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FUN WITH FORMULI

In this article, we shall briefly dissemble common mathematical equations used in determining the financial strength of a company. As many of you are aware, Warren Buffett considers a high return on equity to be one of the key ingredients necessary for running a successful business. What few people know is that return on assets is virtually the same thing. Let us see how.

Return on shareholder equity (ROE) is equal to (net income / shareholder equity)

In order to create new formula from a fraction, individuals often separate the denominator and numerator and couple them with other variables. This is known as 'expansion'. The ROE equation can then be written like this:

ROE = (net income / 1) x (1 / shareholder equity)

In this case the '1's cancel. They do not have to be '1's of course. Since they cancel anyway, we can place any variables there. The Motley Fool does a great job of determining what should go in place of these '1's in an article located here. To continue, let us try 'revenues'.

ROE = (net income / revenues) x (revenues / shareholder equity)

There, that's better. Well the 'revenues' cancel so that's good. Let's see, the first term (net income / revenues) is net profit margin. The second, (revenues / shareholder equity) is cool, but we can do better than that. Since it's another fraction, we can expand this too.

ROE = (net income / revenues) x (1 / shareholder equity) x (revenues / 1)

The 'revenues' still cancel out and the newly created '1's cancel too. Now, all we need to do is replace the '1's again. Lets try using 'assets'.

ROE = (net income / revenues) x (assets / shareholder equity) x (revenues / assets)

Now we're getting somewhere. The first term, (net income / revenues) is 'net profit margin'. The second term, (assets / shareholder equity) is 'leverage' and the third term, (revenues / assets) is 'asset turns'.

ROE = NPM x L x AT

We can now see that ROE is dependent on three terms. We could probably expand these fractions until we break down each and every penny of a business, but that would probably be a bit extreme.

With companies such as Coke, net margin makes a larger contribution to return on equity than in businesses such as Jacobs Engineering and Walmart. With low margin operations, asset turns (more sales per asset) contribute more to ROE. In an inflationary world however, lower margin operations will be hurt to a far greater degree than their high margin counterparts as capital expenditures skyrocket.

Nevertheless, this shows that if you can sell more and sell fast, even a low margin operation can produce extremely high rates of return.

The formula above is related to return on assets. How? Let's expand the ROA formula and find out. As we know:

ROA = (net income / assets)

Expanding the faction as before,

ROA = (net income / 1) x (1 / assets)

Replace the '1's with something,

ROA = (net income / revenues) x (revenues / assets)

In this case, the first substitution reveals (net income /revenues) or 'net profit margin' and (revenues / assets) or 'asset turns'. Since these are usable quantities, we'll stop here.

Summarizing we get,

ROA = net profit margin x asset turns
ROA = NPM x AT

Examining ROA we see that it is made up of two terms. Net margin and asset turns (sales velocity). If, for example, a company's ROA is 20% but it has a net margin of 10% we can assume that it is selling it's product at an extremely efficient pace - probably at a revenue to asset ratio of 2 (ie. 2 units of sales per unit of assets employed).

Does the ROA formula look familiar? Let's look back to our previous ROE formula,

ROE = net profit margin x leverage x asset turns
ROE = NPM x L x AT

Can you see the ROA hidden within the ROE? Pretty devious isn't it? Let us substitute it back.

ROE = NPM x L x AT
ROE = (NPM x AT) x L
ROE = ROA x L

Leverage is defined here as (assets/equity). With little or no liabilities the assets would equal shareholder equity and the leverage term would approach 1.

What does this mean? Well basically, in excellent companies, ROE should equal (or approximate) ROA. If it doesn't then leverage is being applied. The only factor separating ROE and ROA is the (assets/equity) term.

So, not only did we find that return on shareholder equity is a function of net profit margin, leverage and asset turns, but hidden within the formula is the return on assets. Since Mr. Buffett shuns extreme leverage, we now can see that his focus on ROE is really a focus on ROA.

Cheers,
Jim Chuong