1. What you are buying when you pay a price: the list of assumptions that comes with it

Level 1: The price is a forecast

When you buy a share you think you are placing a bet on a company. What you are really doing is accepting as reasonable a list of numbers somebody else has already written for you. A price is not a mood, nor a vague impression of whether the company is doing well or badly. It is a closed calculation, with quantified assumptions about how much it will sell, at what margin, how much capital it will consume to get there, and at what rate all of it is discounted. Learning to read that calculation backwards, instead of building your own from scratch, is the craft Alfred Rappaport and Michael Mauboussin named expectations investing.

A price is not an opinion: it is a closed calculation

The difference between the two ways of looking is one of kind, not of degree. The traditional analyst forecasts: he estimates sales, margins and profits, works out a value and compares it with the price. The problem is obvious the moment you state it: to make money that way you have to forecast better than thousands of professionals who have covered that sector for years, with more data and more access than you have.

The alternative reverses the order. Instead of asking what the company is worth, you ask what would have to happen for today's price to be right, and then judge whether that is achievable. You are not competing on forecasting ability. You are competing on something far more within reach: reading a list of assumptions honestly and deciding whether the world can deliver them.

The levers inside any price

Every price, whether or not the person paying it realizes it, contains these pieces:

• The rate of sales growth, year by year, over a specific number of years.
• The operating margin the company will sustain on those sales.
• The effective tax rate the state will take out of that margin.
• Incremental investment: how many cents of working capital and fixed assets have to go in for every additional euro of sales.
• The cost of capital, that is, the return demanded by whoever puts up the money for bearing that risk.

The first four describe the money coming out of the business; the fifth, what that money is worth today. The mechanics of each lever are covered in the next level. Here it is enough to hold on to something uncomfortable: when somebody says a share is expensive or cheap without being able to name any of these figures, they are not valuing anything, they are feeling something.

The minimum arithmetic: what growth you are paying for

There is one calculation you can do in your head that dismantles half the conversations about the stock market. The value of a cash flow growing at a constant rate for ever is that cash flow divided by the difference between the required return and the growth rate. If you demand 8% a year, the multiple you can pay on next year's free cash flow comes from dividing one by that difference:

• With no growth, eight minus zero: you pay 12.5 times.
• Growing at 3%, eight minus three: you pay 20 times.
• Growing at 5%, eight minus five: you pay 33 times.
• Growing at 6%, eight minus six: you pay 50 times.

Read it backwards and you have your first piece of reverse-engineering. A company trading at 50 times its free cash flow, against a required return of 8%, has growth of 6% a year for ever built into its price, in an economy whose long-run nominal growth is around 4%. Nobody has said that out loud; it is written into the price all the same.

The full exercise, with numbers

Take a company with €10 billion in sales, a 12% operating margin and a 25% tax rate. Its operating profit after tax is €900 million. It has to invest 30 cents for every additional euro of sales.

If it grows 5%, sales rise by €500 million, incremental investment takes 150 of that, and free cash flow comes to €750 million. Discounted at 8% with that perpetual growth rate, the business is worth 750 divided by 0.03: €25 billion.

Now suppose the market prices it at €18 billion. The useful question is not whether your 25 billion is right, but what growth rate it takes to get to 18. Rearranging, the difference between required return and growth has to be 4.17%, so the implied growth rate is around 3.8%. Refining it would mean recalculating the investment at that lower growth rate, and the answer would move by a few tenths; the order of magnitude does not change.

That 3.8% is what you have actually bought. And now the question is no longer philosophical: can this business grow at 3.8% a year indefinitely? That is a question about the world, answerable with what you know about the sector, not a question about your model.

Real case: Cisco, March 2000

In March 2000, Cisco Systems briefly became the most valuable company in the world, with a market cap in the region of $500 billion. Its sales for the 2000 financial year came to around $19 billion and its net profit ran to a few billion. It was, beyond argument, an excellent company: it grew fast, dominated its market and made real money.

Let us do the calculation backwards. If you demand 8% a year, that $500 billion would have to be worth some $1.08 trillion ten years later. Assuming the market valued it then at around 20 times earnings, generous for a mature company, that would take close to $54 billion of annual profit in 2010. Starting from about $3 billion, that means multiplying profit by eighteen: roughly 33% a year sustained for a decade.

That was the assumption being bought by whoever paid that price. You did not need to get the next quarter right to see it. You only needed to write it down. Cisco went on growing over the following twenty-five years, with sales that ended up more than doubling, and even so its share price had still not recovered that peak long afterwards.

The lesson is not that Cisco was a bad company. It is that the price contained a list of assumptions nobody had read out loud, and that turned out to be impossible to meet.