MRR results
monthly step model
Assumptions
Time step is monthly. Churn applies to existing MRR each month.
Fixed net-new model: MRR(t+1) = MRR(t)·(1 − churn) + netNew
Constant % model: MRR(t+1) = MRR(t)·(1 + expansion − churn)
Diminishing % model:
expansion(t) = end + (start − end)·2^(−t/halfLife) →
MRR(t+1) = MRR(t)·(1 + expansion(t) − churn)
Logistic model:
MRR(t+1) = MRR(t)·(1 − churn) + r·MRR(t)·(1 − MRR(t)/cap)
“Profit” is monthly: revenue − COGS − salary% − overhead (no taxes, no balance sheet).
Plateau (detected) is a heuristic: average ΔMRR over a trailing window below a chosen $ threshold.
Plans & funnel results
3 plans
Assumptions
Fractional customers are allowed (think “average customers”).
Each month: churn customers, then add new customers from demos.
New customers per plan: demos · demoShare · closeRate. Churn:
customers · churnRate.
Simple plan LTV: (price · grossMargin) / churn (monthly churn; ignores expansion).