Closely held companies – which is what you’re describing – aren’t listed on a stock exchange and don’t have a simple valuation of their shares. Person B’s interest is valued at whatever they can get someone else to pay them for it. Until they have a buyer lined up for their shares, the “value” is whatever Person B thinks it is.
Person B generally can’t force Person A to sell their shares. If Person A is running the business in a way that is detrimental to Person B, then it is *possible* that Person B may be able to convince a court to force Person A to buy Person B’s shares. How the share are valued in that situation depends on the state where the company is incorporated and how big it is.
There are plenty of accounting firms that will value companies based on their assets and income. The more common option is valuation would be that both Person A and Person B will hire one of those firms to value the company and try to convince the judge that their valuation is correct. But there are a lot of other possibilities as to how a court can determine the proper valuation of a company in that situation.
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