MKT 626 · Forecasting churn and CLV: Tool 2
From survivor table to CLV distribution
The survivor curve and the CLV distribution look like separate analyses. They are not. Both come straight from the rows of one table. Hover a row, or a point on either chart, and follow the same lifetime everywhere.
The survivor-value table
Hover to trace. Click or press Enter to lock a row.
Survivor curve
S(t) is the share of the original cohort still active at the start of month t+1.
CLV if the customer lasts L months
Longer realized lifetimes sit lower in the table and higher in value.
Probability of each lifetime, P(L)
Who never pays back
How likely is each possible customer lifetime value?
Left: P(L) by lifetime in months. Right: the same spikes at the same heights, moved to x = CLV(L). Both panels share one y-scale, so each dashed connector runs flat from a lifetime to its CLV twin: only the x-axis changes. The gold guides mark L = 12, 24, 36, 48 and 60 months: evenly spaced in months, but squeezed together in dollars, because discounting makes each extra year of lifetime add less. Everyone still here at n* = 1000 months is worth the maximum, max PAV less CAC, so they share one spike placed exactly there. Connectors show for the first six lifetimes and that spike; hover or click any lifetime, here or in the table, to follow it.
Model, row mapping, and source notes
Fitted inputs. Class 7 - BG and CLV.xlsx: Beta Geometric (BG)!B1:B2 supplies a and b. BG CLV!E1:E5 supplies AOF, AOV, margin, monthly contribution, and discount rate. Retention, survival, churn probability, discounting, and value formulas follow BG CLV!C9:J594.
Tail row. The visible table shows lifetimes 1 to 60 plus a 61+ aggregate. Its probability is S(60), and its displayed PAV and CLV are the probability-weighted conditional average of the remaining model tail, so the tail is not treated as a single lifetime.