculate the justified leading P/E.

Answer:

The justified leading P/E is payout ratio / (r - g) = 0.60 / (0.14 - 0.05) = 0.60 / 0.09 = 6.666... ≈ 6.67. This matches the earlier calculation.

EXAMPLE: Calculating justified P/E ratio

A stock has a payout ratio of 40%. Shareholders require a return of 11% and expected dividend growth is 5%. Calculate the trailing and leading P/E multiples based on these fundamentals.

Answer:

Leading P/E = payout ratio / (r - g) = 0.40 / (0.11 - 0.05) = 0.40 / 0.06 = 6.666... ≈ 6.67.

Trailing P/E = Leading P/E × (1 + g) = 6.67 × 1.05 ≈ 7.00.

Justified P/B Multiple

Using the sustainable growth relation g = ROE × b and observing that E1 = B0 × ROE, the justified P/B derived from the Gordon model is:

P0 / B0 = (ROE - g) / (r - g) (equivalently rearranged in standard derivations).

Conclusions about fundamentals affecting P/B:

• P/B increases with ROE, all else equal.
• P/B increases as the spread between ROE and r increases, because the firm is creating more value from retained earnings.

EXAMPLE: Calculating justified P/B ratio

A firm's ROE is 14%, its required rate of return is 8%, and its expected growth rate is 4%. Calculate the firm's justified P/B based on these fundamentals.

Answer:

(Use the formula above to compute P/B.)

Justified P/S Multiple

Because net profit margin PM0 = E0 / S0, the Gordon model can be restated to show P/S as a function of profit margin, payout/retention, growth, and required return. Net profit margin influences P/S directly and through its effect on sustainable growth.

The P/S ratio will increase, all else equal, if:

• Profit margin increases.
• Earnings growth rate increases.

Also, algebra shows:

P/S = (P/E) × (E/S), i.e., P/S = (P/E) × profit margin.

EXAMPLE: Calculating justified P/S ratio

A stock has a payout ratio of 40%, ROE of 8.3%, EPS of $4.25, sales per share of $218.75, expected growth of 5%, and required return 10%. Calculate the justified P/S multiple.

Answer:

Profit margin E0 / S0 = 4.25 / 218.75 = 0.0194. Using relations above, compute P/S accordingly.

Justified P/CF Multiple

The justified P/CF based on fundamentals is found by valuing the equity using a DCF model (for example, single-stage FCFE) and dividing equity value by the chosen measure of cash flow. P/CF will increase, all else equal, if the required return decreases or growth increases.

Justified EV/EBITDA Multiple

The justified EV/EBITDA is enterprise value (from fundamentals) divided by EBITDA forecast from fundamentals. The ratio is:

Positively related to the growth rate in free cash flow to the firm (FCFF) and EBITDA.

Negatively related to firm risk and the weighted average cost of capital (WACC).

Justified Dividend Yield

The dividend yield relative to fundamentals may be derived from the Gordon model: D0 / P0 = (r - g) × (1 - b) in rearranged forms. Dividend yield is positively related to the required rate of return and negatively related to the expected growth rate in dividends. Choosing high dividend-yield stocks reflects a value rather than a growth investment approach.

LOS 22.h

Calculate and interpret a predicted P/E, given a cross-sectional regression on fundamentals, and explain limitations to the cross-sectional regression methodology.

Cross-sectional regression uses contemporaneous observations across firms to relate P/E to fundamental explanatory variables (for example, expected growth, beta, payout ratio). Limitations:

• The predictive power for different time periods or different samples is uncertain.
• The relationships between P/E and fundamentals may change over time.
• Multicollinearity (high correlation among independent variables) complicates interpretation of coefficients.

EXAMPLE: Calculating predicted P/E

An analyst is valuing a public utility with a dividend payout ratio of 0.50, beta of 0.95, and expected earnings growth of 0.06. A regression on other public utilities produces the equation:

(regression equation omitted in source; given in answer key below)

The firm's actual P/E is 12.0. Calculate the predicted P/E using the regression and determine whether the stock is over- or underpriced.

Answer:

Actual P/E is greater than predicted P/E, so the firm is overpriced.

PROFESSOR'S NOTE

This is an example of predicting a dependent variable (P/E) from an estimated regression, as in quantitative methods. A P/E prediction model could form the basis for a quantitative exam question.

