Equities · Reading 45

Relative Value Equity Valuation Approaches

CFA Level I · Equities · Reading 45 · about 57 min

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What you'll learn

LOS 45.a Explain how the method of comparables and the method of forecasted fundamentals set a benchmark multiple, and how PEG ratios and regression reconcile them.
LOS 45.b Calculate and interpret price multiples (P/E, P/B, P/S, dividend yield, P/FCFE) and enterprise value multiples (EV/EBITDA, EV/FCFF, EV-to-book), and describe when each is appropriate.
LOS 45.c Determine a peer group using industry classification or statistical factor exposures, and recognize the limitations of each.
LOS 45.d Describe how multiples based on past, current and projected values are used, including historical comparisons and terminal values.

Module 45.1

Price Multiples and Equity Valuation

This reading compares the method of comparables with the method of forecasted fundamentals and shows how to calculate justified P/E and P/B ratios, the PEG ratio and regression-based multiples. It then covers the calculation and use of price, enterprise value and cash flow multiples, the choice of an industry-based or factor-based peer group, and multiples built on past or forecast values, including a terminal value from a justified multiple.

LOS 45.a — Comparables versus forecasted fundamentals

Relative valuation judges a stock by comparing what investors pay for it with some measure of value. Two families of ratios are used:

Price multiples put the share price over a per-share measure: earnings (P/E), book value (P/B), sales (P/S), dividends or free cash flow to equity.
Enterprise value (EV) multiples put EV over a firm-level measure that belongs to all capital providers: EBITDA, EBIT, free cash flow to the firm (FCFF) or revenue.

The timing of the denominator matters:

Label	Denominator	Example
Trailing multiple	value for the most recent past period	$P_{0} / E_{0}$
Leading multiple (also forward multiple)	forecast for the next period	$P_{0} / E_{1}$
Justified multiple	the multiple a fairly priced stock should carry, estimated by the analyst	from peers or from a DCF model

The multiple must make economic sense for the company. A P/E is meaningless when earnings are negative, and a dividend-based multiple does not work for a peer group that includes non-payers.

The decision rule for price multiples: a stock whose multiple is above the benchmark looks overvalued, and one whose multiple is below the benchmark looks undervalued.

Method of comparables

The method of comparables takes the benchmark from a peer group, usually the mean or median multiple of similar companies. Its economic rationale is the law of one price: similar assets should sell at similar multiples.

Peers must genuinely be similar in competitive position, risk and earnings growth. Different accounting methods, nonrecurring items and different fiscal year-ends all weaken comparability.
When the peers' multiples are skewed by a few extreme values (often caused by temporarily depressed earnings), the median is the better benchmark because outliers do not pull it. The alternative is to remove the outliers before computing the mean.

Applying the method:

Compute the benchmark multiple from the peer group.
Compare the subject company's multiple with the benchmark.
For a value estimate, multiply the benchmark by the subject company's own per-share measure for the same period: forecast EPS for a leading P/E, trailing EPS for a trailing P/E.

Example. Five peers trade at P/Es of 11, 13, 14, 15 and 37. The median is 14, while the single high multiple pulls the mean up to 18. The subject company earns $2.50 per share and trades at $40.00, a P/E of 16. Against the median it looks overvalued, with an implied value of $14 \times 2.50 = $35.00$ . Against the mean it would wrongly look undervalued, with an implied value of $18 \times 2.50 = $45.00$ .

Method of forecasted fundamentals

The method of forecasted fundamentals derives the benchmark from a discounted cash flow model, typically the constant growth (Gordon) model $P_{0} = D_{1} / (r - g)$ . Dividing by next year's earnings gives the justified leading P/E:

Key concept

\frac{P _{0}}{E _{1}} = \frac{D _{1} / E _{1}}{r - g} = \frac{payout ratio}{r - g}

The trailing version multiplies by $(1 + g)$ : $P_{0} / E_{0} = payout \times (1 + g) / (r - g)$ .

The justified P/E rises with the earnings growth rate (g) and falls as the required rate of return (r, which reflects the company's risk) rises. With r and g held constant, a higher payout ratio raises it.

