Price multiples: P/E, earnings yield, P/S, P/B and dividend yield

Which figure belongs under the price?

A price multiple has the share price (or market capitalization) on top, so the figure underneath must belong to shareholders: net income or earnings per share (EPS), book value of equity, dividends or free cash flow to equity (FCFE). Sales are the exception that needs care, covered below.

Prices are taken on the valuation date (sometimes averaged over a period). Share counts and balance sheet figures come from the latest reported statements. Learning Module 5 introduced book value and market capitalization, and Lesson 1 showed how to choose the multiple and the peers.

What are trailing and forward P/E?

The price-to-earnings ratio (P/E) divides the share price by earnings per share. EPS is net income divided by the weighted average shares outstanding during the period. The trailing P/E uses the last four quarters of EPS, $EPS_t$. The forward P/E uses analysts’ consensus EPS for the next 12 months, $EPS_{t+1}$.

$$\text{P/E} = \frac{P_t}{\text{EPS}}, \quad \text{Trailing: EPS}_t, \quad \text{Forward: EPS}_{t+1}$$

Use the same basis for every firm you compare. Lesson 5 covers the time bases.

What are earnings yield and the present value of growth opportunities?

The earnings yield is the inverse of the P/E, EPS divided by price. It is a common measure of equity return. On forward EPS it shows how much of the price the market pays for growth.

A firm with no growth opportunities pays out all its earnings and is worth $EPS_{t+1} \div r_e$, where $r_e$ is the cost of equity. Anything the market pays above that is the present value of growth opportunities (PVGO) .

$$P_t = \frac{\text{EPS}_{t+1}}{r_e} + \text{PVGO}, \quad \frac{\text{PVGO}_t}{P_t} = 1 - \frac{\text{EPS}_{t+1}/P_t}{r_e}$$

PVGO can be negative. Halbrook Utilities trades at 32.00 with forward EPS of 4.00 and a cost of equity of 11%. Its earnings yield is 12.50%, and PVGO ÷ P = 1 − 0.125 ÷ 0.11 = −13.6%: the no-growth value, 36.36, is above the price. A negative PVGO means the market expects reinvestment to destroy value, so the earnings would be better paid out.

Compare earnings yields only after allowing for different costs of equity. Two shares with the same earnings yield can price in very different growth if their costs of equity differ.

What P/E do fundamentals justify?

Divide the constant growth model by trailing EPS and the drivers of P/E appear: payout, growth and the cost of equity. The justified trailing P/E is the P/E those drivers support. The payout ratio is dividends per share (DPS) divided by EPS.

$$\frac{P_t}{\text{EPS}_t} = \frac{\text{Payout ratio} \times (1 + g)}{r_e - g}$$

Higher growth raises the P/E, a higher cost of equity (more risk) lowers it, and a higher payout raises it if growth stays the same. At a 60% payout:

Cost of equity \ growth	3%	4%	5%	6%
8%	12.36	15.60	21.00	31.80
9%	10.30	12.48	15.75	21.20
10%	8.83	10.40	12.60	15.90

The payout and growth trade-off needs care. A firm that pays out more keeps less to reinvest, so it grows more slowly. Take a return on equity (ROE) of 12.5% and growth of (1 − payout ratio) × ROE, with a cost of equity of 9%:

Payout ratio	Growth	Justified trailing P/E
40%	7.5%	28.67
60%	5.0%	15.75
80%	2.5%	12.62

Here raising the payout lowers the justified P/E, because the firm earns more on retained earnings (12.5%) than shareholders require (9%). A firm cannot raise its multiple just by paying out more.

The justified forward P/E drops the $(1 + g)$: payout ratio ÷ ($r_e$ − g) = 0.60 ÷ 0.04 = 15.00. Trailing equals forward times $(1 + g)$. Questions in this module ask for the trailing form unless they say forward.

Go deeper Where the formula comes from

The constant growth model says $P_t = Div_{t+1} \div (r_e - g)$. Next year’s dividend is the payout ratio times next year’s EPS, and next year’s EPS is this year’s EPS grown by $g$: $Div_{t+1} = \text{Payout ratio} \times \text{EPS}_t \times (1 + g)$. Divide both sides by $\text{EPS}_t$ and you have the justified trailing P/E. Divide by $\text{EPS}_{t+1}$ instead and the $(1 + g)$ drops out, which is the forward form.

Which earnings go into the P/E? Core, normalized and diluted

A P/E is only as good as its EPS. EPS that is zero, negative or tiny relative to the price makes the P/E misleading or not meaningful, and accrual accounting makes recurring earnings hard to separate from one-off items.

Analysts therefore use core earnings , which are earnings with the non-recurring items removed before computing the P/E: gains and losses on asset sales, write-downs, goodwill impairment, provisions for future losses, changes in accounting estimates, and income or losses from discontinued operations. A retailer that posts a small operating loss but large interest income on its cash pile can have barely positive EPS and a P/E of several hundred. The number is positive but tells you nothing about the business.

For a cyclical firm, normalized EPS is EPS under mid-cycle conditions. There are two methods. The historical average EPS method takes the average EPS over the most recent full cycle. The average return on equity method takes the average ROE over the cycle times the current book value per share (BVPS). The ROE method is usually preferred when the company’s size has changed a lot, because average EPS does not adjust for size.

$$\text{EPS}_{norm} = \overline{\text{EPS}}_{cycle} \;\text{or}\; \overline{\text{ROE}}_{cycle} \times \text{BVPS}_t$$

One more adjustment is dilution : analysts also consider what EPS would be if all executive options, warrants and convertible bonds were exercised, which means more shares and lower EPS. The effect of dilution on EPS is covered in Financial Statement Analysis.