Warm-Up: Benchmarks

PROFESSOR'S NOTE

"Benchmark value of a multiple" is another name for the justified multiple using the method of comparables. The method of comparables proceeds in these steps:

• Step 1: Select and calculate the multiple to be used.
• Step 2: Select the benchmark and calculate the mean or median multiple for comparable stocks.
• Step 3: Compare the stock's multiple to the benchmark.
• Step 4: Examine whether differences are explained by fundamentals and make appropriate adjustments.

Common benchmarks include the multiple of a similar company, the average or median industry multiple, the multiple of an equity index, or the stock's own historical average.

LOS 22.l - 22.m

Evaluate whether a stock is overvalued, fairly valued, or undervalued based on comparisons of multiples and explain the importance of fundamentals in the method of comparables.

The method of comparables compares a stock's multiple to a benchmark multiple. Firms with multiples below the benchmark are undervalued, and vice versa, but only after ensuring comparability in fundamentals (growth, risk, accounting conventions, etc.). For example, a lower P/E can be explained by lower expected growth or higher required return.

EXAMPLE: Evaluating P/E ratios with the method of comparables

An analyst has gathered P/E information on two stocks, Allbright Interiors and Basic Designs.

Market data on Allbright Interiors and Basic Designs.

EXAMPLE: Evaluating P/B and P/S ratios with the method of comparables

Crisco Systems belongs to the Networking Products industry and Soothsayer to the Enterprise Software/Services industry. Recall that Crisco's P/B = 4.45 and Soothsayer's P/B = 10.04; their P/S ratios were 6.60 and 6.71. Determine whether the stocks are overvalued or undervalued compared with peer group means and medians.

Basic data from the Computer Industry.

Answer:

Crisco's P/B exceeds the peer mean (2.065) and median (1.170) → overvalued by this measure. Its P/S exceeds peer mean (3.733) and median (0.900) → overvalued.

Soothsayer's P/B exceeds peer mean (7.866) and median (2.770) → overvalued. Its P/S exceeds peer mean (3.341) and median (1.920) → overvalued. Notice the disparity between means and medians, indicating outliers.

Evaluate the value and P/E of each stock based on comparables.

Answer:

Allbright has a lower P/E than the peer median despite comparable growth and beta → Allbright is undervalued. Basic Designs has a higher P/E despite lower expected growth and higher beta → Basic Designs is overvalued relative to the benchmark.

The same steps apply when using P/B and P/S, but for P/B analysts typically use trailing book values because forecasts of book value are less widely disseminated. Relative P/B valuation should control for ROE, risk, and expected growth. P/S valuation must control for profit margin, growth, risk, and accounting quality.

For EV/EBITDA, a lower ratio relative to peers indicates potential undervaluation, all else equal. For dividend yield, compare the target's yield with peers adjusted for comparable risk and expected growth; a higher dividend yield (relative to benchmark) may indicate undervaluation if fundamentals are similar.

PROFESSOR'S NOTE

When backtesting screening strategies that use price multiples, avoid look-ahead bias: do not use information that was not contemporaneously available at the historical selection date.

The Fed and Yardeni Models

The Fed model views the overall market as overvalued when the earnings yield (E/P) on the S&P 500 is lower than the yield on 10-year U.S. Treasuries, and undervalued when E/P is higher than the 10-year yield.

The Yardeni model incorporates expected earnings growth into the comparison. The Yardeni model in one common form is:

E/P = Y - d × g (where Y is a bond yield and d is a parameter; rearrangements and reciprocal forms show the P/E relationship to interest rates and growth).

Taking reciprocals (and ignoring the error term) shows P/E is negatively related to interest rates and positively related to expected growth.

LOS 22.j

Calculate and interpret the P/E-to-growth (PEG) ratio and explain its use in relative valuation.

The PEG ratio is defined as P/E divided by expected earnings growth rate (g). PEG = P/E / g. It measures P/E per unit of expected growth. Lower PEGs are more attractive, assuming comparable risk.

Drawbacks:

• The relationship between P/E and g is not linear, making comparisons approximate.
• PEG does not account for risk differences.
• PEG ignores the duration of the high-growth period in multistage models; short-term growth forecasts may distort PEG.

EXAMPLE: Calculating and using the PEG ratio

Med-Ready, Inc. has a leading P/E of 28.75 and a 5-year consensus growth rate forecast of 14.5%. Median PEG for comparable firms is 2.34. Calculate Med-Ready's PEG and assess valuation.

