Equity valuation

Level 1 Plain words

For every reader: the idea in plain words, no formulas.

A share is a claim on future profits

Owning a share means owning a small piece of a company: its buildings, brands, patents and, most of all, its future profits. Some of those profits come back to you as dividends. The company keeps the rest to grow the business or uses it to buy back its own shares, which leaves each remaining share with a bigger slice.

What a share is worth today depends on three questions. How much profit will the company make in the years ahead? How fast will that profit grow? And how much return do investors demand for waiting and for the risk that the profits disappoint? A high answer to the first two raises the value. A high answer to the third lowers it.

Price and value

Price means what the market charges today. Value is our estimate of what the future profits are worth. The two can differ for years. Prices swing with fear and enthusiasm; value changes more slowly, as the business itself changes. Benjamin Graham's line is the one most people remember: in the short run the market is a voting machine, and in the long run a weighing machine.

The multiple: price over earnings

The quickest way to describe a stock's price is the price-to-earnings ratio, or P/E: the share price divided by a year's profit per share. A company earning $5 a share and trading at $100 has a P/E of 20. Flip it over and you get the earnings yield, 5 %: the profit you buy for each dollar paid.

A high P/E means buyers expect profits to grow fast, or they accept a low return, or both. A low P/E means the opposite, or that buyers fear the profits will shrink. Two companies with the same earnings can deserve different prices, and much of this chapter explains why.

What a moat is

Warren Buffett popularised the word moat for whatever protects a business from competitors, the way a moat protects a castle. A strong brand, a network that gets more useful as it grows, customers who find it costly to switch, or costs that rivals cannot match: each lets a company keep earning high profits on the money invested in it. Without a moat, high profits attract rivals, and competition grinds them down to ordinary levels. Chapter 5 explains moats from the economics side. In this chapter we show that a moat changes what growth is worth, and in Level 3 we put a number on it.

Moats are easier to describe than to measure. Plenty of famous brands have lost their protection when tastes or technology changed, and plenty of dull businesses (a regional quarry, a waste hauler with the only licensed landfill nearby) keep high returns for decades because no rival can enter. When we look for a moat, we look first at the numbers: has the company earned high returns on its capital for many years, through good and bad times? Then we ask what stops a competitor from copying it. If we cannot name the barrier, the high returns may not last.

Why prices swing more than profits

Stock prices move far more than the profits behind them. A company whose earnings rise or fall 5 % in a year can see its share price move 30 %. The reason is that the price reflects all future profits, not just this year's. When investors grow more hopeful about the next twenty years, or demand a lower return for waiting, the price of the whole stream rises at once. A small change in the long-run view moves the price a lot, in the same way that a small change in rates moves a long bond a lot. Level 3 measures this as the duration of a stock.

Level 2 How it works

For readers who want the mechanism, with the diagrams.

Beginner path stops here

Two families of valuation

Analysts value shares in two broad ways. Intrinsic methods forecast the cash a business will produce and discount it back to today: a dividend discount model uses dividends; a discounted cash flow model, or DCF, uses the free cash flow the business throws off before anyone is paid. Relative methods compare a company's multiples (price to earnings, to book value, to sales, or enterprise value to operating profit) with those of similar firms. Relative methods answer "is this cheap next to its peers?" and inherit any mispricing of the peers. Intrinsic methods answer "is this cheap next to its cash?" and inherit every error in the forecast. Most analysts use both and look hard at any gap between them.

The multiples analysts use

The P/E is one of several multiples, each suited to a different kind of business.

Enterprise value, equity value plus net debt, measures what a buyer of the whole business would pay, debt included. Dividing it by a profit measure taken before interest makes companies with different debt levels comparable, which a P/E cannot do. Every multiple is a shorthand for a DCF with assumptions hidden inside it. A P/E of 30 says the market expects either fast growth, high returns on new investment, or a low discount rate; Level 3 shows the formula that links them.

Dividends, buybacks and total payout

A company can return cash in two ways. A dividend sends cash to every shareholder. A buyback uses the cash to retire shares, so each remaining share owns more of the company. Since the 1980s US companies have shifted much of their payout to buybacks, partly for tax reasons (a holder who does not sell pays no tax on a buyback) and partly for flexibility (cutting a buyback draws less attention than cutting a dividend).

For valuation, what matters is total payout plus what reinvestment earns. A buyback at a fair price neither creates nor destroys value for the holders who stay; it raises earnings per share, as Level 3 shows, and leaves the company smaller in the same proportion. A buyback at too high a price transfers value from the holders who stay to the ones who sell.

Growth and the discount rate

Every intrinsic model has the same two inputs at its centre: how fast the cash grows, and the rate at which we discount it. The Gordon growth model, the simplest of them, shows how sensitive the answer is. A stock paying $4 next year, growing at 4 % forever and discounted at 8 %, is worth $100. Raise growth to 5 % and the value rises to $133; raise the discount rate to 9 % instead and it drops to $80.

