Collection of functions that compute Expected Customer Lifetime Value in a subscription (contractual) setting based on research by Fader and Hardie. More on Rpubs.

This approach only requires two inputs:

• Active Customers in period $t$
• Churned customers in period $t$

Given these we plug it into the shifted-beta-geometric probability model to get retention rates for any given customer in period t. Paired with spend we are able to project customer's lifetime value.

Usage

We will use the example data from paper 1 in the references section.

# Load the functions
source("lib-BG.R")

# Example from paper
# Data
activeCust = c(869,743,653,593,551,517,491)
lostCust = c(131,126,90,60,42,34,26)

# Estimate the maximum likelihood function to get the alpha, beta values
# Alternative function to estimate MLL
# estimateMLL2(active.cust = activeCust,
#             lost.cust = lostCust)$par
alphabeta = estimateMLL(active.cust = activeCust,
            lost.cust = lostCust)$par

alphabeta

## [1] 0.6677123 3.8024773

# Survival probabilities for 10 periods
periods = 1:10
sProb = survivalBG(alphabeta[1],alphabeta[2], periods)
# Churn probabilities for 10 periods
cProb = churnBG(alphabeta[1],alphabeta[2],periods)
# Get the retention rates for 10 periods
rProb = retentionRates(alphabeta[1],alphabeta[2],periods)
# create plot
dat = data.frame(sProb,cProb,rProb)
matplot(dat, type = c("b"), ylab = 'probability', xlab='period', 
        pch=1:3,col=c('darkgray','red','blue'), lty=1:3, 
        main='Shifted Beta Geometric Model Probabilities, t=10')
legend(x=1,y=0.5, legend=c("Survival Prob", "Churn Prob","Retention Prob"), 
       col=c('darkgray','red','blue'), lty=1:3, pch=1:3) 

sProb

##  [1] 0.8506300 0.7467988 0.6697305 0.6098676 0.5617912 0.5221811 0.4888802
##  [8] 0.4604211 0.4357680 0.4141671

cProb

##  [1] 0.14937002 0.10383116 0.07706834 0.05986291 0.04807638 0.03961007
##  [7] 0.03330090 0.02845911 0.02465310 0.02160086

rProb

##  [1] 0.8506300 0.8779362 0.8968017 0.9106164 0.9211691 0.9294932 0.9362273
##  [8] 0.9417872 0.9464553 0.9504304

# Discounted Expected Lifetime
DEL(alphabeta[1],alphabeta[2],discount = 0.1)

## [1] 5.920551

# Discounted Expected Residual Lifetime
DERL(alphabeta[1],alphabeta[2],discount = 0.1, renewals = 4)

## [1] 6.893253

# Expected Lifetime Value per customer assuming expected net cash flow is 100$ per period
DEL(alphabeta[1],alphabeta[2],discount = 0.1)*100

## [1] 592.0551

# Expected Residual Lifetime Value per customer who renewed 4 times
# assuming expected net cash flow is 100$ per period
DERL(alphabeta[1],alphabeta[2],renewals = 4, discount = 0.1)*100

## [1] 689.3253

References

1. How to Project Customer Retention by Peter Fader and Bruce Hardie (2007)

2. Fitting the sBG Model to Multi-Cohort Data by Peter Fader and Bruce Hardie (2007)