Answer:

PEG = 28.75 / 14.5 = 1.98. Given peer median PEG of 2.34, Med-Ready appears undervalued. Check that peer PEGs are based on leading P/Es and that peer risk is comparable.

LOS 22.k

Calculate and explain the use of price multiples in determining terminal value in a multistage DCF model.

Terminal value at the end of the explicit forecast horizon can be estimated using terminal price multiples (P/E, P/B, P/S, P/CF). Terminal value = (chosen price multiple) × (terminal fundamental variable). There are two ways to estimate the terminal multiple:

• Fundamentals approach: use the justified price multiple based on forecasted fundamentals (growth, required return, payout) and multiply by the forecasted fundamental variable.
• Comparables approach: use a benchmark price multiple from comparable firms and multiply by the forecasted fundamental variable.

Strengths/weaknesses: the comparables approach uses market data only, but if the benchmark is mispriced it transfers error to terminal value. The fundamentals approach relies on estimates of growth, r, and payout.

EXAMPLE: Calculating terminal value with price multiples

An analyst estimates EPS of Polar Technology in five years to be C$2.10, EPS in six years to be C$2.32, and the median trailing industry P/E to be 35. Calculate the terminal value in Year 5.

Answer:

Terminal value in Year 5 = benchmark P/E × EPS in Year 6 (if using trailing P/E) or P/E × EPS in terminal year depending on convention; using the data provided the calculation gives the terminal value.

LOS 22.n

Explain alternative definitions of cash flow used in price and enterprise value multiples and describe limitations of each definition.

Common cash-flow definitions used in P/CF ratios include:

• Earnings plus noncash charges (CF): CF = net income + depreciation + amortization. Limitation: ignores noncash revenue and changes in working capital.
• Cash flow from operations (CFO): reported on cash flow statement; often adjusted for nonrecurring cash flows. Classification differences across accounting standards (US GAAP vs IFRS) require care.
• Free cash flow to equity (FCFE): CFO - capital expenditures - net principal payments to/from debtholders. Theory prefers FCFE, but it is volatile; averaged FCFE may be appropriate.
• EBITDA: pretax, pre-interest measure; represents cash flow before capital structure effects and is a flow to both equity and debt holders.

Analysts usually use trailing P/CF based on the most recent four quarters of the chosen cash flow definition.

EXAMPLE: Calculating P/CF

Data Management Systems, Inc. (DMS) reported net income of $32 million, depreciation & amortization of $41 million, net interest expense of $12 million, and cash flow from operations of $44 million. Tax rate is 30%. Calculate P/CF using earnings-plus-noncash-charges (CF) as the proxy. DMS has 25 million shares outstanding, trading at $47 per share.

Answer:

CF = net income + depreciation + amortization = $32m + $41m = $73m. CF per share = $73m / 25m = $2.92. P/CF = $47 / $2.92 ≈ 16.10 (rounded).

LOS 22.o

Calculate and interpret EV multiples and evaluate the use of EV/EBITDA.

Enterprise value (EV) = market value of equity + market value of debt + preferred equity + minority interest - cash and short-term investments. The rationale for subtracting cash and investments is that an acquirer pays net of target liquid assets; EV reflects total company value to both debt and equity holders.

EV/EBITDA = EV divided by EBITDA. Advantages:

• Useful in comparing firms with different capital structures.
• EBITDA is useful for capital-intensive businesses with high depreciation & amortization.
• EBITDA is commonly positive even when EPS is negative.

Drawbacks:

• If working capital is growing, EBITDA will overstate cash from operations (CFO).
• EBITDA ignores capital expenditures; FCFF is more closely linked to valuation theory unless capex ≈ depreciation.

EXAMPLE: Calculating EV/EBITDA

An analyst gathered the following data for Boulevard Industries [all amounts in Swiss francs (SF)]:

Based on this information, calculate EV/EBITDA for Boulevard Industries.

Answer:

An alternative measure of company value is total invested capital (TIC) or market value of invested capital, which equals the market value of the company's equity and debt. Unlike EV, TIC includes cash and short-term investments.

Analysts also use enterprise value multiples with EBIT, FCFF, or sales in the denominator (for example, EV/S). EV/S is appropriate when comparing companies with different capital structures.

LOS 22.p

Explain sources of differences in cross-border valuation comparisons.

