Quantification

QUANTIFICATION

To talk sense, is to talk in quantities. It is no use saying that the nation is large,

• How large? It is no use saying that radium is scarce, - How scarce?

-Alfred North Whitehead (from The Aims of Education)

Quantification helps us compare magnitudes, understand relationships, and check whether the consequences of our assumptions make sense. And math is stable. Two plus two is four was true 1 million years ago and will be true 1 million years from today.

When we translate something into numbers we can make comparisons. A relevant yardstick makes the comparison clearer, even when some important considerations cannot be expressed as numbers.

Some things can't be measured exactly, so estimating a range is the next best alternative.

"It is better to be roughly right than precisely wrong," said J.M. Keynes. Don't overweigh what can be counted and underweigh what cannot. Beware of false concreteness - often we believe that data based on figures with lots of decimal places are more accurate than words alone. Charles Munger says:

You've got a complex system, and it spews out a lot of wonderful numbers that enable you to measure some factors. But there are other factors that are terribly important and there's no precise numbering you can put to these factors. You know they're important but you don't have the numbers. Well, practically everybody overweighs the stuff that can be numbered, because it yields to the statistical techniques they're taught in academia, and doesn't mix in the hard-to-measure stuff that may be more important.

Let's illustrate the importance of quantification with examples from the world of business and investing.

How much capital is needed to produce a dollar of cash flow?

Does return on invested capital make a difference? Assume two businesses - X and Y - generate the same cash earnings of $10 million and "perpetual" growth of 5%. The difference lies in how much capital they use to produce these earnings. X needs $100 million and Y $40 million. This means that their return on invested capital is 10% and 25%, respectively. This also means that they differ in the free cash flow (after reinvesting) or distributable cash they generate. X generates

$5 million and Y $8 million. Return on invested capital makes a difference in value.

	Business X	Business Y
Invested capital	100	40
Cash earnings before reinvestment	10	10
Reinvested capital	-5	-2
Return on reinvested capital	10%	25%
Available cash flow for distribution	5	8
Value at 10% discount rate	100 (5/(0.1-0.05))	160

Warren Buffett describes what businesses are best to own:

Leaving the question of price aside, the best business to own is one that over an extended period can employ large amounts of incremental capital at very high rates of return. The worst business to own is one that must, or will, do the opposite - that is, consistently employ ever-greater amounts of capital at very low rates of return.

Should higher earnings automatically impress us?

Warren Buffett gives an example from one of Berkshire's subsidiaries:

While an increase in earnings from $8 million to $72 million sounds terrific - and usually is -you should not automatically assume that to be the case. You must first make sure that earnings were not depressed in the base year. If they were instead substantial in relation to capital employed, an even more important point must be examined: how much additional capital was required to produce the additional earnings?

We need to understand what is behind the numbers. Warren Buffett says that, "return on beginning equity capital" is "the most appropriate measure of single year managerial performance. Informed use of that yardstick, however, requires, an understanding of many factors, including accounting policies, historical carrying values of assets, financial leverage, and industry conditions."

The account emphasizes the long-run return that the underlying business produces on its invested capital over time. Charles Munger says:

Over the long term, it's hard for a stock to earn a much better return than the business which underlies it earns. If the business earns 6% on capital over 40 years and you hold it for that 40 years, you're not going to make much different than a 6% return - even if you originally buy it at a huge discount. Conversely, if a business earns 18% on capital over 20 or 30 years, even if you pay an expensive looking price, you'll end up with a fine result.

Sustaining returns of 20% or more on invested capital while reinvesting most earnings for a decade or longer is demanding. Competition, customer behavior, and other conditions can change, so a valuation should not simply assume that such returns persist.

Warren Buffett reveals the limits of earnings growth and how lofty predictions lead to dumb behavior:

Examine the record of, say, the 200 highest earning companies from 1970 or 1980 and tabulate how many have increased per-share earnings by 15% annually since those dates. You will find that only a handful have. I would wager you a very significant sum that fewer than 10 of the 200 most profitable companies in 2000 will attain 15% annual growth in earnings-per-share over the next 20 years.