Dividing the same model by book value per share, and substituting that growth relation, gives the justified P/B ratio:

Key concept

\frac{P _{0}}{B _{0}} = \frac{R O E - g}{r - g}

The P/B therefore depends on the spread between ROE and the required rate of return on equity (the cost of equity). With $r > g$ , the justified P/B is above 1.0 if ROE is above r, exactly 1.0 if ROE equals r, and below 1.0 if ROE is below r.

Example. A firm pays out 50% of earnings, r = 12% and g = 7%. Its justified leading P/E is $0.50/0.05 = 10.0$ . A second firm has ROE = 15%, r = 10% and g = 6%, so its justified P/B is $(0.15 - 0.06) / (0.10 - 0.06) = 2.25$ .

Reconciling the two methods

The two methods can disagree. A firm may deserve a P/E above its peer average because it grows faster, for example. Two tools adjust for fundamentals:

The price/earnings-to-growth ratio (PEG) adjusts for one fundamental, growth:

P E G = \frac{P / E}{g} (g in whole percentage points)

A PEG higher than the peers' benchmark means the P/E is high relative to growth, so the stock looks overvalued. A lower PEG points to undervaluation. Example. A P/E of 18 and growth of 9% give a PEG of 2.0. Against a peer median of 1.6, the stock looks overvalued.

The regression approach adjusts for several fundamentals at once. The observed multiple (the dependent variable) is regressed on fundamentals such as ROE, growth, payout and risk (the independent variables) across the peer group. The fitted equation then gives the subject company's justified multiple:

P / B_{i} = b_{0} + b_{1} R O E_{i} + b_{2} g_{i}

Example. With $b_{0} = 0.60$ , $b_{1} = 8.0$ , $b_{2} = 5.0$ , ROE = 10% and g = 4%, the justified P/B is $0.60 + 0.80 + 0.20 = 1.60$ . The intercept is part of the estimate, and the ROE input is the firm's actual ROE rather than its required return. At Level I, candidates interpret regression output; they are not asked to estimate the regression.

Key concept

Tool	Controls for	Weakness
Peer mean/median	nothing (assumes peers are alike)	peers may differ, or be mispriced
PEG ratio	growth only	ignores risk, ROE and payout differences
Regression	several fundamentals simultaneously	needs a peer sample; relationships can change

Terminal values from multiples

A justified multiple estimated for the end of the forecast horizon can also supply the terminal value in a present value model. LOS 45.d gives the formula and an example.

Common exam traps

Using the mean of a skewed peer distribution instead of the median. In the example, the mean of 18 gives an implied value of $45.00 instead of $35.00 from the median of 14.
Mixing up the rationales. The law of one price underlies comparables; a DCF model underlies forecasted fundamentals.
Calculating PEG as g/(P/E), or entering g as a decimal (0.12 instead of 12). In the PEG example, $g / (P / E)$ gives 0.5 and entering growth as 0.09 gives 200, instead of 2.0.
Reading a low PEG as overvalued. For PEG, as for P/E, a value below the peers' signals undervaluation.
In the justified leading P/E, using the retention ratio instead of the payout ratio, or dividing by r instead of r − g. In the example, dividing the 50% payout by r = 12% gives 4.17 instead of 10.0.
Leaving out the intercept in a regression-based justified multiple. In the example, dropping $b_{0} = 0.60$ gives 1.00 instead of 1.60.

Exam shortcuts

With r above g, the justified P/B is above 1.0 exactly when ROE is above r, so the side of 1.0 can be read from ROE and r before any calculation.

Bottom line

Price multiples put the share price over a per-share measure, EV multiples put EV over a firm-level measure belonging to all capital providers, a trailing multiple uses the most recent past period and a leading multiple uses next period's forecast.
The method of comparables takes its benchmark from the mean or median multiple of a peer group and rests on the law of one price, and when a few extreme values skew the peers' multiples the median, or the mean after removing outliers, is the better benchmark.
A stock whose price multiple is above the benchmark looks overvalued, and one whose multiple is below the benchmark looks undervalued.
The justified leading P/E from the constant growth model is $payout ratio / (r - g)$ , the trailing version multiplies it by $(1 + g)$ , and it rises with g, falls as r rises and, with r and g constant, rises with the payout ratio.
The justified P/B is $(R O E - g) / (r - g)$ , so with r above g it is above 1.0 if ROE exceeds r, equal to 1.0 if ROE equals r and below 1.0 if ROE is below r.
The PEG ratio, $(P / E) / g$ with g in whole percentage points, adjusts for growth only and a PEG above the peers' benchmark looks overvalued, while the regression approach adjusts for several fundamentals at once and its fitted equation, intercept included, gives the justified multiple.

