Work out the price-to-earnings ratio and explain what it means

CFA® Level I · Equities · Relative Value Equity Valuation Approaches · EQ.5.a

The idea

The price-to-earnings ratio is price per share over earnings per share - what the market pays for a unit of current profit. Trailing P/E uses reported earnings and is factual but backward-looking; forward P/E uses a forecast and is relevant but only as good as the forecast. A high P/E is not by itself expensive: it can mean growth is expected, or that earnings are temporarily depressed, and the second case is why P/E becomes meaningless as earnings approach zero and undefined when they are negative. Multiples are comparisons, so they only mean anything against a peer, a history or a justified value derived from expected growth and required return.

Formulas

Price-to-earnings ratio

price-to-earnings = price per share ÷ earnings per share

price per share: the current market price
earnings per share: the last four quarters for a trailing ratio, the next four for a leading one

Trailing and leading multiples are not comparable with each other. Negative earnings make the ratio meaningless rather than low, which is the usual reason to reach for a different multiple.

Justified leading price-to-earnings

justified leading price-to-earnings = payout ratio ÷ (r − g)

payout ratio: the share of earnings paid out as dividends
r: the required return on the equity
g: the sustainable growth rate

The Gordon model divided through by earnings, so it says what multiple the fundamentals justify rather than what the market is paying. The gap between the two is the argument for buying or not.

A practice question

From the question bank, with the reason each wrong option is wrong.

The price-to-earnings ratio is price per share divided by:

earnings per share - correct
book value per shareWhy not: That gives price-to-book, a multiple of what the company holds rather than of what it earns.
dividends per shareWhy not: That is the inverse of the dividend yield, and it reflects the payout decision rather than the profit itself.

The price-to-earnings (P/E) ratio shows how much investors pay for each unit of profit. Formula: P/E = price per share / earnings per share (EPS, the company's profit divided by its number of shares). Example: price $40 and EPS $2 gives P/E = 20, so investors pay $20 for each $1 of yearly profit. Dividing by book value gives price-to-book, and dividing by dividends gives a different ratio.

A harder one

A high price-to-earnings ratio may indicate expected growth, or that current earnings are:

unusually highWhy not: Unusually high earnings make the denominator large, which pushes the multiple down rather than up.
temporarily depressed - correct
exactly at trendWhy not: At trend the multiple carries no distortion at all, so it cannot be the explanation for an unusually high one.

Formula: P/E = price / earnings per share (EPS). A high P/E can happen for two reasons: investors expect strong growth, or current earnings are unusually low, which makes the bottom of the fraction small. Example: a firm that normally earns $5 per share at a price of $50 has a P/E of 10. If a downturn cuts EPS to $1 with the price unchanged, P/E = 50/1 = 50, though nobody is more optimistic. This trap is common with cyclical firms, whose profits rise and fall with the economy.

The hardest tier

Fabrizio Neri, an equity analyst, values Quill Instruments, which has just reported earnings per share of $3.00 and pays out 60% of earnings as dividends. He expects earnings and dividends to grow at 4% a year indefinitely and requires a return of 9%. The shares trade at $36.00. What is the justified trailing P/E, and how does the market's trailing multiple compare?

12.5; the market multiple is below it - correct
12.0; the market multiple equals itWhy not: This uses the leading formula, payout / (r - g), which omits the (1 + g) factor needed for a multiple based on the earnings just reported. It also hides the small gap to the market's 12.0.
6.9; the market multiple is above itWhy not: This divides by the required return alone, 0.60 x 1.04 / 0.09, instead of by (r - g). Leaving growth out of the denominator understates the multiple and reverses the comparison.

A justified P/E is the multiple the fundamentals support. Formula (trailing): P/E = payout x (1 + g) / (r - g), where payout is the share of earnings paid as dividends, g is growth and r is required return. Here: 0.60 x 1.04 / (0.09 - 0.04) = 0.624 / 0.05 = 12.48, about 12.5. The market's trailing P/E is 36.00 / 3.00 = 12.0, which is below 12.5, so the shares look slightly cheap. The formula 0.60 / 0.05 = 12.0 is for the leading P/E (based on next year's earnings), so it should not be mixed in.

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