Where you are. Last lesson put the two doors on a balance sheet: equity buys a residual slice with no promise attached, debt buys a promise and ranks ahead of it. This lesson walks through the equity door and asks the obvious follow-up question, which is what the slice actually gets you. The answer is arithmetic, and so is most of the vocabulary built on top of it.
Ten shares out of a hundred
A workshop has issued a hundred shares. The founders hold seventy, an early investor holds twenty, and you hold ten, bought last year.
Nobody has given you anything since. No cheque has arrived. Your ten shares sat in an account and did nothing at all, which is the normal condition of a share and worth sitting with for a moment: the claim exists whether or not it pays this year.
Then the workshop has a good year and the directors decide to distribute fifty of profit to the owners. Your ten shares out of a hundred are a tenth of the company, so five of that fifty is yours. Not because anyone negotiated it, and not because you asked; the slice decides, and the slice is arithmetic.
The idea in one paragraph
A share is a fractional claim on what a company has left after everyone else is paid, and every number quoted about shares is that fraction, multiplied by something. Multiply the fraction by a distribution and you get your dividend. Multiply the price of one share by the number of shares and you get what the market thinks the whole company is worth. Divide the company’s profit by the shares outstanding and you get profit per share, which lets holdings of different sizes be compared. Divide the price by that and you get how many years of current profit the market is paying for. None of this is deep, and all of it is worth being fluent in, because the same arithmetic is what dilution quietly changes when new shares are issued.
What the slice is worth
Market capitalisation is the most quoted number in equities and the most casually misread. It is not what the company would fetch if sold, and it is certainly not cash in anyone’s hand. It is the last traded price for one small slice, multiplied out as though every remaining slice could be sold at that same price, which they could not.
Two more numbers follow the same shape. Earnings per share is the company’s profit divided by the shares outstanding, so that a holder of ten shares can multiply by ten and see their portion of the year’s profit. The price-to-earnings ratio is one share’s price divided by that per-share profit, and it answers a single question: how many years of profit, at today’s rate, is the market paying for a share? A high number means the market expects the profit to grow, or is wrong, and telling those apart is what equity investing is.
What the slice pays
A dividend is the company handing profit back to its owners, split by the slice. In the exercise, fifty is distributed across a hundred shares: the founders take thirty-five, the early investor ten, and you five. The three payments sum to exactly fifty, and the company is exactly fifty poorer.
That is worth watching on the ledger rather than taking on faith, which is why the exercise settles the payments through the miniledger instead of just printing numbers. Money leaves the firm’s account and arrives in three others; the total across all accounts is unchanged. A dividend moves money, it does not create any. The company is smaller afterwards by precisely what the owners are richer by.
The one that catches people
Suppose the workshop issues a hundred more shares to raise money. You still hold ten. But there are two hundred shares now, so your claim has gone from a tenth of the company to a twentieth. The next fifty of dividends pays you two and a half, not five.
Nobody took anything from your account. Your holding was not touched. The denominator moved.
Check yourself
1. A company’s market capitalisation is one billion. Explain why that is not what the company would sell for.
Because it is one small trade’s price multiplied out across every share as though all of them could be sold at that price. In an actual sale the buyer must persuade every holder, including those who will not sell at that price, which is why acquisitions are usually agreed at a premium. Market cap is a price extrapolated, not a valuation performed.
2. Two companies both earn 100 of profit. One trades at a price-to-earnings ratio of 8, the other at 40. What is the market saying, and what could it be getting wrong?
It is paying eight years of current profit for one and forty for the other, which is a statement that the second company’s profit is expected to grow much faster, or be much more durable, or both. It could be wrong in either direction: the growth may not arrive, or the cheap one may be cheap because its profit is about to fall. The ratio is a question, not an answer.
3. You hold ten shares of a hundred. The company issues a hundred more and uses the money to buy a second workshop that doubles its profits. Are you better or worse off?
Your fraction halved, from a tenth to a twentieth, and the profit doubled, so your share of profit is roughly unchanged. Whether you are better off depends on what the doubled profit is worth against what the halved fraction gave up, which is a judgement about price, not arithmetic. What is certain is that the dilution alone is not the answer.
4. The dividend moved money from the firm’s account to three holders’ accounts. Why does the total across all four accounts stay the same, and what would it mean if it did not?
Because a dividend is a transfer, not a creation: every credit to a holder is a debit to the firm, exactly as module 1 taught for any payment. If the total moved, a posting went in without its pair, and the ledger’s own invariants would refuse it. Distributions are constrained by the same double-entry discipline as everything else in this course.
Do this
Compute the entitlements, pay the dividend through the ledger, and prove nothing was conjured.
python3 code/share_slice.pyThe starter leaves you dividend_split, which returns each holder’s share of the distribution in proportion to their holding. The assertions check the split sums to exactly the dividend, that the three payments settle through the miniledger, and that total money across every account is unchanged. Success prints each holder’s fraction and payout, and the line:
the slice decides everything: your tenth of the firm is a tenth of the payout, and the firm is 50 poorer either wayThe completed version is in solutions/share_slice.py.
What you can now do. You can take a holding and say what it entitles you to, in votes, in dividends and in a wind-up, and you can compute the numbers quoted around it without treating any of them as magic. You can also say precisely what dilution does and does not take. The next lesson asks a question this one quietly assumed: your ten shares are recorded somewhere, and it is not where you think.