Quick check

Question 1Core

Beatriz Almeida is valuing Penhallow Instruments with the method of comparables. The leading P/E ratios of the five companies in her peer group are 13.5, 14.5, 16.0, 20.0 and 48.0. The 48.0 multiple belongs to a peer whose earnings next year are expected to be temporarily depressed by a plant refit. Penhallow earned $2.60 per share over the last 12 months, and the consensus forecast of its EPS for next year is $2.95. Almeida's estimate of Penhallow's value per share is closest to:

Show answer and explanation

Correct answer: B

The method of comparables values a stock at the benchmark multiple of its peer group, applied to the stock's own value driver. One peer's multiple is inflated by temporarily depressed earnings, so the median, which a single extreme value does not pull, is the appropriate benchmark. A leading P/E has next year's forecast EPS in its denominator, so the benchmark is applied to Penhallow's forecast EPS of $2.95. Its trailing EPS would pair with a trailing multiple.

Sort the peers' leading P/Es: 13.5, 14.5, 16.0, 20.0, 48.0. With five values, the median is the third one:

median leading P / E = 16.0

Apply the benchmark to next year's EPS:

V_{0} = benchmark \frac{P _{0}}{E _{1}} \times E_{1} = 16.0 \times $2.95 = $47.20

Dropping the 48.0 outlier and averaging the other four peers gives the same benchmark: $(13.5 + 14.5 + 16.0 + 20.0) /4 = 64.0/4 = 16.0$ . The mean of all five, $(13.5 + 14.5 + 16.0 + 20.0 + 48.0) /5 = 112.0/5 = 22.4$ , is higher than four of the five peers because of the single 48.0 value.

Why the other options are wrong

A. $16.0 \times $2.60 = $41.60$ applies a leading multiple to trailing EPS. The peer multiple and the subject's earnings must cover the same period, so a leading P/E is paired with forecast EPS.
C. $22.4 \times $2.95 = $66.08$ uses the mean leading P/E of all five peers. The 48.0 multiple reflects one peer's temporarily depressed earnings and drags the mean well above the typical peer, so the median is the better benchmark.

Key takeaway Comparables-based value $=$ benchmark multiple $\times$ the subject company's own value driver. Match the timing (a leading multiple with forecast EPS, a trailing multiple with trailing EPS), and use the median when a few extreme multiples skew the peer group.

Module 45.2

Price and Enterprise Value Multiples

LOS 45.b — Price and enterprise value multiples: calculation, interpretation and uses

Value = assets in place + growth opportunities

A share's value can be split into the value of assets in place (next year's earnings as a no-growth perpetuity, $E_{1} / r$ ) and the present value of growth opportunities (PVGO):

Key concept

P_{0} = \frac{E _{1}}{r} + P V GO \Rightarrow \frac{P V GO}{P _{0}} = 1 - \frac{E _{1} / P _{0}}{r}

The earnings yield is $E / P$ , the inverse of the P/E. $E_{1} / P_{0}$ is the forward earnings yield, the reciprocal of the leading P/E, so the same split can be written $E_{1} / P_{0} = r (1 - P V GO / P_{0})$ . A negative PVGO suggests management is investing in negative-NPV projects and should pay out more of its earnings.

Example. With $P_{0} = 50$ , $E_{1} = 3.00$ and $r = 8%$ , assets in place are worth $37.50$ and PVGO is $12.50$ , which is 25% of the price.

