Question

c. Write the equations for ROA, ROE, and EM; and explain the equations.

Answer 1

Return on assets (ROA)

Return on assets (ROA) is an indicator of how profitable a company is relative to its total assets. ROA gives a manager, investor, or analyst an idea as to how efficient a company's management is at using its assets to generate earnings. Return on assets is displayed as a percentage.

ROA=Average Total AssetsNet Income ​

Average total assets are used in calculating ROA because a company's asset total can vary over time due to the purchase or sale of vehicles, land or equipment, inventory changes, or seasonal sales fluctuations. As a result, calculating the average total assets for the period in question is more accurate than the total assets for one period. A company's total assets can easily be found on the balance sheet.

Net profit or net income which is found at the bottom of the income statement is used as the numerator. Net income is the amount of total revenue that remains after accounting for all expenses for production, overhead, operations, administrations, debt service, taxes, amortization, and depreciation, as well as for one-time expenses for unusual events such as lawsuits or large purchases.

Net profit also accounts for any additional income not directly related to primary operations, such as investment income or one-time payments for the sale of equipment or other assets.

Return on equity (ROE)

Return on equity (ROE) is a measure of financial performance calculated by dividing net income by shareholders' equity. Because shareholders' equity is equal to a company’s assets minus its debt, ROE is considered the return on net assets. ROE is considered a measure of how effectively management is using a company’s assets to create profits.

Return on Equity=Average Shareholders’ EquityNet Income​​

ROE is expressed as a percentage and can be calculated for any company if net income and equity are both positive numbers. Net income is calculated before dividends paid to common shareholders and after dividends to preferred shareholders and interest to lenders.

Net income is the amount of income, net of expense, and taxes that a company generates for a given period. Average shareholders' equity is calculated by adding equity at the beginning of the period. The beginning and end of the period should coincide with the period during which the net income is earned.

Net income over the last full fiscal year, or trailing 12 months, is found on the income statement—a sum of financial activity over that period. Shareholders' equity comes from the balance sheet—a running balance of a company’s entire history of changes in assets and liabilities.

It is considered best practice to calculate ROE based on average equity over a period because of the mismatch between the income statement and the balance sheet.

Efficient Market Hypothesis (EMH)

The efficient market hypothesis (EMH), alternatively known as the efficient market theory, is a hypothesis that states that share prices reflect all information and consistent alpha generation is impossible. According to the EMH, stocks always trade at their fair value on exchanges, making it impossible for investors to purchase undervalued stocks or sell stocks for inflated prices. Therefore, it should be impossible to outperform the overall market through expert stock selection or market timing, and the only way an investor can obtain higher returns is by purchasing riskier investments.