Say 5 people start a business — you and 4 friends. You each pay $100, and you’re all equal partners owning 20% (or 1/5) of the company. The $500 goes into the company’s bank account.
Now let’s calculate how much your shares are worth. You own 20% of a company worth $500, your shares are worth $100. Easy.
If the company does a buyback, and buys Bob’s shares for $90, the bank account now has $410 and the remaining 4 people have 25% of the company.
Now let’s calculate again how much your shares are worth. You own 25% of a company worth $410, your shares are worth $102.50.
Look at it like this: In the beginning everybody paid $100 to get in as an investor. The company paid Bob $90 to get out. Bob lost $10 by selling his shares for $10 less than he paid for them. The company gained $10, and it’s split 4 ways among the stock value of the company’s remaining owners. The company underpaid relative to what the shares were worth, and made money from Bob.
This can happen in reverse: If the company buys Bob’s shares for $110, everybody else’s shares are worth 1/4 of $390, or $97.50. The company overpaid relative to what the shares were worth, and lost money to Bob.
“What the shares are worth” is easy to calculate in our examples because our simple example company didn’t actually do any business, it was just some money sitting in a bank account. A real-world business has sales / income / loans / employees / long-term contracts / stuff like branding or technology. It can be a lot harder to put numerical value on what the company’s worth, which makes it more difficult to decide whether a buyback makes sense numerically.
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