Earnings-based multiples: core and normalized earnings

A P/E built on earnings that contain large one-off items is misleading, so analysts use core earnings (also called persistent or continuing earnings). Core earnings strip out nonrecurring items, for example discontinued operations, write-downs, gains or losses on asset sales, changes in accounting estimates and provisions for future losses. EPS should also reflect dilution from options, warrants and convertible bonds.

For cyclical firms, analysts estimate normalized earnings, the EPS expected in the middle of the business cycle:

Key concept

Method	Normalized EPS	Comment
Method of historical average EPS	average EPS over the most recent business cycle	ignores growth in firm size
Average ROE method	average ROE over the cycle × current book value per share	captures changes in firm size better

Example. EPS over a four-year cycle of 2.10, 2.50, 1.70 and 2.90 gives a historical average of $2.30$ . An average ROE of 11% times current BVPS of 22.00 gives 2.42.

Price-to-sales (P/S)

The price-to-sales (P/S) multiple is used when earnings are negative or not comparable across firms. It suits mature and cyclical firms with similar revenue recognition. Sales belong to both debt and equity holders while price is an equity measure, so P/S fits firms with little or no leverage. For more leveraged firms, an EV multiple may be more appropriate.

\frac{P _{0}}{S _{0}} = \frac{P _{0}}{E _{0}} \times \frac{E _{0}}{S _{0}} = \frac{payout \times ( 1 + g )}{r - g} \times profit margin

Example. With a payout of 50%, g = 4%, r = 9% and a margin of 6%, the trailing P/E is $0.52/0.05 = 10.4$ and the justified P/S is $10.4 \times 0.06 = 0.624$ .

Enterprise value multiples

E V = market value of common and preferred stock + market value of debt - cash and short-term investments

Firm value is the same figure without subtracting cash. EBIT, EBITDA and FCFF belong to all capital providers, so they are paired with EV.

E V = \frac{F C F F _{1}}{W A C C - g}, F C F F = E B I T D A (1 - t) + Dep \times t - CapEx - WCInv

The justified EV/EBITDA multiple is this EV divided by EBITDA. It rises with g and falls with WACC. It is popular in capital-intensive industries with large depreciation.

Example. EBITDA is 500, depreciation 100, CapEx 150, working capital investment 30, t = 25%, WACC 8% and g = 3%. FCFF is $375 + 25 - 150 - 30 = 220$ , EV is $220/0.05 = 4, 400$ , and EV/EBITDA is 8.8x.

Balance-sheet multiples

P/B is most useful when the firms compared hold mainly tangible assets and have similar accounting methods, leverage and asset mix. Banks are often valued on price-to-tangible book value, which excludes intangible assets such as goodwill from book value.
The value-to-book multiple is (market value of equity + market value of debt) / (book value of equity + book value of debt). It is useful when leverage differs or book equity is negative.
The enterprise value-to-book ratio subtracts cash from both numerator and denominator. It can be written in terms of fundamentals. Return on capital (ROC) is $E B I T (1 - t) / book value of capital$ . Reinvestment is the spending on fixed capital (net of depreciation) and working capital, the part of EBIT that is not available to debt and equity holders. Exam convention: the reinvestment rate is reinvestment as a proportion of EBIT, and $F C F F = E B I T (1 - t) (1 - reinvestment rate)$ . Current practice: that FCFF identity holds exactly only when the rate is measured against after-tax EBIT, $(capital expenditures - depreciation + working capital investment) / [E B I T (1 - t)]$ . When a question states the reinvestment rate, use it as given. Then:

\frac{E V}{B V of capital} = \frac{R O C \times ( 1 - reinvestment rate )}{W A C C - g}

Example. With ROC of 8%, a reinvestment rate of 50%, WACC of 9% and g of 4%, the justified ratio is $0.08 (1 - 0.50) / (0.09 - 0.04) = 0.8$ x. The growth rate matches the reinvestment: $0.50 \times 8% = 4%$ .

