What Is the After-Tax Real Rate of Return?

The after-tax real rate of return is the actual financial benefit of an investment after accounting for the effects of inflation and taxes. It is a more accurate measure of an investor’s net earnings after income taxes have been paid and the rate of inflation has been adjusted for. Both of these factors must be accounted for because they impact the gains an investor receives. This can be contrasted with the gross rate of return and the nominal rate of return of an investment.

Understanding the After-Tax Real Rate of Return

Over the course of a year, an investor might earn a nominal rate of return of 12% on his stock investment, but the real rate of return, the money he gets to put in his pocket at the end of the day, will be less than 12%. Inflation might have been 3% for the year, knocking his real rate of return down to 9%. And since he sold his stock at a profit, he will have to pay taxes on those profits, taking another, say 2%, off his return, for an after-tax real rate of return of 7%.

The commission he paid to buy and sell the stock also diminishes his return. Thus, in order to truly grow their nest eggs over time, investors must focus on the after-tax real rate of return, not the nominal return.

The after-tax real rate of return is a more accurate measure of investment earnings and usually differs significantly from an investment’s nominal (gross) rate of return, or its return before fees, inflation, and taxes. However, investments in tax-advantaged securities, such as municipal bonds and inflation-protected securities, such as Treasury inflation protected securities (TIPS), as well as investments held in tax-advantaged accounts, such as Roth IRAs, will show less discrepancy between nominal returns and after-tax real rates of return.

Example of the After-Tax Real Rate of Return

Let’s be more specific about how the after-tax real rate of return is determined. The return is calculated first of all by determining the after-tax return before inflation, which is calculated as Nominal Return x (1 – tax rate). For example, consider an investor whose nominal return on his equity investment is 17% and his applicable tax rate is 15%. His after-tax return is, therefore:
$0.17 \times (1 – 0.15) = 0.1445 = 14.45\%$0.17×(1−0.15)=0.1445=14.45%

Let’s assume that the inflation rate during this period is 2.5%. To calculate the real rate of return after tax, divide 1 plus the after-tax return by 1 plus the inflation rate, then subtract 1. Dividing by inflation reflects the fact that a dollar in hand today is worth more than a dollar in hand tomorrow. In other words, future dollars have less purchasing power than today’s dollars.

Following our example, the after-tax real rate of return is:

$\frac{(1 + 0.1445)}{(1 + 0.025)} – 1 = 1.1166 – 1 = 0.1166 = 11.66\%$(1+0.025)(1+0.1445)​−1=1.1166−1=0.1166=11.66%

That figure is quite a bit lower than the 17% gross return received on the investment. As long as the real rate of return after taxes is positive, however, an investor will be ahead of inflation. If it’s negative, the return will not be sufficient to sustain an investor’s standard of living in the future.

The Bottom Line

When you are assessing the value of your investments, it’s important to look at not just your nominal rate of return but also the after-tax real rate of return, which takes into account the taxes you’ll owe and inflation’s effect. The after-tax real rate of return can tell you if your nest egg investments will allow you to maintain your standard of living in the future.

What Is the Accounting Equation?

The accounting equation states that a company’s total assets are equal to the sum of its liabilities and its shareholders’ equity.

This straightforward relationship between assets, liabilities, and equity is considered to be the foundation of the double-entry accounting system. The accounting equation ensures that the balance sheet remains balanced. That is, each entry made on the debit side has a corresponding entry (or coverage) on the credit side.

The accounting equation is also called the basic accounting equation or the balance sheet equation.

Understanding the Accounting Equation

The financial position of any business, large or small, is based on two key components of the balance sheet: assets and liabilities. Owners’ equity, or shareholders’ equity, is the third section of the balance sheet.

The accounting equation is a representation of how these three important components are associated with each other.

Assets represent the valuable resources controlled by the company, while liabilities represent its obligations. Both liabilities and shareholders’ equity represent how the assets of a company are financed. If it’s financed through debt, it’ll show as a liability, but if it’s financed through issuing equity shares to investors, it’ll show in shareholders’ equity.

