How stocks work: shares, profit and price

A company's money goes out in an order, and the order is not a matter of goodwill. Suppliers and employees are paid because they hold contracts. Interest and repayments go to lenders and bondholders because they hold contracts too. Tax is assessed on the profit that survives the interest, though not on what survives the repayment of principal, which is a use of profit rather than a cost of earning it. Preferred shareholders, where a company has them, rank next: no ordinary dividend is paid until theirs has been, though a board can choose to skip both. Only then does anything reach the ordinary shareholder, and what reaches them is whatever remains.

That remainder is the residual, and a share is a claim on it. Nothing about it is promised. A bond states a coupon, a date and an amount. A share states none of the three: no maturity, no schedule, no guaranteed size.

Being last changes how much the claim moves. Many of the claims in front are fixed in the short run, so a change in revenue lands disproportionately on the end of the queue. Index a base year's revenue at 100 and hold the cost structure still:

A 10 percent move in revenue becomes a 42.5 percent move in the residual, and it is 42.5 percent whichever way revenue goes: the amplification is even, not a bias toward bad news. That is operating leverage stacked on financial leverage, since the fixed block above holds operating costs and interest together. It is one reason a share price swings further than the sales of the business behind it. The other is that the price of a dollar of profit moves as well, which the sections below take up.

One asymmetry sits at the bottom. A holder of shares in a limited company can lose everything paid for them and no more: the residual stops at zero rather than turning into a bill for the company's unpaid debts. Downside is capped at the stake. Upside is not capped at all.

A dollar of profit goes to exactly one of two places. It leaves as a dividend, or it stays inside as retained earnings and pays for inventory, equipment, hiring, acquisitions or debt repayment. A buyback is the first route in different clothes: the company buys some of its own shares, so remaining holders own a larger fraction of the same business.

A dividend is not new money arriving on top of a holding. When a share goes ex-dividend the price drops by roughly the dividend, and not because the cash has left the building, which happens later on the payment date. It drops because a buyer from that morning onward no longer receives it. The holder is not richer at the moment of payment: the same value has moved from the company's account into theirs. What it does is convert an uncertain future claim into cash in hand today, which is a service rather than a return.

A bond does the same thing to its own price when it goes ex-coupon, so the price drop is not what separates the two. What separates them is that the coupon is promised and the dividend is not.

So the question is never whether a company pays a dividend. It is what the company earns on a dollar it keeps against what the holder could earn elsewhere at comparable risk. A business reinvesting at 12 percent while its holders can earn 7 percent on equally risky alternatives creates value by keeping the money. Swap the rates and it destroys value. The worked examples put ten years and $1,000 through both cases.

Total return, what a shareholder actually got, is the price change plus the dividends received, and quoting either half alone misreads a company with an unusual payout policy. In the United States, dividends paid into a taxable account are generally taxed in the year they arrive, while a gain on an unsold share is not taxed until you sell. Rates and thresholds are set by law and revised over time, so the durable point is the timing difference, which is what tax-advantaged accounts are built to change.

A price is not a record of what a company owns. It is what the market currently pays for a claim on the cash that share is expected to produce, discounted for time and for risk.

$$P_0 = \sum_{t=1}^{\infty} \frac{C_t}{(1+r)^t}$$

Here $C_t$ is the cash expected to reach the shareholder in period $t$, and $r$ is the return demanded for waiting and for bearing the uncertainty. If that cash is expected to grow at a steady rate $g$ below $r$, the sum collapses to $P_0 = C_1 / (r - g)$, which is enough to show the three things a price is made of: expected cash, its growth, and the discount rate.

Two of those three are not about the company at all. When interest rates rise, or investors demand more compensation for risk, $r$ rises and prices fall across companies whose results have not changed by a cent. That is why whole markets move together on days with no company news, and why the yield curve turns up in conversations about shares.

Multiples compress the same statement into one number. The price-to-earnings ratio is price divided by earnings per share, so it says how many dollars the market pays for a dollar of current profit. A high multiple is a claim about future growth and required return, not a verdict on the past. Market capitalisation is price times shares outstanding, which applies the price of the last small parcel traded to every share at once. That is the market's valuation of the whole residual claim rather than a sum anyone has paid, and a buyer of the entire company would normally have to pay more than it for control.

