Assets = Liabilities plus Equity
If there are no liabilities, then the return on equity will equal return on assets as identified here:
Assets = Liabilities plus Equity
Assets = None plus Equity
Therefore: Assets = Equity
Naturally it is rare in business not to have liabilities, especially with small business. Since liabilities are normal, the return on equity equals the return on assets less the portion assigned as return on liabilities. Look at this illustration to further understand.
Preston Light Fixtures
Preston manufactures custom light fixtures for high-end hotels and conference centers. The balance sheet is as follows:
Liabilities and equity combined equals $11,706,400 matching total assets.
Earnings for the year were $903,600 (adjusted for depreciation). Return on assets equals:
Return on Assets = $903,600 = 7.72%
The traditional formula for return on equity is:
Return on Equity = Net Profit
Using the information from above:
Return on Equity = $903,600 = 17.04%
A sophisticated user of ratios is also interested in the return on equity as equity is a ratio of all invested capital (liabilities and equity). To figure this out, first determine ratio of earnings to liabilities and equity both as follows:
Net Profit $903,600 $903,600
Capital Amount $6,402,500 $5,303,900
Return 14.11% 17.04%
Then determine the ratio of the total capital invested. Liabilities are 54.7% of all capital and equity is 45.3% of the total. Now multiply each return by their respective percentage of the total and it should match return on assets. Let’s find out.
Return on Liabilities 14.11% X its percentage of capital 54.7% and its result is 7.72%
Return on Capital 17.04% X its percentage of capital 45.3% and its result is 7.72%
From above, the return on assets is 7.72%.
A secondary method is to allocate the earnings to the two respective pools of capital, determine their results as a percentage of all capital and to simply add the two results together. It should match return on assets. Let’s find out.
Net Profit X 54.7% for liabilities is $494,269 divided by $11,706,400 = 4.22%
Net Profit X 45.3% for equity is $409,331 divided by $11,706,400 = 3.50%
Total Profit divided by all Capital (which equals all assets) = 7.72%
This modified version allocates the net profit between the liabilities and equity to formulate the relationship between liabilities and equity in the aggregate. It is of the utmost importance that the reader understand the relationship between the traditional definition and the summation result. The outcomes are completely different and a user of ratios needs to understand the underlying variances to truly evaluate how effective a company generates value for the investor. In a traditional formula the denominator is a lower value therefore the result is higher. When using this formula, understand both elements of the results as follows:
Traditional Return on Equity = 17.04%
Relational Return on Equity Element = 3.50%
Every organization utilizes debt, thus there will always be a significant difference in the two values. As the two values get closer, it is an indication that the organization relies less and less on debt to fund its capital.
As an example, there will always be a large disparity between the two values for debt based industries. For example, real estate investment trusts (REITs) will have assets financed with long-term debt at 70% or more. Therefore the disparity will be significant, look at this simple illustration.
Cumberland Woods Apartments Assets $10,500,000
Total Debt $8,500,000
Return on Equity 45%
Relational Return on Equity 1.63% (of the total 8.57% return on assets, equity is 1.63%, debt is 6.94%)
Similar to what was explained in return on assets, the return on equity is not a pure or perfect formula. The user must make adjustments in order to get an accurate result. To help the reader understand this particular business ratio and its application, the reader must first understand how equity is derived in business. With this knowledge the formula’s nuances are explained and how various changes impact the outcome. Finally, this lesson explains proper application and interpretation of the ratio. There are pitfalls to this formula and a sophisticated user is on the lookout for them. If they exist, there are other options to evaluate performance.
Equity in Business
Equity in business is commonly referred to as owner’s investment (outside money) in the business operation. It has multiple names depending on the type of entity as illustrated in the following chart.
Equity Title Legal Entity
Capital Account/Units Partnership/Limited Partnerships
Capital Account/Units Limited Liability Company (multiple members)
Corpus Trust/Business Trusts
Fund Balance Non-Profit Organization
There are actually several more.