Cash-flow multiples and yields

The price-to-dividend multiple is $P_{0} / D$ , and its reciprocal is the dividend yield. A trailing dividend yield uses the dividend paid over the past year. A leading dividend yield divides the dividend expected over the next year by the current price.
The justified dividend yield can be computed two ways:

\frac{D _{0}}{P _{0}} = \frac{D _{0}}{E _{0}} \times \frac{E _{0}}{P _{0}} (payout \times earnings yield) or \frac{D _{0}}{P _{0}} = \frac{r - g}{1 + g}

Example. A payout of 60% and a justified trailing P/E of 15 give an earnings yield of 6.67% and a dividend yield of 4.0%. For a different firm with $r = 9%$ and $g = 3%$ , the second formula gives $0.06/1.03 = 5.83%$ .

Yields work in reverse. An actual yield higher than the justified yield signals an undervalued stock; a lower one signals an overvalued stock. As with multiples, a yield is compared with peers only after allowing for differences in fundamentals such as growth and the required return on equity.
Justified $P_{0} / F C F E_{1} = 1/ (r - g)$ and $E V / F C F F_{1} = 1/ (W A C C - g)$ . FCFE matches price (equity) and FCFF matches EV (all capital). Cash flow from operations can also serve as a denominator, but FCFE measures the cash actually available to shareholders more accurately. The main concern with free-cash-flow multiples is that capital expenditures and working capital investment are cyclical, so free cash flow can swing over the cycle.
Industry-specific multiples (e.g., EV per unit of reserves in mining or oil) cannot be compared across industries and can let a whole industry become mispriced.

Which multiple when?

Key concept

Situation	Preferred measure
Negative or non-comparable earnings, mature/cyclical, low leverage	P/S
Capital-intensive, leverage differs across peers	EV/EBITDA
Mostly tangible assets, similar accounting and leverage; banks	P/B; price-to-tangible book for banks
Book equity negative or leverage differs	value-to-book or EV-to-book
Peer group includes non-dividend payers	avoid dividend-based multiples

Common exam traps

For the PVGO share, subtract assets in place from price and then divide by price. $E_{1} / P_{0}$ is the earnings yield, a different quantity. In the example, $E_{1} / P_{0}$ is 6%, while the PVGO share is 25%.
In FCFF, add the depreciation tax shield $Dep \times t$ . EV/EBIT is a different multiple from EV/EBITDA. In the example, leaving out the 25 shield gives FCFF of 195, EV of 3,900 and EV/EBITDA of 7.8x instead of 220, 4,400 and 8.8x.
The justified P/S uses the trailing P/E, which includes $1 + g$ . In the example, the leading P/E of 10.0 gives 0.60 instead of 0.624.
The average ROE method multiplies by current BVPS. Next year's EPS plays no part.
For dividend and earnings yields, a value above the justified level means undervalued.

Exam shortcuts

Match the multiple to the situation: negative or non-comparable earnings point to P/S, a capital-intensive industry with different leverage across peers to EV/EBITDA, negative book equity to value-to-book or EV-to-book, and a peer group with non-payers rules out dividend-based multiples.

Bottom line

A share's value is $P_{0} = E_{1} / r + P V GO$ , so the PVGO share of the price is $1 - (E_{1} / P_{0}) / r$ , and a negative PVGO suggests management is investing in negative-NPV projects.
Core earnings strip out nonrecurring items, and for cyclical firms normalized EPS is either the average EPS over the most recent cycle, which ignores growth in firm size, or the average ROE over the cycle times current BVPS, which captures it better.
P/S is used when earnings are negative or not comparable, suits mature and cyclical firms with similar revenue recognition and little or no leverage, and its justified value is the justified trailing P/E times the profit margin.
EBIT, EBITDA and FCFF belong to all capital providers and are paired with EV; the justified EV/EBITDA is $F C F F_{1} / (W A C C - g)$ divided by EBITDA, rising with g and falling with WACC.
P/B works best for firms with mainly tangible assets and similar accounting, leverage and asset mix, banks are often valued on price-to-tangible book, and value-to-book or EV-to-book helps when leverage differs or book equity is negative.
The justified dividend yield is $(r - g) / (1 + g)$ or payout times earnings yield, and for yields the rule is reversed: an actual yield above the justified yield signals an undervalued stock.

