Formula and accounting assumptions
Acquired tokens equal cash budget × (1 − execution fee) divided by average execution price. Burned tokens equal acquisitions × burn fraction. Subtract the burn from circulation and divide the unchanged holder balance by the new supply. The relative increase in that ownership fraction is original supply divided by remaining supply, minus one. It is a change in proportional ownership, not a market return or cash distribution to the holder.
Worked hypothetical example
Suppose circulation is 1,000 tokens and an unchanged holder owns ten. A $100 buyback at an average price of $1 with no fee and a 100% burn fraction retires 100 tokens. The holder's share rises from 1% to approximately 1.111111%, a relative increase of 11.111111%. A higher average execution price buys and burns fewer tokens with the same budget. Nothing in those figures requires the market capitalization or token price to remain fixed.
Interpret the scenarios and limits
The model assumes purchases come from other holders and that burned tokens actually leave the relevant circulating supply. It rejects acquisitions above the tokens those holders can provide, independently of the burn fraction, and rejects any burn that leaves no supply denominator. The unchanged holder is assumed not to sell into the buyback. Market impact, treasury opportunity cost, vesting changes and emissions are excluded. A burn mechanism does not itself confer rights to protocol revenue, so use the ownership calculation separately from any cash-flow valuation.