Equity not only includes the initial investment (outside money) but it also includes the lifetime earnings (inside money) to date net of lifetime distributions/dividends and draws dispersed to date. The equity section is divided into four sub groups as explained below.
- Initial Investment – This section identifies the initial stock authorized and outstanding (sold) to investors. It includes any shares sold from the inception date. In corporation status, it consists of the par value (face value) plus any amounts (capital) paid in excess of par for the stock from initial investors (owners).
- Treasury Balance – Sometimes when companies perform well, the company buys back some of the outstanding equity and gives up assets (cash) in exchange; it is commonly shown as a negative value in the equity section.
- Retained Earnings – Represents the lifetime to date earnings less amounts paid in the form of dividends, distributions, draws or benefits disbursed to the holders of an ownership interest.
- Current Earnings – Those earnings to date for the current calendar/fiscal year as reported on the income statement.
Depending on the legal form of existence the four sections will have different titles but essentially have a similar meaning. For example, with partnerships, the treasury balance refers to capital accounts for retired or inactive partners. It is similar to a trust balance that is paid out over time in accordance with the partnership/trust agreement.
The following is an example of the equity section of a corporation.
Grantsville Pilot Beef & Cattle, Inc.
Balance Sheet – Equity Section Only
November 30, 2016 (Fiscal Year-End)
Preferred Stock – 2,000 Shares @ 5% $2,000,000
Common Stock – Par Value $1.00/Share 10,000
Common Stock – Capital Paid In Excess of Par 792,400
Sub-Total Stock $2,802,400
Preferred Stock Redemption – 800 Shares (Nov 2015) (800,000)
Retained Earnings Net of Dividends Paid
Earnings Dividends Net
Prior $2,647,591 ($102,000) $2,545,591
2011 402,752 (150,000) 252,752
2012 317,809 (73,000) 244,809
2013 596,937 (281,000) 315,937
2014 773,868 (400,000) 373,868
2015 906,482 (450,000) 456,482
Sub-Totals $5,645,439 ($1,456,000) 4,189,439
Net Profit Year-To-Date $1,261,318
Dividend Payments (Tax Payments on Behalf of Owners) (380,000)
Net Earnings 881,318
Total Equity $7,073,157
Along with liabilities the capital is used to purchase buildings, fencing, cattle, feed, supplies etc. The sale of beef cattle generates revenue which in turn has costs ending in a profit of $1,261,318. The profit generates a tax liability for the owners of which Grantsville Pilot paid $380,000. Thus the comparative profit to a publicly traded entity is $881,318. Take note, the net profit is the result of using the land, buildings, equipment, feed, veterinarian skills, even water and waste management to maximize the weight of cattle. All those assets were used to fulfill this single goal.
However, the assets were not purchased from equity alone, debt is used too. An investor is interested in the return on the equity component of all this.
Nuances with Return on Equity
In Grantsville’s case total equity exists because of three sources. First is the initial investment by outside entrepreneurs, i.e. other people’s money. In this case, it is $2,002,400. This outside money is composed of both preferred, common and treasury stock. Please note, the initial overall investment was $2,802,400 and $800,000 of that was bought back by the company via treasury stock.
The second source is inside money denoted as retained earnings. Retained earnings are the lifetime to date profits as of the beginning of the year. The last source is current earnings net of any current year dividends/distributions or draws.
As explained in return on assets, the more accurate denominator is the beginning balance of the equity section. In Grantsville’s case the beginning balance is the actual stock value (outside money) plus retained earnings through the prior year as follows:
Stock (Outside) $2,002,400
Retained Earnings (Inside) 4,189,439
Beginning Balance of Equity $6,191,839
The correct formula for return on equity is:
Net Profit = $881,318 = 14.23%
Beg. Bal. Equity $6,191,839
The traditional results are:
Net Profit = $881,318 = 12.46%
Total Equity $7,073,157
Notice how including all equity increases the denominator reducing the result.
