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Let's say I have five investors, each owning 20% of a company that is worth 1,000,000. One investor wants to be bought out. So the other investors would, to maintain their equal proportion after the buyout, each pay 50,000 and hence would now have 25% of the company.

This makes sense to me. However, when the numbers are not equal, I am unsure how to figure out how much each person would pay.

For example, let's say:

  • Investor 1 owns 50%
  • Investor 2 owns 20%
  • Investor 3 owns 15%
  • Investor 4 owns 12%
  • Investor 5 owns 3%

Investor 2 wants to sell. If the company is worth $1,000,000, how would one calculate how much each investor would have to pay Investor 2 to keep their proportionate share in the company?

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Let $S$ be the sum of the percentages controlled by the other investors. In this case, $S=0.8=80\%$.

For what Investor $1$ pays, calculate $(200000)\frac{0.5}{S},$ and similarly for the others. If you prefer, you can work with percentages. Investor $1$ pays $(200000)\frac{50}{80}$, Investor $3$ pays $(200000)\frac{15}{80}$, and so on.

So all of the quantities you calculated should be divided by $0.8$, or equivalently multiplied by $1.25$. The idea is that although your calculation gives the right proportions, the sum is only $160000$. To get it up to the required $200000$, you need to multiply each payment you calculated by $\frac{200000}{160000}$.