One percentage point of either input moves the value by a fifth to a third. This is why analysts argue so much about long-run growth and the cost of capital, and why small changes in interest rates can swing whole markets.

Where the discount rate comes from

The discount rate for a share is the return investors require to hold it, its cost of equity. Chapter 11 derives it from the capital asset pricing model: a risk-free rate plus a premium scaled by how much the stock moves with the market. For a whole company, analysts blend the cost of equity with the after-tax cost of its debt, weighted by how much of each the company uses. That blend is the weighted average cost of capital, or WACC. It is the hurdle every investment the company makes must clear.

Growth stocks and value stocks

Investors sort stocks into growth and value. Growth stocks trade at high multiples because buyers expect fast-rising profits; value stocks trade at low multiples, often because their businesses look dull or troubled. Over the long history of US data, value stocks as a group have earned more than growth stocks, a pattern Fama and French measured and Chapter 11 discusses, with long stretches when the opposite held. In valuation terms a growth stock has much of its worth in the distant future, so its price reacts more to changes in the discount rate, much as a long bond reacts more to a change in yield.

Moats in valuation terms

A moat shows up in one number: the return a company earns on the capital invested in it, its return on invested capital (ROIC), set against its cost of capital. A company with a ROIC of 20 % and a WACC of 8 % creates 12 cents of value a year for every dollar it invests. One with a ROIC of 8 % creates nothing, however fast it grows.

Morningstar's equity analysts sort the sources of a moat into five kinds: intangible assets (brands, patents, licences), switching costs, network effects, cost advantages and efficient scale (a market too small for a second entrant to earn its cost of capital). Each one slows the fade of ROIC toward the cost of capital. Without a moat, the fade is fast: competitors copy the product and cut prices until returns are ordinary. With one, high returns can last for decades. The difference between those two fades is a large share of what separates a P/E of 12 from a P/E of 30.

Valuing a whole market: CAPE

For the market as a whole, Robert Shiller's CAPE (the cyclically adjusted price-to-earnings ratio) divides the index level by the average of ten years of inflation-adjusted earnings. Averaging over a decade smooths out the swings of the business cycle, so a recession's collapsed profits do not make the market look expensive, and a boom's inflated profits do not make it look cheap.

High CAPE readings have been followed by low ten-year returns and low readings by high returns, with a lot of scatter around the line. CAPE says little about the next year. It has said much more about the next ten.

Level 3 The math

For Series 65 and CFA readers: formulas and worked examples.

Series 65 path stops here

The Gordon growth model

John Burr Williams set out in 1938 that a share is worth the present value of its future dividends. Myron Gordon gave the version with constant growth that bears his name. With next year's dividend $D_1$, a required return $r$ and growth $g$ below $r$, the sum of all future dividends has a closed form.

In words, the value of a share equals next year's dividend divided by the gap between the required return and the growth rate.

Rearranged, the model also says what return a buyer can expect: $r = D_1/P_0 + g$, the dividend yield plus growth. That form is the one Level 4 uses on whole markets.

Equity duration

The Gordon value is a bond-like sum of cash flows, so it has a duration. Differentiating with respect to $r$ gives the sensitivity.

In words, the percentage fall in a Gordon value for a unit rise in the discount rate equals one over the gap between the required return and growth.

At $r = 8\%$ and $g = 4\%$ the equity duration is 25 years, three times the duration of a 10-year Treasury in Chapter 8. A one-point rise in $r$ cuts the value by −20.0 %; a one-point fall raises it by +33.3 %. The two moves differ in size because equity, like a bond, has convexity. This is the arithmetic behind the claim that long-duration growth stocks suffer most when rates rise, as they did in 2022.

Justified P/E and the earnings yield

If a company pays out a fraction $b$ of its earnings, then $D_1 = b E_1$, and dividing the Gordon formula by $E_1$ gives the P/E the model justifies.

In words, a justified forward P/E equals the payout ratio divided by the gap between the required return and growth.

With half of earnings paid out, $r = 8\%$ and $g = 4\%$, the justified P/E is 12.5. A P/E of 20 corresponds to an earnings yield of 5.0 %; when that yield sits far below bond yields, buyers are counting on growth to close the gap.

Growth, ROIC and the value of a moat

Growth costs money. To grow earnings at $g$, a company must reinvest a share $g / \text{ROIC}$ of its earnings, and only the rest can be paid out. Substituting that payout into the Gordon model gives the value of growth.

In words, a firm's value equals next year's earnings, less the share it must reinvest to grow, divided by the gap between the required return and growth.

The cost of capital

The WACC blends the cost of equity $r_E$ and the after-tax cost of debt $r_D(1 - t)$ by their weights in the company's financing.

In words, the weighted average cost of capital is the cost of equity times the equity share plus the after-tax cost of debt times the debt share.