Quick check

Question 2Core

Over its most recent business cycle, Dunmore Engineering earned an average return on equity of 16%. Its current book value per share is $31.50, its expected EPS for next year is $4.80, and its EPS averaged $4.35 over the same cycle. Using the average ROE method, Dunmore's normalized EPS is closest to:

Show answer and explanation

Correct answer: C

Normalized earnings estimate mid-cycle EPS for a cyclical company. Under the average ROE method, normalized EPS equals the average ROE over the most recent cycle multiplied by the current book value per share.

Normalized EPS = R O E \times B V P S_{current} = 0.16 \times 31.50 = $5.04

Why the other options are wrong

A. $4.35 is normalized EPS under the method of historical average EPS. That method does not reflect changes in firm size as well as the average ROE method does.
B. $4.80 is simply next year's expected EPS, which is not adjusted for where the firm is in the business cycle.

Key takeaway Average ROE method uses current BVPS, so it captures growth in the firm's size; historical average EPS does not.

Module 45.3

Peer Groups and Multiples-Based Valuation

LOS 45.c — Choosing a peer group

Comparables-based valuation benchmarks a company against the mean or median multiple of a peer group. There are two ways to form that group.

Industry-based peer group

An industry-based peer group contains firms in the same principal business activity. Because they face much the same competitive forces, supply chains and technology, their cash flows should behave similarly. Industry classification systems are the usual starting point. Good peers should also match on cyclicality, life cycle stage and market structure, and the analyst still has to check fundamentals such as leverage.

Industry peers are hard to find for:

unique firms with few or no genuinely similar companies;
industries whose members are at widely different life cycle stages (start-ups next to mature incumbents);
firms exposed to different tax or regulatory jurisdictions;
multi-industry companies (conglomerates), whose blend of businesses, markets and fundamental factors (risk, growth, leverage) may leave them with no close peers at all.

Statistical factor-based peer group

A statistical factor-based peer group groups companies whose exposures to risk-return factors are the same or close, regardless of industry. The CAPM is a single-factor model that measures only systematic risk (beta). Multifactor models are the usual tool for finding factor-based peers.

The advantage is independence from industry labels, which helps with firms that industry lists handle badly.
The disadvantage is that the statistical relationships are estimated from past data and may not persist, so the model can be misspecified going forward.

Key concept

Feature	Industry-based	Statistical factor-based
Grouping criterion	same business activity	similar factor exposures
Typical tool	industry classification system	multifactor model
Main weakness	conglomerates, unique firms, mixed life cycles, jurisdictions	historical relationships may not hold in future

LOS 45.d — Multiples based on past, current and future values

Weaknesses of current-value comparables

Mispriced peers. If the whole peer group is overvalued or undervalued, a stock that looks cheap or expensive relative to its peers may not be cheap or expensive in absolute terms.
Distorted current figures. Multiples built on current, unadjusted numbers can be skewed by accounting choices, nonrecurring items or cyclicality. The remedies are core or normalized earnings, or a comparison with multiples from past periods (below), which span different points in the cycle.

Using historical values

Historical values of the subject company's multiples: today's multiple is compared with the company's own past multiples. Changes can be linked to changes in its fundamentals, and the analysis does not rely on the current pricing of peers.
Historical averages of peer group multiples: the company is compared with its peers over a whole period, such as a business cycle. This reduces the risk of benchmarking against a peer group that is mispriced at the moment.

Fundamental differences such as growth and required return still have to be controlled for. Historical data do not remove that need.

Using projected future values

A forecast multiple can be applied to a forecast metric to estimate a terminal value for a present value model:

Key concept

T V_{n} = justified leading P/E_{n} \times E_{n + 1}, justified leading P/E_{n} = \frac{payout}{r - g}

Example. EPS in year 5 is expected to be 4.00, after which growth settles at 3% with a 60% payout and r = 9%. The justified leading P/E is $0.60/0.06 = 10.0$ and $E_{6} = 4.00 \times 1.03 = 4.12$ , so $T V_{5} = 41.20$ . The justified trailing P/E of 10.3 applied to $E_{5}$ gives the same value.

