Corporate equity is retained earnings plus common shares outstanding.
On a corporate balance sheet, the retained earnings and the outstanding common stock capitalization combined would be considered the corporate equity, also called shareholder’s equity / owner’s equity.
Of the total corporate equity, the portion representing common stock equity is only the capital raised through the issuance of shares in an IPO (initial public offering), where payment for those shares was paid to the company. Subsequent trading in those shares does not affect the common stock equity on the company books.
Some states require the corporate accountant to record a par value or stated value for the shares, which will be extremely low and has no economic significance, and the excess collected in fair market value for the issued securities is recorded as Paid-In Capital.
Shareholder demand for those shares in the secondary market exchanges will be affected by the earnings of the company, some of which will be dispensed in dividends, some of which will become part of the retained earnings.
The value of the retained earnings will grow or shrink depending on net profit or net losses. So, the retained earnings and the common stock equity are the total book value of the corporate equity.
The price at which the stock trades has to do with expectations of growth and other factors. Some corporations are privately owned, and this can be called private equity. This type of equity is not as liquid as publicly traded companies but can trade over-the-counter if the investors observe SEC regulations.
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