Now let’s break the return on equity into the sub components of return on initial stock and retained earnings, i.e. outside and inside money.
The original investment is $2,002,400 and all other types of investment are various forms of leverage (see leverage ratio) in business. Therefore, the amount truly at risk for the owners are the original invested dollars, $2,002,400. The return on the original investment is:
Net Profit = $881,318 = 44.01%
Outside Money $2,002,400
Again, a smaller denominator increases the result.
Similar to outside money, a user can evaluate the return on investment for inside money as:
Net Profit = $881,318 = 21.04%
Inside Money $4,189,439
Notice the denominator is larger reducing the result.
There are some interesting twists to the above. In accordance with the equity breakout, Grantsville’s current net earnings are $881,318. Suppose Grantsville dedicated those earnings to buying back preferred stock. Just as in 2015, it buys back an additional $800,000 (800 shares) of preferred stock. The outside money is now $1,202,400. The return on outside money increase to 73.3% as follows:
$881,318 = 73.3%
The above identifies a flaw with this evaluation. The beginning balance of equity did not actually change as the above formula is really using the ending balance of outside money.
The return on equity analysis for inside and outside money is never used in publicly traded companies for two reasons. First, the outside money is actually what the company has sold in shares initially and doesn’t reflect what the current owners paid for the stock. Only current owners can evaluate their return on equity from the perspective based on what they paid for the stock in the market. Secondly, inside money is in a constant state of flux as shareholders often demand dividend payments changing the value of retained earnings.
With small business, both inside and outside money are locked as small business uses inside money to pay for growth and outside money rarely if ever changes hands. Given this, the return on outside money is the most appropriate ratio to evaluate closely held entities.
Overall, return on equity works best if looking at total equity and not broken out into the respective equity groups. But this analysis is different when evaluating for all capital invested into assets.
Leverage and Return on Equity
One of the drawbacks to relying on return on equity is it isn’t really a ratio for comparison purposes. This is because leverage (the use of debt) is different across the various business sectors. As debt increases the net profit earned will change. If leverage is properly utilized, net profit should increase to pay the principal component of the debt service payment. This increase in net profit results in a higher return on equity as an increase in the numerator without a change in the denominator results in higher returns on equity.
To illustrate, let’s assume Grantsville’s net profit is equal per dollar value of capital (liabilities and equity combined). It currently has four million dollars of debt for total beginning balance of $10,191,839 (liabilities of $4,000,000 plus equity of $6,191,839). Therefore, the net earnings per dollar of capital is:
$881,318 = 8.647 cents per dollar
Using this value, if Grantsville’s debt increase to eight million and the net earnings per dollar is the same (remember, leverage should increase the earnings per dollar of capital), then the net earnings equals:
$14,191,839 times .08647 = $1,202,048
Now the return on equity (beginning balance) is:
$1,202,048 = 19.41%
The return on equity increases dramatically; this is due to the use of leverage in business. When comparing two different entities in the same business sector, take into consideration the amount of leverage used by each. Look at the earnings per dollar of capital as a better comparative tool then return on equity. As an example, let’s combine Grantsville Pilot with total capital of $10,191,839 ($4,000,000 of debt) to an apartment complex with $9,000,000 of debt and $1,000,000 of equity.
Grantsville Pilot Apartment Complex
Debt $4,000,000 $9,000,000
Equity (Beg Bal) 6,191,839 1,000,000
Net Earnings 881,318 202,707
Return on Equity 14.23% 20.27%
Earnings/$of Capital 8.647 cents/dollar 2.027 cents/dollar
The apartment complex is by far an inferior performer of earnings, yet leverage boosts the return on equity. Both have $10,000,000 of capital invested (yes I know that Grantsville is $10,191,839 but it is only 1.92% more).
The lesson here is to evaluate return on equity considering leverage. Do not use return on equity to compare dissimilar business operations. To be effective, a user of this ratio should properly apply the formula.