Common exam traps

The problem with a conglomerate is the lack of close industry peers. A factor-based peer group built with a multifactor model can still be formed.
Factor-based peers usually come from multifactor models. Industry codes describe industry-based peers, and the single-factor CAPM captures beta only.
A mispriced peer group is handled with historical multiples (the company's own or peer averages). Forecasts built on current peer prices carry the same mispricing.
A leading P/E is applied to next-period earnings ( $E_{n + 1}$ ). In the example, applying 10.0 to $E_{5} = 4.00$ gives 40.00 instead of 41.20.

Exam shortcuts

When next-period earnings are $E_{n} (1 + g)$ , the justified trailing P/E applied to $E_{n}$ gives the same terminal value as the justified leading P/E applied to $E_{n + 1}$ , so either pairing can be used.

Bottom line

An industry-based peer group holds firms with the same principal business activity, and suitable peers are hard to find for unique firms, industries with members at widely different life cycle stages, firms in different tax or regulatory jurisdictions and conglomerates.
A statistical factor-based peer group, usually formed with a multifactor model, holds firms with the same or close exposures to risk-return factors regardless of industry, but its relationships are estimated from past data and may not persist.
Comparables can mislead when the whole peer group is overvalued or undervalued, and multiples built on current unadjusted figures can be distorted by accounting choices, nonrecurring items or cyclicality.
Comparing a stock with its own past multiples or with peer averages over a whole business cycle reduces the risk of benchmarking against a currently mispriced peer group, though differences in growth and required return still have to be controlled for.
A terminal value can be estimated as $T V_{n} = justified leading P/E_{n} \times E_{n + 1}$ , with the justified leading P/E equal to $payout / (r - g)$ .

Quick check

Question 3Core

Which of the following is most likely a limitation of relying on an industry-based peer group?

Show answer and explanation

Correct answer: B

Multi-industry companies are a recognized problem for industry-based peer groups. A conglomerate's mix of businesses gives it a blended risk and growth profile, and a single set of industry peers is unlikely to match that profile.

Why the other options are wrong

A. Industry-based peer groups make no automatic assumption that all members have identical leverage. Analysts are told to check leverage differences among industry peers.
C. The law of one price is the rationale for comparables. It does not require factor models for firms with international operations.

Key takeaway Industry-peer problems: unique firms, mixed life cycle stages, different tax/regulatory jurisdictions, and multi-industry companies.

Practice Questions

Question 4Core

Carys Morgan forecasts that Norrland Timber will earn $6.00 per share in Year 7. From then on she expects earnings and dividends to grow at 5% a year indefinitely, with 40% of earnings paid out, and she requires a 10% return. Using a justified leading P/E ratio, Norrland's terminal value per share at the end of Year 7 is closest to:

Show answer and explanation

Correct answer: B

A forecast multiple can be applied to a forecast metric to estimate a terminal value. A justified leading P/E at the end of Year 7 must be multiplied by earnings expected for the following year (Year 8).

Justified leading P/E = \frac{0.40}{0.10 - 0.05} = 8.0

E_{8} = 6.00 \times 1.05 = 6.30

T V_{7} = 8.0 \times 6.30 = $50.40

Check: trailing P/E $= 8.0 \times 1.05 = 8.4$ ; $8.4 \times 6.00 = $50.40$ .

Why the other options are wrong

A. $48.00 applies the leading P/E of 8.0 to Year 7 earnings ( $8.0 \times 6.00$ ) instead of Year 8 earnings.
C. $75.60 uses the retention ratio (0.60) in place of the payout ratio, giving a P/E of 12.0.

Key takeaway Leading P/E × next-year earnings (or, equivalently, trailing P/E × current earnings) gives the terminal value.

This reading has 34 questions in the full bank. Practice all of them.

Key Takeaways

Comparables-based value $=$ benchmark multiple $\times$ the subject company's own value driver. Match the timing (a leading multiple with forecast EPS, a trailing multiple with trailing EPS), and use the median when a few extreme multiples skew the peer group.
Average ROE method uses current BVPS, so it captures growth in the firm's size; historical average EPS does not.
Industry-peer problems: unique firms, mixed life cycle stages, different tax/regulatory jurisdictions, and multi-industry companies.
Leading P/E × next-year earnings (or, equivalently, trailing P/E × current earnings) gives the terminal value.