Cross-border relative valuation is challenging due to differences in accounting practices, culture, risk, growth opportunities, and regulatory environments. Accounting differences commonly affect goodwill, deferred taxes, foreign exchange adjustments, R&D treatment, pension expense, and revaluation of tangible assets. These differences affect the reliability of price multiples: P/FCFE is least affected, while P/B, P/E, P/EBITDA, and EV/EBITDA are more sensitive to accounting choices.

LOS 22.q

Describe momentum indicators and their use in valuation.

Momentum indicators relate market price or fundamentals (such as EPS) to their historical or expected time-series values. Common momentum indicators include:

• Earnings surprise = reported EPS - expected EPS.
• Standardized unexpected earnings (SUE) = (reported EPS - expected EPS) / standard deviation of forecast errors.
• Relative strength compares price/return performance to its own history or to peers.

Positive earnings surprises can be associated with persistent abnormal returns; standardized measures scale surprises by historical forecast error variability.

SUE definition

The SUE measure is the forecast error scaled by the historical standard deviation of forecast errors, making a given size forecast error more meaningful when historical errors are small.

LOS 22.r

Explain the use of arithmetic mean, harmonic mean, weighted harmonic mean, and median to describe central tendency of a group of multiples.

The portfolio (or index) P/E is not equal to the arithmetic mean of individual stock P/Es. For example, consider two stocks: Stock A price $10 with EPS $1 (P/E = 10) and Stock B price $16 with EPS $2 (P/E = 8). A portfolio with one share of each has total price = $26 and total EPS = 3, so portfolio P/E = 26 / 3 = 8.67. This is the weighted harmonic mean of individual P/Es when weights are market-value or portfolio weights. The harmonic mean gives more weight to smaller values; the median is robust to outliers. Analysts must be aware how index/portfolio P/Es are calculated; with extreme outliers the arithmetic mean is most affected, while the harmonic mean and median may be preferred.

MODULE QUIZ 22.2, 22.3, 22.4

1. An analyst researching Blue Ridge Camping has determined that the firm has:

• A payout ratio of 75%.
• A return on equity (ROE) of 18%.
• An earnings per share (EPS) of $5.35.
• Sales per share of $342.
• Expected earnings/dividends/sales growth of 4.5%.
• Shareholders required return of 15%.

The firm's justified price to sales ratio (P/S) multiple based on the above fundamentals is closest to:

• A. 0.0780.
• B. 0.1114.
• C. 0.1164.

Use the following information to answer Questions 2 through 4.

Pfeiffer belongs to the Medical-Drugs group and Mapps belongs to the Applications Software group.

2. The current price-to-book and price-to-sales ratios for Pfeiffer are closest to:

3. The current price-to-book and price-to-sales ratios for Mapps are closest to:

4. Which of the following statements is most accurate, given the financial data on Pfeiffer, Mapps, and the two industries?

• A. Both stocks are relatively overvalued.
• B. Both stocks are relatively undervalued.
• C. One stock is relatively overvalued and the other is relatively undervalued.

5. Jeremiah Claxton, CFA, is a junior portfolio manager... Claxton has gathered the following information.

Claxton has also determined that the CAPM betas of the two firms are not significantly different at the 1% level. Based on the information in the table, which statement is most accurate?

• A. Only one of the stocks is relatively overvalued.
• B. Both stocks are relatively undervalued.
• C. Both stocks are relatively overvalued.

Use the following information to answer Questions 6 through 9.

Lois Fischer, CFA, is a senior analyst selecting a retail stock based on P/B. She has a list of five stocks: Wally's, Home Decor, Redrug, Lester's, and Harmon's.

Annabelle Clementi, CFA, prefers P/B for retail stocks, but for home improvement segment (asset-efficient firms) she prefers cashflow measures.

Lester's financial statements (period ending 31 December 2022) are prepared under US GAAP. Interest paid was $240m (included in CFO net of tax savings). Marginal tax rate 37%. Lester's trading at $42.10 per share. Income statement figures follow (preserve data as presented):

Total Revenue 22,111,108,000

Cost of Revenue (15,743,267,000)

Gross Profit $ ...

Operating Expenses: Depreciation 534,102,000; SG&A 3,379,253,000; Nonrecurring 139,870,000; Other operating expenses 516,828,000; Total Operating Expenses $ ...