Application and Interpretation
As a performance ratio the return on equity is really measuring the overall ability to create value for the organization. Value is a result of thousands of decisions summed up into one single number. Throughout the year the management team via policies of the company generate long-term profitability by making good decisions. Good decisions lead to positive long-term results. To properly interpret management’s performance look at the trend line for performance. Using Grantsville’s equity report, let’s look at a five-year trend for performance. Step one is to set-up a chart (table) of required information. Since Grantsville is a small closely held company and dividend payments are directly tied to owner needs and not consistently applied, it is best to use gross earnings and not net earnings for evaluation purposes. Here is the table:
Year Earnings Equity Balance on Equity
2012 $317,809 $5,600,743 5.67%
2013 596,937 5,845,552 10.21%
2014 773,868 6,161,489 12.56%
2015 906,482 6,535,357* 13.87%
2016 1,261,318 6,191,839 20.37%
Average $771,283 $6,066,996 12.71%
The trend line would be a continuous increase with a steeper slope from 2015 to 2016.
* In 2015, Grantsville paid the preferred stockholders $800,000 to buy back some of the stock. This is either because the stock certificates mandated this step or the Board of Directors decided to buy it back voluntarily. Either way, the equity balance decreased during 2015 as follows:
Beginning Balance 2014 $6,161,489
Earnings in 2014 773,868
Dividend Payments (400,000)
Ending Balance 11/30/2014 $6,535,357
Beginning Balance 12/01/15 6,535,357
Earnings in 2015 906,482
Dividends in 2015 (450,000)
Buy Back of Preferred Stock (800,000)
Ending Balance 11/30/15 $6,191,839
In 2016, the return on equity accelerates to 20.37%, a significant increase over 2015. The buy back reduces the equity balance thus increasing the return on equity. If the buy back had not occurred, the equity would have been $6,991,839 and the return on equity would now be 18.04%.
To properly evaluate performance, all variables must be consistently applied. Therefore the 2016 beginning balance of equity is adjusted to $6,991,839 and the trend line results in a dampened output for the transition period from 2015 to 2016, i.e. it isn’t as steep.
It is easy for the Board to manipulate return on equity by simply buying back stock. Some readers may wonder, well assuming this, why don’t dividends/distributions affect the results? Actually they do; however, dividends are customarily a consistent percentage of earnings as illustrated here:
Year Earnings Dividends Dividends as a %
2012 $317,809 $73,000 22.97%
2013 596,937 281,000 47.07%
2014 773,868 400,000 51.69%
2015 906,482 450,000 49.64%
2016 1,261,318 380,000 30.13%
Notice in general the dividend payments are consistently between 20 and 50% of earnings. The key attribute is consistency. If dividends were not paid, equity increases would dampen the successive results for return on equity. In effect, the entire trend line would simply shift downward as a whole. The ratio evaluates the performance of management and the Board of Directors with their ability to make good long-term decisions. An upward trend line identifies good decision-making, a downward trend line is a sign to replace the management team.
As with all business ratios, there are drawbacks and volatility issues to address. In Grantsville’s case, the market price of beef greatly affects the revenue and doesn’t affect costs to raise cattle. Therefore, volatile price changes affect profit thus impacting return on equity. The trend line results would be more ups and downs and not a smooth line in a distinct direction. For industries that are easily affected by outside forces, specifically market trends, relying on the return on equity as a performance gauge is inappropriate. Other business ratios are used to evaluate management decisions.
Summary – Return on Equity
Return on equity is one of the performance ratios used to evaluate management and the Board of Directors. Over several years a positive trend line indicates good policies and decisions. The ratio is easily manipulated but with a clear understanding of equity and its underlying elements a sophisticated user can adjust for manipulations to obtain more accurate results.
The basis formula is:
Return on Equity = Net Profit
Always use the fiscal/calendar year’s beginning balance for the equity value as the denominator. Take the information one step further by evaluating both debt and equity in relation to each other to determine the impact leverage has with the ratio. ACT ON KNOWLEDGE.