Earnings for the P/Ea P/E is only as good as its EPS

• Core earnings Use it strip non-recurring items
• Normalized EPS Use it cyclical firms
  • Average EPS over the cycle the simple method
  • Average ROE × current BVPS better when size changed
• Dilution Know the idea options, warrants, convertibles lower EPS
• Not meaningful Use it zero, negative or tiny EPS

When does price-to-sales work?

The price-to-sales ratio (P/S) divides the share price by annual net sales per share, where net sales are total sales minus returns and customer discounts. Sales are the broadest income statement figure. They are usually positive when earnings are not, less open to manipulation when revenue recognition is similar, and more stable than earnings. P/S suits mature, cyclical and loss-making firms.

The justified P/S follows from the justified P/E, because dividends divided by sales equal the net profit margin times the payout ratio. So the justified P/S is the net profit margin times the justified trailing P/E.

$$\frac{P_t}{\text{Sales}_t} = \frac{\text{Net profit margin} \times \text{Payout ratio} \times (1 + g)}{r_e - g}$$

The drawbacks are real. Sales belong to lenders and shareholders, the price only to shareholders. Use P/S for firms with little or no debt. For firms with significant debt use enterprise value to sales (EV/sales), covered in Lesson 3. P/S also ignores cost structure, so high sales growth with weak margins can mislead, and it depends on revenue recognition practices. Two firms can have equal justified P/S and still not be comparable on it if their leverage differs.

What do price-to-book and price to tangible book show?

The price-to-book ratio (P/B) compares the price with the net assets shareholders own on the books. A higher P/B goes with a higher ROE relative to the cost of equity (the justified P/B of Lesson 1) and a higher payout. The price to tangible book value removes intangible assets such as goodwill from book value.

$$\text{P/B} = \frac{P_t}{\text{BVPS}_t}, \quad \text{Price to tangible book} = \frac{P_t}{\text{BVPS}_t - \text{intangibles per share}}$$

P/B works for firms with similar leverage and asset profiles and consistent accounting. Banks are the classic case: few fixed assets, similar balance sheet items and high regulated leverage. For banks analysts also use price to tangible book. Distortions come from intangibles, historical cost and depreciation methods, and large share buybacks. Learning Module 5 covers book value distortions.

How does dividend yield work?

The price-to-dividend multiple is the price divided by dividends per share. It is usually shown upside down as the dividend yield , dividends per share divided by price. For a non-payer the price-to-dividend multiple is undefined and the yield is zero. Investors like it because dividends are often a more predictable part of total return than price gains.

The dividend rate is the most recent periodic dividend, annualized. The trailing dividend yield is the dividend rate divided by the current price, $Div_t \div P_t$. The leading dividend yield is the forecast dividends per share for the next year divided by the current price, $Div_{t+1} \div P_t$.

The justified dividend yield comes from the constant growth model. A higher cost of equity raises it and higher growth lowers it.

$$\text{Trailing: } \frac{Div_t}{P_t} = \frac{r_e - g}{1 + g}, \quad \text{Leading: } \frac{Div_{t+1}}{P_t} = r_e - g$$

The yield also links to the P/E, because dividends over price equal the payout ratio times the earnings yield. Rearranged, the actual P/E is the payout ratio divided by the dividend yield.

$$\frac{Div_t}{P_t} = \frac{Div_t}{\text{EPS}_t} \times \frac{\text{EPS}_t}{P_t}$$

Exam tip A yield below its justified level means the price is too high, not too low.

Dividend yield is only one part of total return. It is zero for non-payers and low for firms that pay out little of their FCFE. Compare it only among firms with clear, consistent dividend policies.

What about cash flow multiples?

Multiples built on cash flow, the cash flow multiples , link more directly to discounted cash flow value and are harder to manipulate than earnings. Practitioners often use a rough “cash flow” of net income plus depreciation and amortization. More precise measures are cash flow from operations (which includes working capital changes), FCFE (closest to value for shareholders, but sensitive to the timing of capital spending and to borrowing) and free cash flow to the firm (FCFF, covered in Lesson 3).

The price to free cash flow to equity is the price divided by next year’s FCFE. Under constant growth it is the reciprocal of the gap between the cost of equity and growth. It suits firms with stable FCFE, and it swings with capital spending, working capital and debt.

$$\frac{P_t}{\text{FCFE}_{t+1}} = \frac{1}{r_e - g}$$

For example, a cost of equity of 9% and growth of 5% give 1 ÷ 0.04 = 25.0.

Which price multiple suits which company?

Multiple	Driven by	Suits
P/E	payout ratio, growth, cost of equity	firms with positive, recurring EPS
Dividend yield	dividend size and growth	mature dividend payers
P/S	net profit margin (plus the P/E drivers)	firms with little or no debt; cyclical or loss-making firms
P/B	ROE against cost of equity	firms with similar leverage and asset profiles, such as banks
Price to FCFE	FCFE growth	firms with stable FCFE

Lesson 3 adds the enterprise value rows.

Price multiplesprice over a shareholder figure; same basis for every firm

• P/E Memorize payout, growth, cost of equity; trailing or forward
• P/S Memorize profit margin; only for low-debt firms
• P/B and price to tangible book Memorize ROE against cost of equity; banks
• Dividend yield Memorize trailing or leading; mature payers
• Price to FCFE Know the idea 1 ÷ (r_e − g); stable FCFE