Book value is the other number people reach for, and it answers a different question. It records what the assets cost less what is owed, so it looks backward while a price looks forward. The gap between them is widest where the value sits in things an accountant never recorded: brands, research, and the habits of customers.

Ownership is a fraction rather than a fixed quantity: shares held divided by shares outstanding. The denominator moves. New shares appear when a company raises capital, pays staff in stock, converts debt into equity, or has options exercised against it. Every one of those cuts the percentage an existing share represents. A holder's own percentage is a further step: it falls too, unless the new shares are offered to existing holders in proportion and the holder takes the entitlement up in full, which leaves that holder exactly where they were.

What it does to value per share is a separate question with a different answer. If a company issues shares at what they are worth and puts the cash to work at the return investors were already demanding, the pie grows by exactly what each slice gives up, and nobody is worse off per share. If it issues them cheaply, or spends the proceeds on something that earns less than the required return, value moves from the holders who were there to the ones who just arrived. Dilution of ownership is automatic. Dilution of value is a decision.

One thing to separate out: buying a share on an exchange sends money to the previous owner, not to the company. Only a new issue puts cash into the business, which is why share issues rather than daily trading are the thing to watch here.

All of which is why per-share figures are the ones a shareholder owns. Total profit is the company's performance; profit per share is yours. The worked examples follow a company whose profit rose from $40 million to $60 million in five years, compounding at 8.45 percent a year, while its share count rose from 10 million to 15 million. The count grew by the same multiple over the same span, so it compounded at the same rate, and the two cancelled exactly. Profit per share finished at $4.00, where it started. With no new shares it would have reached $6.00.

A price already contains what the market expects. That is what makes it a price. So a shareholder's return does not come from a company performing well; it comes from the company performing differently from what the price assumed.

Take a company whose earnings per share tripled from $2.00 to $6.00 in eight years, which is 14.72 percent a year compounded. A strong run by any standard. Now the share: it started at $60, which was 30 times earnings, and ended at $90, which was 15 times. The holder earned 5.20 percent a year, and since the company paid no dividend, that is the entire return.

Nothing went wrong at the company. What changed was the price of a dollar of its earnings. Price is the product of two things:

$$\text{price} = \text{earnings per share} \times \text{multiple}$$

so their growth rates multiply as well. Earnings compounded at a factor of 1.147203 a year and the multiple at 0.917004, a decline of about 8.3 percent a year, and $1.147203 \times 0.917004 = 1.051990$. Close to two thirds of the earnings growth was absorbed by the market repricing each dollar of those earnings.

The same arithmetic runs the other way. A business growing at 3 percent that the market had priced for decline can hand its holders a strong return when the multiple expands, without ever becoming admirable. This is the gap between a company and its shares, and it is why whether this is a good company and whether this share is priced well are two questions rather than one. It is also why beating a market average, without simply carrying more risk than the market carries, means being right about something the price does not already hold, which is the subject of index funds against active management. Put both growth rates through the CAGR calculator above to see the gap.

A share carries three things: a vote on matters put to shareholders, the residual claim, and the right to sell to somebody else. It does not carry a claim on any particular asset, a right to direct what the company spends, or a date on which money comes back. Even the vote is not uniform, since some companies issue classes of stock with different voting rights, which lets founders keep control while holding a minority of the economic claim.

The shape of the residual claim also decides what a portfolio of individual companies does. A share cannot fall below zero but it can rise several times over, which is enough to tilt long-run outcomes across individual companies to the right. How far they tilt is a question for the record rather than for the reasoning, and in the long-run record of listed shares the tilt has been pronounced: the typical company has returned less than the average company, with the average pulled up by a small number of very large winners. Where that holds, missing the few winners costs more than avoiding the failures saves.

That is an argument about spread rather than about picking, and it is a separate argument from the usual one. Holding many companies pulls a result toward the average rather than the median, which is what the skew makes worth doing. Separately, and by a different mechanism, holdings whose bad years do not all arrive together cancel part of each other's movement, which is why company-specific risk shrinks as holdings are added while market-wide risk does not. Both sit behind diversification. What is left after that is the risk a market pays you to carry, which is the subject of risk and return.

None of this makes a share a lottery ticket or a savings account. It leaves it as what it was at the start: the last claim in the queue on a real business, priced today for what the market believes that business will produce.