Divide the numerator and denominator of the three figures.

If there are preferred shares and non-controlling interests, you must select the portion attributable to common shareholders. Since earnings are a flow over a period, use the weighted average number of shares for EPS and generally average equity for ROE. BPS is a value that uses the ending balance and the number of shares at the end of the period.

Let's calculate using a hypothetical company.

If annual earnings attributable to common shares are 25,000,000 dollars and both the mid-year and year-end share counts are 10,000,000 shares, the EPS is 2.50 dollars. Dividing by the year-end common equity of 200,000,000 dollars gives a BPS of 20 dollars. Assuming the average equity at the beginning and end of the period is 200,000,000 dollars, the ROE is 12.5%.

EPS of 2.50 dollars is not automatically deposited to shareholders. Whether to distribute a portion of profits as dividends or reinvest them is a separate decision. BPS of 20 dollars is also not a guaranteed refund, and ROE of 12.5% is not the shareholder's actual stock return.

Basic EPS and Diluted EPS

Basic EPS is based on the weighted average of actual outstanding common shares. Diluted EPS reflects the dilutive effect of potential shares such as convertible securities and stock options on earnings. Depending on the conversion assumption, both the denominator and the numerator may be adjusted. Since anti-dilutive items that make losses appear smaller are excluded, the two being equal does not necessarily mean there is no potential dilution.

If the number of shares increases faster than earnings due to capital increases or stock-based compensation, EPS may decrease even if the company's net income rises. Since stock splits can adjust comparative EPS and BPS, do not mix pre-split stock prices with post-split per-share figures.

A high ROE is not always a good sign.

For a company generating the same profit of 25, if equity is 200, the ROE is 12.5%; if equity is 100, it is 25%. If the denominator decreases due to share buybacks, dividends, or accumulated losses, the ROE can increase without profit growth. If shares are bought back with debt, the burden of interest and repayment may also increase.

If equity is very small or negative, ROE may become an inappropriate comparative metric. Do not rank the ROE of banks and software companies using the same standard; instead, consider debt, cash flow, and business risks together.

Understand ROE in three parts.

Simplified DuPont analysis breaks down ROE into net profit margin × asset turnover × equity multiplier. These represent how much is kept from sales, how much revenue is generated from assets, and how much assets are held relative to equity, respectively. The formula only connects if the period and average balance criteria are aligned.

ROA is a profitability metric calculated by dividing net income by average total assets. When viewed alongside ROE, you can ask whether high profitability is due to operational efficiency or high reliance on borrowing. Neither metric is a price multiple that indicates whether a stock is cheap.

Check what you have read.

• Did you distinguish between dollars/share and %?
• Has the number of shares increased or decreased?
• Did you distinguish between year-end equity and average equity?
• Is the cause of the high ROE a decrease in the denominator?

Apply what you read to the actual screen

Try it on WAPE

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