Tuesday, January 12, 2010

DuPont Formula, P/E Game, and BCG Matrix

One of the most useful tools for financial statement analysis, particularly in the beginning stages, is the "DuPont Formula", also known variously as the "DuPont Model" and "Strategic Profit Formula." The DuPont approach---named after the company and used by Alfred Sloan when he was managing General Motors for DuPont---is used to calculate a firm's return on equity (ROE). Today's blog entry will be a walk through the DuPont Formula. The ROE calculation that is the end product will then be used again and again as we get into the theoretical limits of a firm's growth rate (which, given certain controlling assumptions, is ultimately dependent on ROE); a financial game that was quite popular in the 1990s and used to make and lose a great deal of money; and a clever conceptual tool that was developed by the Boston Consulting Group, a prestigious management consultancy, to generate some logical, generic strategies for clients to follow (and was widely imitated by other consulting firms).

Return on Assets
The first inputs into the DuPont Formula concern a company's basic business model, or how it generates profits. There are two components to this: 1) profit margins, or the difference between the sales price and what it costs the company to make the product; and 2) turnover, or the volume of sales.

Margin x Turnover = Return on Assets (ROA)

We can now factor each of these to get inputs that can be found on the company's financial statements:

Margin = Profit after Tax / Sales

Turnover = Sales / Assets

There is normally an inverse relationship between margin and turnover unless the company enjoys a monopolistic position. This is because high profit margins attract competitors, as blood in the water attracts sharks. In order to defend margins, a company typically has to have a very strong brand, patent protection (as a pharmaceutical company would), or both. In essence, the company's products must be differentiated from those of its competitors in order for it to be able to charge a premium. Another strategy that is often attempted is to rapidly create new versions of an existing product line and to add features; this strategy runs the risk of overshooting what customers actually want/are willing to pay for, a problem that is discussed at length in a book called The Innovator's Dilemma.

On the other hand, competition erodes profit margins over time and tends to lead to products becoming more and more similar to each other. The closer they get, the more they start to resemble standardized goods, or commodities. Commodities are a volume business---you become the lowest-cost producer and you charge slim profit margins, which drives competitors out of that business. The money is made by volume, by running the most efficient factories possible.

Sometimes the globally lowest-cost producer can be defeated, at least temporarily. If the product in question has a low-bulk value, then high relative shipping costs can create pockets of opportunity for local producers to succeed. Another technique is to leverage local political capital in order to create a market price distortion---a tariff on foreign products or a subsidy for yourself---that benefits you at the cost of the consumer, who must one way or another pay more than necessary for an identical, protected product. The Florida sugar industry is a good example of how successful lobbying can create a protective price distortion of this type, although there are so many that it is depressing.

One of the most important advances in the creation of the global economy was the standardized shipping container, which dramatically reduced the costs of transportation and allowed countries that produce lower bulk-value goods to compete across oceans and borders. The history of the shipping container and its impact are discussed in a nice book called The Box, by Mark Levinson.

Just off the top of my head, an example of a company that competes on profit margin (Profit after Tax/Sales) would be the high-end jewelry store Tiffany & Co. Tiffany has differentiated itself by the fiery cut of its diamond jewelry and by its prestigious brand name, and this allows the company to work at a high profit margin (as many of us men have learned on a rather visceral level). On the other hand, the stores do not have high turnover---frequently each customer makes multiple non-sale visits to the store before converging on a final purchase decision.

The classic example of a high-turnover business is the grocery store. Grocery stores frequently sell many of the same products, and those products tend to have expiration dates (Tiffany does not have that problem, as we all know that gold does not rust and diamonds are forever). The grocery store model is to find the most popular brands, give them the most convenient/visually effective shelf space, and get product out the door as quickly as possible.

Which is best---nice profit margins or high volume? There is no right answer. Salespeople will tend to say that they like the profit margins, because this gives them flexibility in terms of being able to respond to price wars by offering discounts or having special sales days. Generally speaking, boutique shops are going to seek the margins and try to offer a more luxurious shopping experience, while "big-box" sellers like Walmart and Costco are going to go for turnover and try to run streamlined service operations and no-frills, cavernous warehouse-like stores.

