3. Three worked cases with numbers

Level 3: Reverse valuation

Time to apply the procedure three times to three profiles that demand very different things. The mechanics are always the same; what changes is where the delicate point sits in each one.

House rule: round, invented figures

Before we start, a warning that is meant seriously. All three cases are teaching examples with rounded, invented figures. They do not correspond to any particular company, they are not real data and they must not be read as an opinion on any listed stock. They are built so that the arithmetic comes out clean and the mechanism is visible. As soon as you work with real data the numbers will be ugly and the conclusions blurrier: that is normal and it does not invalidate the method.

Case 1: the large-cap mature company

Market capitalization 120,000 million, net debt 20,000, so enterprise value 140,000. Sales 90,000 million, after-tax operating margin 9%, cost of capital 7%, incremental investment of 20 cents per euro of new sales.

After-tax operating profit is 90,000 times 0.09, that is 8,100 million. The no-growth value is 8,100 divided by 0.07: 115,700 million. Since the price is 140,000, the expectation to be justified is 24,300 million, barely 17% of the price.

Each euro of new sales leaves 9 cents, which at 7% is worth 1.286 euros; less the 20 cents of investment, that leaves 1.09 euros of value created per euro of sales. The 24,300 million divided by 1.09 gives some 22,300 million of additional sales: going from 90,000 to 112,300, 25% more. Spread over ten years, 2.3% a year.

The reading: the price is not asking for a miracle. It is asking the company to grow at the pace of the economy without losing margin. The relevant question is not whether it can grow, but whether it can hold the 9%.

Case 2: the growth company on a high multiple

Market capitalization 60,000 million, cash of 5,000 and no debt, so enterprise value 55,000. Sales 4,000 million, after-tax operating margin 5%, cost of capital 9%.

Current profit is 200 million. The no-growth value is 200 divided by 0.09: 2,200 million. Against a price of 55,000, that means 96% of the price rests on results that do not yet exist. That is not a criticism, it is a description: whoever buys here is buying almost nothing but the future.

To solve it you have to fix a horizon. Assume ten years, and assume that over that time the company reinvests everything it earns, so that today's price has to be justified entirely by what it is worth in year ten. At 9%, 55,000 million today is equivalent to 130,200 million ten years out. To be worth that without creating any further value, after-tax operating profit in year ten has to be 130,200 times 0.09, that is 11,700 million.

Now the frontier. With a final margin of 20%, you need 58,600 million of sales: 14.6 times the current figure, which means growing at 31% a year for ten years. With a margin of 30%, you need 39,000 million of sales: 9.8 times, or 26% a year. With a margin of 12%, you need 97,500 million: 24.4 times, or 38% a year.

The reading: the price demands both that sales multiply tenfold or fifteenfold and that the margin goes from 5% to four or six times that figure. Those two things usually pull in opposite directions, because taking market share quickly is paid for in margin. That is the delicate point of this case.

Case 3: the cyclical

Market capitalization 12,000 million, net debt 3,000, so enterprise value 15,000. Sales 20,000 million. The after-tax operating margin has swung between 1% and 12% over the past decade and is now at 12%. Cost of capital, 9%.

If you use today's margin, profit is 2,400 million and the no-growth value comes out at 2,400 divided by 0.09: 26,700 million. Since the price is 15,000, it would look as though the company trades 44% below what it would be worth frozen. An outrageous bargain.

It is not. That calculation assumes the peak margin lasts for ever, and the definition of a cyclical is precisely that it does not. Do it again with a normalized margin of 5%: profit becomes 1,000 million and the no-growth value 11,100 million. Now there are 3,900 million left to justify. With incremental investment of 30 cents per euro, each new euro leaves 5 cents which at 9% are worth 0.56, less 0.30, leaving 26 cents of value per euro of sales. The 3,900 million divided by 0.26 require some 15,000 million of additional sales: 75% more, or 5.8% a year for ten years.

There is another way of saying the same thing, and it is the more useful one. To be worth 15,000 without growing at all, profit would have to be 1,350 million, that is a margin of 6.75% sustained for ever. That is the real content of the price: neither the 12% of the peak nor the 1% of the trough, but a mid-to-high point of the cycle held indefinitely.

The three of them, side by side

Lined up, the comparison reads at a glance:

• The mature company has 83% of its price already covered by what it earns today and asks for 2.3% a year. Its delicate point is the 9% margin, not growth.
• The growth company has 96% of its price up in the air and asks for 31% a year together with a margin that quadruples. Its delicate point is that the two demands get in each other's way.
• The cyclical looks like a giveaway on today's margin and expensive on the trough margin. Its delicate point is neither growth nor the multiple: it is deciding what a normal year looks like.

The mature company's price asks for continuity. The growth company's asks for a double, simultaneous transformation. The cyclical's does not ask for spectacular growth: it asks for a definition. Three prices, three different questions, and exactly the same procedure to get to them.