The return a price implies

Rearranging the Gordon formula gives the long-run return a buyer can expect at today's price: the dividend yield plus growth. Applied to the whole market with Shiller's numbers, and using real dividend growth of 1.2 % a year (the 1871 to 1999 average) for $g$, the implied real return was 2.4 % in December 1999 and 4.8 % in March 2009.

In words, the return a buyer can expect over the long run equals the dividend yield plus the growth rate of dividends.

The two estimates are crude. Since the 1980s buybacks have replaced part of the dividend, so the dividend yield understates the payout, and a fuller version adds the net buyback yield. Even so, the gap between the two dates, more than two points of expected return a year, matches the direction of what followed. An investor who demanded the historical real return of about 6.5 % could see in 1999 that the market offered much less.

A five-year discounted cash flow

A DCF forecasts free cash flow year by year for a few years, then puts a single terminal value on everything after.

In words, the value of a business equals each forecast year's free cash flow discounted at the WACC, plus a terminal value for the years beyond, itself a Gordon value discounted back from the end of the forecast.

Buybacks and earnings per share

Take a company with $1bn of earnings and 100 million shares trading at a P/E of 20, so a share costs $200. If it spends the whole $1bn on a buyback, it retires 5 million shares, and earnings per share rise from $10.00 to $10.53, a gain of +5.3 %. That gain equals what a 5 % dividend would have paid. EPS growth from buybacks is real per share, and it comes from shrinking the company; analysts separate it from growth in the business itself.

Level 4 History, analysed

For readers who want past episodes run through the Level 3 math.

1929 to 1932: the deepest fall

Valuation explains the start and the end of the fall. In September 1929 the S&P Composite's CAPE was 32.6, high for the time, and the following ten years returned −1.4 % a year after inflation. By June 1932 the CAPE had fallen to 5.6, an earnings yield above 17 %, and the following decade returned +9.7 % a year in real terms. In between, earnings and dividends collapsed with the economy, the money supply shrank and banks failed. A cheap market can keep getting cheaper while the economy contracts, and the gain-to-recover arithmetic shows why depth matters so much: a 50 % loss needs a +100 % gain; an 89 % loss needs more than eight times the money back.

1999 to 2002: the technology bubble

The broad market was dear too. In December 1999 the S&P Composite's CAPE reached 44.2, the highest in Shiller's data from 1881, an earnings yield of 2.3 %. The dividend yield stood at 1.17 %.

We can ask what growth that price assumed, with the Gordon model turned around: $g = r - D_1/P_0$. If investors wanted a real return of 6.5 % a year, near the long-run real return of US stocks, the dividend yield of 1.17 % required real dividend growth of 5.3 % a year forever. Real dividends of the S&P Composite had grown about 1.2 % a year from 1871 to 1999 (Shiller). Either growth would run four times faster than its long history, or investors would earn far less than 6.5 %. The second happened: the ten years from December 1999 returned −3.2 % a year after inflation.

Buybacks narrow the gap somewhat, since part of the payout no longer came as dividends, yet no plausible buyback yield closes a gap of four points. What surprised us when we ran these numbers is how plainly the 1999 price showed the problem with nothing more than a dividend yield and a long-run growth rate.

2009: earnings collapse, and why CAPE averages ten years

Trailing reported earnings tell a very different story at the same date. From October 2007 to March 2009 they fell from $74.46 to $6.86 per index unit, a drop of −91 %, as banks and insurers wrote off huge losses. On those earnings the market's P/E in March 2009 was about 110, a reading that made the market look absurdly expensive at one of its cheapest moments. CAPE's ten-year average looks through that collapse, which is the reason Shiller built it that way.

What the three cases share

All three episodes fit the Gordon relation between price, payout and growth. At the tops of 1929 and 1999, prices assumed growth far above anything in the history of earnings and dividends; at the bottoms of 1932 and 2009, prices assumed that profits would stay depressed for years. CAPE caught both extremes. It would have been a poor timing tool: CAPE was already above 30 in 1997, two years and a large gain before the peak, and markets can stay dear for a long time. Its value lies in the ten-year horizon, where the starting multiple has explained a large share of the variation in real returns.

The DCF example of Level 3 helps explain why prices at tops and bottoms move so far. Most of a stock's value sits in the terminal value, years away, and the terminal value depends on the gap between the discount rate and growth. When investors feel sure of fast growth and accept low returns, that gap narrows and prices soar; when fear returns, the gap widens and prices fall faster than profits. Nothing in the businesses needs to change for the market's value to halve.

The CAPE readings of 1966 add a less famous case. At 24.1 the market did not look extreme, yet with inflation rising through the 1970s the next decade returned −1.8 % a year after inflation. The discount rate rose as inflation rose, and the multiple fell, the same equity-duration arithmetic that hit growth stocks in 2022.