He continues:

Finally, be suspicious of companies that trumpet earnings projections and growth expectations. Businesses seldom operate in a tranquil, no-surprise environment, and earnings simply don't advance smoothly (except, of course, in the offering books of investment bankers).

Charlie and I not only don't know today what our businesses will earn next year - we don't even know what they will earn next quarter. We are suspicious of those CEOs who regularly claim they do know the future - and we become downright incredulous if they consistently reach their declared targets. Managers that always promise to "make the numbers" will at some point be tempted to make up the numbers.

Suddenly demand goes down and price competition rises.

How does a change in growth rate change business value? Business value is a function of the amount and timing of future cash flows. If expected cash flows decrease or arrive later, business value declines.

Warren Buffett illustrates how valuations must change when growth expectations are revised:

A few years ago the conventional wisdom held that a newspaper, television or magazine property would forever increase its earnings at 6% or so annually and would do so without the employment of additional capital for the reason that depreciation charges would roughly match capital expenditures and working capital requirements would be minor. Therefore, reported earnings (before amortization of intangibles) were also freely distributable earnings, which meant that ownership of a media property could be construed as akin to owning a perpetual annuity set to grow at 6% a year. Say, next, that a discount rate of 10% was used to determine the present value of that earnings stream. One could then calculate that it was appropriate to pay a whopping $25 million for a property with current after-tax earnings of $1 million (1/0.1-0.06).

Now change the assumption and posit that the $1 million represents "normal earning power" and that earnings will bob around this figure cyclically. A "bob-around" pattern is indeed the lot of most businesses, whose income stream grows only if their owners are willing to commit more capital (usually in the form of retained earnings). Under our revised assumption, $1 million of earnings, discounted by the same 10%, translates to a

$10 million valuation. Thus a seemingly modest shift in assumptions reduces the property's valuation to 10 times after-tax earnings.

Do we pay the same price for a business financed with debt as for a business with no debt?

The following simplified example holds operating cash flow and the unlevered valuation fixed. It illustrates accounting for debt and excess cash; it does not establish a universal equity discount rate after leverage changes. Assume Mary is interested in buying a furniture store. The business is stable with no growth, free cash flow of 15 and financed with 75 in equity. A price of 100 (15/0.15) will give her a 15% return. Does debt make a difference? Yes, the seller could then make extra money by leveraging the business before selling it. If the seller refinances the business with 50 in debt (and the business can borrow at 6% interest) and withdraws 50 as a dividend, income after interest would be 12 (15-3). If Mary then buys the store for 80 (12/0.15) the seller would have made an extra 30 (50+80-

100. without any change in the underlying operations of the business.

Instead Mary should assume she acquires a debt-free business and adjust for 50 of debt and pay 50 (15/0.15-50). She should also correct (add to the price) for excess cash - cash or cash assets that aren't needed to conduct the business.

This is the same type of reasoning as when we buy a house. If we for example

buy a house for $500,000 and put in $200,000 of our own saved money and mortgage the rest or $300,000, the price of the house is still $500,000.

"The synergies we expected from the merger never materialized They were mere illusions. "

Don't forget to quantify consequences when making acquisitions. Take the profit & loss statement and balance sheet of the acquiring company and the target company. Calculate what happens with volume, prices, cost, and invested capital when the companies combine, considering consequences and behavioral changes of employees, suppliers, customers, and competition. How does business value change? Be realistic. Studies show that most mergers fail to generate value for the acquiring company's owners. The main reason is that the buyer paid too much for synergies that weren't real.

"Of one thing, however, be certain," says Warren Buffett, "If a CEO is enthused about a particularly foolish acquisition, both his internal staff and his outside advisors will come up with whatever projections are needed to justify his stance. Only in fairy tales are emperors told they are naked."

John reads the paper. A company announced a $10 million contract and its market capitalization jumped $1 billion.

Does this make sense? If we assume the contract generates a 15% profit margin,

the implied contract profit is $1.5 million; its contribution to business value also depends on timing, costs, and any continuing business. And even a high-margin project can be a loser if it requires a lot of capital and human resources.

If present value is the same for different businesses, does the timing of the dividend matter?

Assume there are 2 different businesses -X and Y -with the following forecasted dividends. After year 5 the two companies close down.