Operating Income 1,797,788,000

Total Other Income and Expenses, Net 58,431,000

EBIT 1,856,219,000

Interest Expense (231,968,000)

Income Before Tax $ 1,624,251,000

Income Tax Expense 600,989,000

Net Income From Continuing Operations $ ...

Nonrecurring Events, Discontinued Operations, Extraordinary Items, Effect of Accounting Changes, Other Items - NIA

6. Based on the information in the first figure, which of the following statements least likely supports Fischer's recommendation of Home Decor over Lester's?

• A. Home Decor's P/B ratio relative to the industry.
• B. Home Decor's P/B ratio relative to Lester's P/B ratio.
• C. Home Decor's historical P/B ratios.

7. Which of the following statements is least likely a justification of selecting Harmon's over Wally's?

• A. Harmon's level of systematic risk relative to Wally's.
• B. Harmon's P/B ratio relative to the industry.
• C. Wally's P/B ratio relative to the industry.

8. Clementi requests that Fischer calculate several ratios. The P/CF for Lester's using earnings-plus-noncash-charges for cash flow is closest to:

• A. 15.89.
• B. 17.08.
• C. 25.99.

9. Clementi requests P/CFO for Lester's using adjusted CFO (for nonrecurring items). The adjusted P/CFO for Lester's is closest to:

• A. 15.
• B. 17.
• C. 19.

10. Sample Fabrication Company trailing EPS = $1.29 as of 31 Dec 2023. Sample stock trades at $42.50. In Q1 2023 Sample reported an extraordinary loss of $0.22 per share. In Q3 a write-down loss of $0.04 per share. In Q4 a gain of $0.08 per share from change in accounting estimate. Sample's trailing P/E based on underlying earnings is closest to:

• A. 24.6.
• B. 28.9.
• C. 32.9.

11. Average ROE for Lever, Inc. over last business cycle = 32%. Lever's expected EPS next year = $5. Dividend payout ratio = 30%. Current book value per share = $14. Shares trading at $54. Lever's normalized EPS is closest to:

• A. $4.48.
• B. $5.00.
• C. $5.26.

12. Which investment strategy is most consistent with choosing high dividend yield stocks?

• A. Growth.
• B. Momentum.
• C. Value.

13. An analyst valuing an electric utility with payout = 0.65, beta = 0.56, expected earnings growth = 0.032. A regression on other electric utilities produces the equation:

(regression omitted here in statement; see answer key)

The predicted P/E is closest to:

• A. 12.2.
• B. 15.4.
• C. 20.8.

14. Western Graphics Co. paid dividend $0.40 on earnings $1.00 last year. Earnings and dividends expected to grow at 5% forever. Required return = 12%. The justified trailing and leading P/E multiples are closest to:

15. Creative Toys recently paid dividend $1.35. Payout = 67%, ROE = 23%, expected growth = 7.6%, required return = 14%. The justified P/B multiple is closest to:

• A. 1.22.
• B. 1.19.
• C. 2.41.

16. Party Favors, Inc. leading P/E = 18.75 and 5-year consensus growth = 15.32%. Median PEG (based on leading P/E) for comparable companies = 0.92. The stock appears to be:

• A. overvalued because PEG is 0.82.
• B. overvalued because PEG is 1.22.
• C. undervalued because PEG is 0.82.

17. Data for Carolina Steel, Inc. (CSI): calculate EV/EBITDA closest to:

• A. 3.44.
• B. 4.26.
• C. 4.78.

KEY CONCEPTS

LOS 22.a (Key Concepts)

The method of comparables uses a price multiple for a similar firm or the average multiple for a portfolio or index as a benchmark. The underlying argument is that one dollar of earnings (or book value) should command the same value across similar stocks. The method is relative and uses current market values of other stocks.

The method of forecasted fundamentals uses price multiples derived from forecasted fundamental variables (growth, payout, ROE) using a valuation model, for example, P/E = payout / (r - g) as implied by the constant-growth model; this gives an absolute intrinsic value-based multiple.

LOS 22.b

A justified price multiple may be justified either by comparables or by forecasted fundamentals. Stocks with P/Es below their justified P/Es (based on forecasted fundamentals) are judged undervalued; the same logic applies using comparables.

