How equity works - is there a difference between rescaling equity and fixed-equity?

Question

after a colleague of mine left the company, I'd like to provide him/er with an equity for the work done. I'd like this equity to be dynamic, meaning that whenever a new member or investor enters, his/er equity rescales proportionally.
As an example:
Initial Equity of "Person A": 5%
New investor enters and takes: 20%
Final Equity of "Person A": 4%

Is it possible?
P.S. To be more clear, my doubt is that there may be some options in the business sector to get a fixed-equity over time (independently on diluition): for example, in case an investor enters, s/he may say: "I want 20% forever". Is this option real, or am I wrong? So, my question is whether I have to make clear this rescaling condition or it is just a default behaviour.

Grade 'Eh' Bacon · Accepted Answer

Yes, both options are possible.
"Fixed equity %". If I own 20% of a company's shares, then the only thing that will change my % of share ownership is if new shares are issued. So if you decide you want to offer 'permanent equity %', what you are really saying is "we will never issue new shares from the company to anyone else". This does what you are asking, but limits financing opportunities significantly.
"Proportional equity %". If I own 20% of a company's 100 shares, and another 50 shares get issued to other people, suddenly I own 20 shares out of 150, or 13.3%. Note that if shares are being offered for a fair price, then the value gotten by the company when offering new shares (whether receiving $ or by locking in a valuable employee) should be equal to the share % given up, so my new 13.3% should in theory be equal in value to my old 20%.

How equity works - is there a difference between rescaling equity and fixed-equity?

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