So, we can now say that:

(Profit after Tax / Sales) x (Sales / Assets) = Return on Assets

Return on Equity

Calculating the ROE requires us to find out how many Assets the owners are controlling relative to their own capital contributions. This has another name: leverage. To calculate leverage, we take the Assets and divide them by the Equity (in practice it is a bit more calculated than this, as Assets and Equity are balance sheet, snapshot entries and change over time. Normally the analyst uses the average Assets and average Equity by looking at these values on two consecutive annual reports, adding the Assets and Equity together, and dividing by two).

Leverage = Assets / Equity

A higher leverage ratio means that the firm is borrowing money to juice its return on assets for the shareholders. Usually, but not always, the borrowed money is put into inventory and Property, Plant, and Equipment---factories. When you see high leverage, it normally means high fixed costs, and high fixed costs tend to mean that the company is competing on volume. Thus, normally you will find that high leverage, low profit margins, and high turnover tend to come together in a cluster, but there are exceptions.

So now we have this formula, which simply takes the return on assets from before and multiplies it by the leverage factor:

DuPont Return on Equity = (Profit after Tax / Sales) x (Sales / Assets) x (Assets / Equity)


By process of algebraic substitution, you could find that ROE was the same as just taking Profit after Tax/Equity. The point of the DuPont Formula is to use the exploded detail for a more sophisticated and nuanced analysis of how the business makes profits for its owners.

Because different products and business models create shareholder value in different ways, it normally does little good to compare DuPont Formula inputs among wildly different industries. The best way to use the approach is to look at firms in the same industry.

There are modifications to the DuPont Formula that can take into account the effects of taxes and interest payments by adding two additional, simple factors and using a pre-tax, pre-interest payments input into the profit margins calculation, but I think you get the idea.

The Limits of Growth

If you assume that the firm does not have idle capacity, is operating at its maximum safe leverage ratio, and cannot increase selling prices (to increase profit margins) without hurting sales more than it gains from the higher price, then you find that the way for a company to grow is to buy more production capacity (Assets) so that it can sell more products (Sales). If the leverage ratio must remain constant, then shareholder equity cannot be stretched any further: in order to borrow more money to buy more capacity, the firm must also grow its Equity. Thus, ROE becomes the deciding factor on the firm's ability to grow. The amount that the firm can retain for growth is dictated by its dividend policy---whatever it returns to shareholders as cash it cannot use for internal growth.

The Growth Limit (GL) formula is:

GL = ROE x (1 - Dividend Rate) - Inflation

Let's do a simple worked example. Say that a company has an ROE, which we computed using the DuPont method, of 15%. The firm has a policy of paying out 1/3 of its profits in dividends. Inflation is currently running at 3%.

15% x (2/3) - 3% gives us a growth rate of 7% for this company. Unless it increases its ROE, which involves going back to those DuPont inputs and somehow increasing profit margins, turnover, or leverage (not allowed in our strict example), or changes its dividend policy and pays less (this is normally taken by Wall Street as a very bad sign and the company's share price is punished), or can somehow get the Federal Reserve to ease up on the printing presses, the company cannot grow faster than 7%.

If that figure seems low, consider that very large firms in mature industries generally cannot grow faster than the overall economy for long, and the U.S. economy normally grows at about 3% per year.

The P/E Game

The Growth Limit problem is actually quite irritating for many companies, and so various techniques can be employed to try to defeat it, at least temporarily. In the bull market of the 1990s, a popular approach was the Price-to-Earnings Game.

Here is how this worked: most readers will have heard of the P/E ratio, which looks at the price of a company's shares relative to the earnings that the company generates. High P/E ratios are associated with growth stocks. The heuristic frequently used here says that a company with an ROE of, say, 20%, should have a P/E of 20 (trade at a multiple of 20 of earnings). A company with an ROE of only 10% should have a P/E of 10.

The P/E Game is played when a company with a higher P/E purchases a company that has a lower P/E and uses the new earnings to boost its share price. Let's say that a company with a P/E of 20 purchases a company with a P/E of 10---the earnings of the lower-P/E company now go to a corporate structure that trades at higher P/E, which means that a dollar of earnings that once was associated with $10 of share value is now rewarded with $20 of share value, simply because a more expensive company purchased a less expensive one.