LOS 22.c

Rationales and disadvantages for main multiples (summary):

• P/E: earnings power is central; P/E is popular; P/E differences relate to long-run returns. Disadvantages: negative earnings, transitory earnings, accounting discretion.
• P/B: book value is cumulative and stable; appropriate for asset-intensive/liquid asset firms. Disadvantages: ignores nonphysical assets; affected by asset size differences and accounting conventions; inflation/tech change may distort book value.
• P/S: meaningful for distressed firms; sales are less manipulable; less volatile than P/E; suitable for mature/cyclical and start-ups. Disadvantages: high sales do not guarantee profits; ignores cost structure differences; revenue recognition issues.
• P/CF: cash flow is harder to manipulate and more stable; addresses differences in earnings quality. Disadvantages: some cash proxies ignore items affecting actual CFO; FCFE preferred theoretically but more volatile.
• Dividend yield: dividends contribute to return and are often less risky than capital gains. Disadvantages: yield alone ignores capital appreciation; high dividends may reduce growth.

LOS 22.d

Definitions:

• Trailing P/E = market price per share / EPS over last four quarters.
• Leading P/E = market price per share / estimated EPS next four quarters.
• P/S = market price per share / sales per share.
• P/B = market price per share / book value (shareholders' equity) per share.
• P/CF = market price per share / chosen cash flow per share (various definitions available).
• Higher value of these ratios indicates a greater relative stock value. Expected dividend yield = expected dividends next 12 months / current market price.

LOS 22.e

Underlying earnings exclude nonrecurring items. Normalized earnings adjust for business cycles using historical average EPS or average ROE; average ROE method is preferred.

LOS 22.f

A high earnings yield (E/P) suggests a cheap security; a low E/P suggests an expensive security. E/P is useful when P/E is undefined.

LOS 22.g

All else equal:

• P/E is higher with greater expected earnings growth and lower required return.
• P/S is higher with greater net profit margin and lower required return.
• P/CF is higher with greater FCFE growth and lower required return.
• P/B is higher with a larger spread between ROE and required return.
• Dividend yield is higher with higher required return and lower expected growth.

LOS 22.h

Predicted P/E can be estimated from linear regression of historical P/Es on fundamental variables; P/E is the dependent variable and fundamentals (growth, beta, payout) are independent variables.

LOS 22.i

Based on discounted cash flow valuation:

• Justified leading P/E based on forecasted fundamentals: P0 / E1 = payout / (r - g).
• Justified P/B based on fundamentals: derived from ROE, g, r relations (see earlier section).
• Justified P/S based on fundamentals: P/S = (P/E) × (E/S) and can be expressed in terms of margin, payout, growth and required return.

LOS 22.j

The PEG ratio is calculated as P/E divided by expected growth rate. Lower PEGs are preferred, all else equal.

LOS 22.k

Analysts often use price multiples (P/E, P/B, P/S, P/CF) to estimate terminal value; terminal value = expected multiple × terminal fundamental variable.

LOS 22.l

Method of comparables: compare the stock's multiple to a benchmark. Multiples below benchmark → undervalued; above benchmark → overvalued, after accounting for differences in fundamentals.

LOS 22.m

When using comparables, the analyst must adjust for differences in fundamentals: a high P/E may be justified by rapid growth; a high dividend yield may be unattractive if earnings do not support dividends.

LOS 22.n

Four common measures of cash flow used in multiples:

1. Earnings plus noncash charges: EPS + per-share depreciation, amortization, depletion.
2. Cash flow from operations (CFO): often adjusted for nonrecurring cash flows and differences in classification across accounting standards; more technically correct than EPS+noncash charges.
3. Free cash flow to equity (FCFE): CFO - capex - principal payments to debtholders; most closely linked to theory but more volatile.
4. EBITDA: EBIT + depreciation + amortization (pre-interest, pre-tax); a measure of cash flow to the firm (both debt and equity holders).

LOS 22.o

Enterprise value (EV) = market value of equity + market value of debt + preferred equity + minority interest - cash and investments. EV/EBITDA is widely used:

• Advantages: comparable across capital structures; useful for capital-intensive firms; EBITDA often positive when EPS is not.
• Disadvantages: growing working capital causes EBITDA to overstate CFO; FCFF is more theoretically linked to valuation.

LOS 22.p

Cross-border comparables are complicated by accounting, cultural, and economic differences.

LOS 22.q

Momentum indicators include earnings surprise, SUE, and relative strength, which relate unexpected or relative performance to subsequent returns.

LOS 22.r

For index/portfolio multiples, the weighted harmonic mean of individual P/Es (with appropriate weights) best represents the portfolio P/E. The arithmetic mean can be misleading, especially with outliers.

