1. How to work out what the market is assuming

Level 3: Reverse valuation

Conventional valuation works like this: you project a company's future, bring it back to the present and get a number; then you compare that number with the price and decide. The problem is that the number depends entirely on assumptions you chose yourself, and that you almost always end up choosing so that the result confirms what you already thought before you opened the spreadsheet. Rappaport and Mauboussin proposed reversing the order of the operation. That shift, which looks like a matter of nuance, is the heart of this course.

Turning the question around

Instead of asking what the company is worth, you ask: given the price on the screen today, what combination of future results would justify it exactly. The price stops being the thing you compare against and becomes your starting data. What you solve for is the assumption.

The change is not cosmetic, for two reasons:

• It removes the most fragile part of the process. You no longer have to get the future right. You only have to judge whether the future the price takes for granted is reasonable, which is a far humbler task and far easier to do well.
• It turns an opinion into a claim that can be argued with. 'It looks expensive to me' is not something anyone can debate. 'The price requires growth of 12% a year for a decade while holding the current margin' is: you can test it against the size of the market, against what competitors are doing and against what the company itself has managed before.

The three ingredients you have to fix before solving

Before touching a single number you need three explicit decisions. They are not guessed at along the way: they are declared.

• The full price. What the market pays for the business is not the market capitalization but the enterprise value: market cap plus financial debt minus cash. The business generates cash flows for everyone who funds it, not just for the shareholder.
• The cost of capital. This is the bar: the minimum return an investor demands for putting money into that particular risk. You do not need it accurate to the decimal, but you do need it written down, because the whole of the implied demand hangs on it.
• The starting position. Last year's sales, the after-tax operating margin and, very importantly, the incremental investment: how many cents of capital you have to put in for every euro of new sales. Without that figure growth looks free, and it never is.

The procedure, in five steps

First, work out the no-growth value: what the company would be worth if it never grew, dividing after-tax operating profit by the cost of capital. Second, subtract that value from the price; what is left is the slice of the price that is pure expectation. Third, find out how much value each euro of new sales creates: divide the margin by the cost of capital and subtract the incremental investment. Fourth, divide the expectation slice by that value per euro; you get the additional sales required. Fifth, spread those sales over a reasonable horizon and turn them into an annual rate.

It is a rough calculation, and it is worth saying so out loud: it ignores the fact that new sales take time to arrive and are therefore worth less. Once you discount them properly, the real demand goes up. The approximation is there for the order of magnitude, which is what decides.

You do not get a number: you get a frontier

Here lies the power of the method, and also the trap that catches the people who apply it badly. Solving does not give you an answer, it gives you a frontier of combinations: infinitely many pairs of growth and margin that produce exactly the same price. A high margin with modest growth and a mediocre margin with ferocious growth can be worth the same.

That is why the right question is never 'how much is it worth?', but 'is any point on that frontier credible?'. And that is why two honest analysts can arrive at different figures without either of them being wrong: they have picked different points on the same frontier.

A worked case: what a price of 60 euros demands

A teaching example with rounded figures, not a real company. The share trades at 60 euros, there are 1,000 million shares and net debt is 5,000 million: enterprise value is 65,000 million. Sales are 32,500 million, the after-tax operating margin is 10%, the cost of capital is 8% and incremental investment is 25 cents per euro of new sales.

Step one: after-tax operating profit is 32,500 times 0.10, that is 3,250 million. Divided by 0.08, the no-growth value is 40,600 million.

Step two: 65,000 minus 40,600 leaves 24,400 million of pure expectation, 37.5% of the price.

Step three: each euro of new sales leaves 10 cents of profit, which capitalized at 8% is worth 1.25 euros; less the 25 cents you have to invest, exactly 1.00 euro of created value per euro of sales remains.

Step four: 24,400 divided by 1.00 is 24,400 million of additional sales. Sales have to go from 32,500 to 56,900, 75% more.

Step five: spread over ten years, that is growing at 5.8% a year. Discount it properly and the demand rises to more like 7%.

Now the frontier. If the margin rose to 12%, the no-growth value would be 48,750, 16,250 would be missing, each new euro would be worth 1.25 and 13,000 million of extra sales would be enough: 40% more, or 3.4% a year. If the margin fell to 8%, the no-growth value would be 32,500, another 32,500 would be missing, each new euro would be worth 0.75 and 43,300 million of extra sales would be needed: 133% more, or 8.8% a year.

Three points on the same frontier, a single price. The question is no longer what the company is worth. It is whether you believe in any of those three futures.