The accounting equation helps to assess whether the business transactions carried out by the company are being accurately reflected in its books and accounts. Below are examples of items listed on the balance sheet.

Assets

Assets include cash and cash equivalents or liquid assets, which may include Treasury bills and certificates of deposit.

Accounts receivables list the amounts of money owed to the company by its customers for the sale of its products. Inventory is also considered an asset.

The major and often largest value asset of most companies be that company’s machinery, buildings, and property. These are fixed assets that are usually held for many years.

Liabilities

Liabilities are debts that a company owes and costs that it needs to pay in order to keep the company running.

Debt is a liability, whether it is a long-term loan or a bill that is due to be paid.

Costs include rent, taxes, utilities, salaries, wages, and dividends payable.

Shareholders’ Equity

The shareholders’ equity number is a company’s total assets minus its total liabilities. 

It can be defined as the total number of dollars that a company would have left if it liquidated all of its assets and paid off all of its liabilities. This would then be distributed to the shareholders.

Retained earnings are part of shareholders’ equity. This number is the sum of total earnings that were not paid to shareholders as dividends.

Think of retained earnings as savings, since it represents the total profits that have been saved and put aside (or “retained”) for future use.

Accounting Equation Formula and Calculation

$\text{Assets}=(\text{Liabilities}+\text{Owner’s Equity})$Assets=(Liabilities+Owner’s Equity)

The balance sheet holds the elements that contribute to the accounting equation:

1. Locate the company’s total assets on the balance sheet for the period.
2. Total all liabilities, which should be a separate listing on the balance sheet.
3. Locate total shareholder’s equity and add the number to total liabilities.
4. Total assets will equal the sum of liabilities and total equity.

As an example, say the leading retailer XYZ Corporation reported the following on its balance sheet for its latest full fiscal year:

• Total assets: $170 billion
• Total liabilities: $120 billion
• Total shareholders’ equity: $50 billion

If we calculate the right-hand side of the accounting equation (equity + liabilities), we arrive at ($50 billion + $120 billion) = $170 billion, which matches the value of the assets reported by the company.

About the Double-Entry System

The accounting equation is a concise expression of the complex, expanded, and multi-item display of a balance sheet. 

Essentially, the representation equates all uses of capital (assets) to all sources of capital, where debt capital leads to liabilities and equity capital leads to shareholders’ equity.

For a company keeping accurate accounts, every business transaction will be represented in at least two of its accounts. For instance, if a business takes a loan from a bank, the borrowed money will be reflected in its balance sheet as both an increase in the company’s assets and an increase in its loan liability.

If a business buys raw materials and pays in cash, it will result in an increase in the company’s inventory (an asset) while reducing cash capital (another asset). Because there are two or more accounts affected by every transaction carried out by a company, the accounting system is referred to as double-entry accounting.

The double-entry practice ensures that the accounting equation always remains balanced, meaning that the left side value of the equation will always match the right side value.

In other words, the total amount of all assets will always equal the sum of liabilities and shareholders’ equity.

The global adherence to the double-entry accounting system makes the account keeping and tallying processes more standardized and more fool-proof.

The accounting equation ensures that all entries in the books and records are vetted, and a verifiable relationship exists between each liability (or expense) and its corresponding source; or between each item of income (or asset) and its source.

Limits of the Accounting Equation

Although the balance sheet always balances out, the accounting equation can’t tell investors how well a company is performing. Investors must interpret the numbers and decide for themselves whether the company has too many or too few liabilities, not enough assets, or perhaps too many assets, or whether its financing is sufficient to ensure its long-term growth.

Real-World Example

Below is a portion of Exxon Mobil Corporation’s (XOM) balance sheet in millions as of Dec. 31, 2019:

• Total assets were $362,597
• Total liabilities were $163,659
• Total equity was $198,938

The accounting equation is calculated as follows:

• Accounting equation = $163,659 (total liabilities) + $198,938 (equity) equals $362,597, (which equals the total assets for the period)