Year	1	2	3	4	5
Dividends from X	10	10	10	10	10
Dividends from Y	0	0	0	0	61

All cash generated by X is each year distributed to its owners. The free cash flow generated by Y is reinvested and not paid out until after the five year period. Discounting at 10%, the present values of the projected dividends from X and Y are both about 38. If X’s dividends can also be reinvested at 10%, they accumulate to about 61 after 5 years; that reinvestment assumption concerns terminal wealth, rather than the present-value calculation itself. Y must generate its projected dividend of 61 after 5 years for that projection to hold. But in both cases the future may turn out different than expected. The business environment may change and competition increase making the dividends from X and Y come out differently from what we expect. The more our calculation depends on cash flows far out in the future, the more opportunities there are for unwanted events, and the more uncertain our expected return.

Do the math!

We can do a simple exercise to test our possible return from investing in a company and if its market valuation makes sense. Work through the assumptions implied by the price.

Below are some examples where we have ignored dividends and options (in reality we need to properly account for options and make sure that the company's accounting reflects reality and the true operational performance.) Think of a stock as part of a business and remember that small changes in assumptions can dramatically change value.

John is thinking of buying 1,000 shares of stock in a public ice cream manufacturer with a market value of $1 billion and no debt or off-balance sheet obligations. How should John reason?

What is my estimated annual rate of return?

John projects the future value, and then compares that value with the present market value of $1 billion. What is his implied annual rate of return? Will the price paid give him an adequate return?

The business has initial cash earnings (earnings+ amortization of goodwill) of

$40 million and an assumed average annual growth rate in cash earnings of 10% for 10 years. This translates into $104 million in cash earnings in year 10. Assume the market pays an average multiple of 15 for this type of business. This implies

$1.56 billion in market value in year 10. If John compares this figure with the present market value, his implied yearly return is 4.5%. John compares this return with the return from other available investment opportunities. A business may have a great track record, but if the math doesn't work, stay away.

What scenario achieves a 15% annual rate of return?

How much must the ice cream manufacturer earn to generate a 15% annual rate of return for John? If the present market value compounds at 15%, what does this imply and is it reasonable?

A present market value of $1 billion and an annual return of 15% imply $4 billion in market value in year 10. This is what $1 billion will grow to in 10 years if it grows 15% per year. An average multiple of 15 implies $270 million in cash earnings in year 10. This translates into an average annual growth rate in cash earnings of 21% (from a base of $40 million). A profit margin of 15% implies

$1.8 billion in sales year 10. He can continue with implied future sales volume, number of users and usage, market share, etc.

John then asks: What causes this future value? What does this imply in numbers today? Is it reasonable regarding evidence of track record in growth, earnings, profit margins, market size/volume growth, market share, competitive advantage, etc? Which factor has the greatest impact on future cash earnings and thereby value? What forces can change this scenario? How can the company lose its advantages?

If the company doesn't make money today, what future free cash flow is implied by their market value if I want a 10% return?

In the midst of the Internet mania, Warren Buffett said:

When we buy a stock, we always think in terms of buying the whole enterprise because it enables us to think as businessmen rather than stock speculators. So let's just take a company that has marvelous prospects, that paying you nothing now where you buy it at a valuation of$500 billion... For example, let's assume that there's only going to be a one year delay before the business starts paying out to you and you want to get a 10% return. If you paid $500 billion, then $55 billion in cash is the amount that it's going to have to

be able to disgorge to you year after year after year. To do that, it has to make perhaps $80 billion, or close to it, pretax. Look around at the universe of businesses in this world and see how many are earning $80 billion pretax - or $70 billion or $60 or $50 or $40 or even

$30 billion. You won't find any.

Whether a business sells nails or telecom equipment, if more money is going out than coming in, on a present value basis, it is worthless. As Warren Buffett says, "Value is destroyed, not created, by any business that loses money over its lifetime, no matter how high its interim valuation may get."

He continues:

There's plenty of magic in short term in rising P/E multiples and the games people play with accounting and so on. But in the end, you can't get more out of a business between now and its extinction than the business makes. And actually you'll make something less depending on who your business managers are, how often there's turnover in the security and how much you pay the investment manager and so on.