The yearly profit change at every churn rate. The crossing with zero is your break-even — the number of walkouts the rise can afford. Hover to explore.
Departed clients take their revenue and its serving cost with them — variable costs scale down — so profit after the rise is the remaining revenue at the new, fatter margin: revenue × (1 − churn) × (margin + rise). The break-even churn is rise ÷ (margin + rise) — the formula’s shape is the lesson: the higher your margin, the more walkouts a rise survives. The chips add the two second-order effects that bite in practice: stayers trimming usage, and the acquisition cost of replacing the leavers.
Fixed costs don’t move with churn and so cancel out of the comparison — but a big enough walkout can strand capacity (staff, licenses) that was sized to the old book. Cross-sell, referral networks and the strategic value of specific logos are outside the arithmetic: losing the anchor client that referred half the book is not 4% churn, whatever the spreadsheet says. A single churn number stands in for a distribution — the scenario table exists because the guess is always wrong in one direction or the other.
profit after = revenue × (1 − churn) × (1 − dip) × (margin + rise)
break-even churn = rise ÷ (margin + rise)
− replacement cost: churned revenue × CAC%
gauge = your expected churn ÷ the break-even