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According to the Investopedia articles, all look to be Total assets - Total liabilities. Then are they the same?

Investopedia: Book Value

The book value of a company is the net difference between that company's total assets and total liabilities

Investopedia: Shareholder Equity (SE)

Shareholder equity (SE) is the owner's claim after subtracting total liabilities from total assets.

Investopedia: Debt-To-Equity Ratio (D/E)

Assets is $120,000 and liabilities is $100,000, so Ed's Equity is $20,000 enter image description here

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Yes they are synonymous. Sometimes, "book value of equity" or just "book value" is used to distinguish it from the market value of equity, which is what a company's shares are currently trading for (also called "market capitalization" or just "market cap").

"Equity" is a more general term since it applies to all companies, while "shareholders' equity" only refers to corporations since they have shareholders. For sole proprietorships, the proper term is "owner's equity". But those are just semantic differences. They all mean the same thing (assets minus liabilities)

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