Typically this is not done through Company A making a cash purchase of Company B---share exchanges are the norm, as this is a non-taxable event and thus helps to reduce some of the transaction frictions. The new company sees a sudden increase in earnings, and this in turn can make it seem to deserve an even higher growth rate---perhaps Company A will soon trade at 25 times earnings, or even 30 times earnings. The process may be repeated again.

Unfortunately, the effects seldom last. Normally the reasons why Company B was trading at a lower earnings multiple are not going to change much after it is purchased by Company A, although in the rare case of true synergistic effects it is possible that Company B's earnings will grow at a much faster rate after the acquisition. But it can be a fun game for many to play for awhile, particularly for the fee-collecting M&A advisory team working at Company A's investment bank. The P/E Game was behind a great deal of the M&A mania that we saw in the late 1990s, and most of that activity (perhaps as much as 70%) ultimately ended up destroying shareholder value.

The BCG Matrix

I will close today's entry with a quick note on a 2x2 matrix that MBA students everywhere are familiar with---the BCG Matrix, also known as the "Product-Market Matrix". Here is a picture of it:







The matrix was created by Bruce Henderson, the founder of the Boston Consulting Group, and it does have an elegant, simple logic to it. Here is how it works: on the vertical axis, which depicts the market growth rate, imagine the term "10%" on the line between the Star on the upper left and the Cash Cow on the bottom left. This 10% is what at the time was the normal ROE for a US company, 15%, multiplied by the normal dividend payout ratio, which was 2/3. Inflation was not taken out. Thus, 10% was the average growth rate for a U.S. company; a result greater than 10% put you in the top half of the matrix, a Star or a Question Mark, meaning that you were in a fast-growing market, while a result less than 10% put you in the bottom half of the matrix, a Cash Cow or a Dog, indicating that you were in a mature, slow-growth market.

Now go to the horizontal axis, and imagine a "1" right between the Cash Cow on the bottom left and the sad, loney Dog on the bottom right. Now take the company's market share divided by the market share of its largest competitor. If you do this calculation and get a number greater than 1, you get to go on the left half of the matrix---the Star or the Cash Cow---because it means that you are the largest competitor in your industry. If you get a number lower than 1, it means that you are not the largest competitor and thus will end up in one of the two boxes on the right side of the matrix, the Question Mark or the Dog.

So every company is going to end up in one of the four squares contained within the BCG Matrix, and placement will depend on whether it is in a high or low growth market and whether it has a high or low market share position. Different strategies will emerge depending on your location, and this is why Henderson creates the vivid imagery of Stars, Cash Cows, Question Marks, and Dogs.

Stars are companies that have the leading market share of high-growth industries. They need to be chiefly concerned with protecting their enviable positions, which as we know means protecting profit margins (branding, patents, political protection) and/or increasing turnover (perhaps by buying capacity and locking-in raw materials so that the company can produce at lower rates if it faces a price war).

Cash Cows are market leaders in mature markets that do not have much growth potential left. The strategy for a Cash Cow is to use the profits it generates to try to fund Stars or Question Marks.

Question Marks are companies or products that are not the market leaders, but which are at least operating in fast-growing markets. The normal generic strategy for a Question Mark is quite high-risk: furiously buying capacity in order to try to seize market share from the leader as the demand for the product continues to grow.

Dogs are in the unfortunate position of being the non-leaders in the dying, low-growth markets. Henderson's prescription for the dogs was to "shoot them"---i.e., liquidate and leave those markets.

If 10% represented the average growth rate for a U.S. company, then by definition half of the companies in America are on the bottom half of the BCG Matrix, and are either Cash Cows or Dogs. Cash Cows represent only the small number of market leaders in each industry, so almost half of the companies in America (or at least half of the products) are, following the BCG Matrix's logic to its conclusion, dogs that should be killed. This seems to be just the attitude that "Neutron Jack" Welch had when he was at the helm of General Electric---you were either #1 in your market or you were in trouble.

I would personally recommend taking things like the BCG Matrix with a lot of salt, but as a basic analytical framework it can be useful. What you will tend to see is that the companies/products that would be labeled "Dogs" under this regime will attempt to differentiate themselves, perhaps by adding features or some other option, in order to reposition themselves in a somewhat different industry and avoid the sort of ruthless, Darwinian culling that might be inevitable if the company were to stay in that box. If the "Dog" is big enough and the competitors are foreign, we can count on cries for political protection.

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