A co-owner in a business may have the right of first refusal (normally the case) in the company’s Memorandum and Articles but it would be very unusual for the remaining shareholder to be compelled to buy them.
The shareholder wishing to sell is then in the situation of having to find a buyer on the open market which, for a private limited company may not be particularly easy.
Unlike a listed company, the shares in a small private company will sell for as much as someone wants to pay and what the seller wants to sell them for. There is no set formula for valuation although obviously the buying price and selling price and how much each party is willing to sell/buy for will be based upon the value of the company. However, it doesn’t matter what the company is worth, if nobody actually wants to buy those shares.
The disadvantage of you not buying them is that you could end up being in business with another shareholder that you don’t want to be in business with.
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