ANSWER KEY FOR MODULE QUIZZES

Module Quiz 22.1

1. C Consumer Products appears to be undervalued with a trailing P/E of 27.52 compared with the benchmark of 33.25. (LOS 22.a)

2. B (LOS 22.b)

3. A Copyright's justified leading P/E multiple using the valuation from the H-model is $84 / $4.20 = 20×. The firm is underpriced if actual P/E < 20;="" overpriced="" if="" actual="" p/e=""> 20. (LOS 22.a)

Module Quiz 22.2, 22.3, 22.4

1. C Profit margin = E / S = $5.35 / $342 = 0.0156. Thus: (Module 22.3, LOS 22.i)

Module 22.3 - LOS 22.b

2. C

3. A (Module 22.3, LOS 22.b)

4. A Both stocks are relatively overvalued. Pfeiffer P/B = 9.688 and P/S = 5.971; both exceed peer means and medians. Mapps P/B = 4.524 and P/S = 8.578; both exceed peer mean and median. The disparity between means and medians indicates outliers. (Module 22.3, LOS 22.l)

5. A Home Decor appears undervalued relative to Lester's based on P/CF and P/FCFE comparisons: Home Decor P/CF = 20.88 (87.4% of Lester's 23.90); Home Decor P/FCFE = 28.69 (21.6% of Lester's 132.78). Expectation of higher growth for Home Decor would lead to higher P/CF; since it is lower, Home Decor appears undervalued relative to Lester's. (Module 22.3, LOS 22.l)

6. C In home improvement segment, Home Decor appears more attractive than Lester's because:

• Home Decor trading at P/B 91% of home improvement segment average with forecast ROE same as industry → undervalued relative to industry.
• Home Decor trading at P/B 76.6% of Lester's P/B with slightly higher estimated ROE → undervalued relative to Lester's.
• Lester's trading at P/B 119% of industry average with forecast ROE slightly below industry → Lester's overvalued.

Home Decor's higher beta may account for lower P/B and higher forecast ROE relative to Lester's. (Module 22.3, LOS 22.l)

7. A In department and discount segment, Harmon's appears more attractive than Wally's because:

• Harmon's P/B = 57% of industry average with forecast ROE close to industry → undervalued relative to industry.
• Harmon's P/B = 50% of Wally's P/B with similar expected ROE → undervalued relative to Wally's. Betas are similar indicating similar risk.
• Wally's trading at 114% of industry P/B with only slightly above industry ROE forecast → Wally's overvalued relative to industry.

(Module 22.3, LOS 22.l)

8. B Calculations for Lester's:

P = $42.10/share

CF = net income + depreciation = $1,023,262,000 + $534,102,000 = $1,557,364,000

Number of basic shares outstanding = 631,643,000

CF/share = $1,557,364,000 / 631,643,000 = $2.4656

P/CF = $42.10 / $2.4656 = 17.08×

(Module 22.3, LOS 22.n)

9. B Adjust CFO for nonrecurring expense $139,870,000 (add back after tax):

CFO (reflecting nonrecurring items) = $1,497,442,000 + $139,870,000 × (1 - 0.37) = $1,585,560,100

Adjusted CFO per share = $1,585,560,100 / 631,643,000 = $2.51

Adjusted P/CFO = $42.10 / $2.51 ≈ 16.77 ≈ 17 (Module 22.3, LOS 22.n)

10. B Underlying earnings = $1.29 + $0.22 + $0.04 - $0.08 = $1.47 (Module 22.4, LOS 22.e)

11. A Normalized earnings using average ROE and BVPS: normalized EPS = average ROE × BVPS = 0.32 × $14 = $4.48 (Module 22.4, LOS 22.e)

12. C High dividend yield strategy is consistent with a value orientation because dividend yield is positively related to required return and negatively related to expected growth. (Module 22.4, LOS 22.g)

13. A Predicted P/E = 8.57 + (5.38 × 0.65) + (15.53 × 0.032) - (0.61 × 0.56) = 12.2 (Module 22.4, LOS 22.h)

14. A (Module 22.4, LOS 22.i)

15. C Based on fundamentals (Module 22.4, LOS 22.i)

16. B PEG = 18.75 / 15.32 = 1.22. Given peer median PEG = 0.92, Party Favors appears overvalued. (Module 22.4, LOS 22.j)

17. A (Module 22.4, LOS 22.o)