Capital equals debt plus equity. We hear this phrase, but do we really understand what it means? The best explanation that I ever head was also the simplest. Capital represents all of the assets of the company. Debt and equity represent who owns those assets.

As an example, if a company has $1,000 in capital assets, and $400 in debt, then equity is equal to $600. The bank, or whoever holds the company’s debt, owns 40% of the capital, and the owner(s) of the company own 60%. The proportion of debt and equity to capital is also known as the company’s capital structure.

We should also note that, although we express these relationships in dollars, we may not be talking about cash in the bank, but about other types of assets that could include buildings or other real estate, equipment, inventory as well as other intangible assets, such as good will (which is another topic completely!).

You will recall from last week that return on equity (ROE) was the ratio at the top of the DuPont pyramid (for an image of the pyramid click here), so let’s start there. ROE represents the earnings that a company makes on each dollar of invested equity. In other words, it is a sign of how each dollar of equity is contributing to the bottom line. The calculation for return on equity is:

Net Income

Equity

So, if a company had net income of $12,000 and equity of $100,000, then ROE would be 12% (ratios are usually expressed as a percentage). In other words, for every dollar of equity, the company returned $.12. One way that the ratio can be useful is to compare it to previous years. For example, if the previous years’ ROE was 8%, you could infer progress.

On the other hand, if the previous year was 16%, you could infer the opposite. Another way to use ROE would be to compare it to your industry’s average. If the industry’s average was 20%, for example, your company could be at a competitive disadvantage.

As we work down the DuPont pyramid, we see that ROE can be broken down into two constituent parts, Return on Capital (ROC) and Leverage. ROC is similar to ROE, in that it expresses the return on each dollar of capital in the company. Its’ formula is:

Net Income

Capital

If the same company as above had $150,000 in capital, then the ROC would be 8% or a return of $.08 on each dollar of capital. As in the previous example, you could compare the ROC to previous years, or to company expectations for this year, or you could compare it to the industry ROC. All would be useful in understanding how your company is performing.

At this point you might exclaim, “Wait a minute, how can ROC be less than ROE!” The answer to the question reveals the power of leverage, as well as the usefulness of the DuPont Analysis. To explain the power of leverage, let’s look at the capital structure of the company, that is, the ratio of Capital, Debt and Equity.

Let’s start out by assuming in a first example, that the company actually had no debt. If that was the case, then there would be no difference between the account of capital (debt + equity) and the amount of equity. Therefore ROE would be $12,000/150,000 = 8% and ROC would also be $12,000/$150,000 = 8%.

In reality, we said that the company had $150,000 of capital. If equity is $100,000 then based on the formula capital equals debt plus equity, then the company has $50,000 in debt. Let’s now look at the formula for Leverage:

Capital

Equity

Based on the formula, our example company has leverage of 150,000/100.000 = 150%., or simply expressed, 1.5 When we apply the principles of the DuPont Analysis, this becomes clear.

Ratios at each level of the DuPont Analysis are equal to the ratio above. So, another formula for ROE is:

ROC x Leverage = ROE

In this case 8% (ROC) x 1.5 (Leverage) = 12%. By using debt to increase the amount of invested equity, the company was able to get a better return. If the company had no debt, they actually would not have had as good a net profit.

We can see then that by deconstructing the top ratio, ROE in to ROC and Leverage, we have a better understanding of the company’s financial structure and why they have made the returns that they have. Next week, we will continue to delve deeper into the DuPont pyramid.

First paragraph, last sentence — “Debt and equity represent who owns those assets.” Not EXACTLY correct. Debt and equity represents those who have claims on those assets. The entity (company, corporation, partnership, etc.) owns the assets. Creditors have claims on them, as do shareholders/partners/members. I understand what you are getting at, though.

Mike,

Technically, you are correct, but I like to keep it simple. It reminds me of the old Tennessee Ernie Ford refrain, “I owe my soul to the company store…”

Thanks for the comment.

Kevin

Under certain circumstances, the debt holders may become the owners, even if they are not considered so today. One way to simplify is to view things on a Total Invested Capital basis (where all “return expecting” funding is aggregated).

[…] with me when I state it like this, but Leverage basically tells us who owns what in a company (see DuPont Analysis: Capital, Debt and Equity). If the total capital in a company is $150,000, and the owner’s equity is $100,000, then that […]