# CLV (Customer Lifetime Value) operations
# M:Margin, r:Retention rate, d:Discount rate
M <- 100 
r <- 0.9
d <- 0.1
CLV <- M*(r/(1+d-r))
CLV

# CLV with initial margin
CLV <- M*((1+d)/(1+d-r))
CLV

# CLV with finite setting up to 5 years
CLV_fin <- 0
for (i in 1:5){
	CLV_year <- M*( r^i /((1+d)^i) )
	CLV_fin <- CLV_fin + CLV_year
	#print(CLV_year)
}
CLV_fin

# CLV with finite setting with initial margin up to 5 years
CLV_fin <- 0
for (i in 0:5){
	CLV_year <- M*( r^i /((1+d)^i) )
	CLV_fin <- CLV_fin + CLV_year
	#print(CLV_year)
}
CLV_fin


# Real case
# Go to http://www.att.com/gen/investor-relations?pid=282
# Download excel file under 'Financial and Operational Results
# Go to sheet 'Business Segment' and 'Business Segment 2' from the excel file
# 'Business Segment' contains Revenue, Expense, and Margin
# 'Business Segment 2' churn (=1-retention rate) and number of subscribers

# Read in data
att <- read.table("C:/R/att.txt", header=F, sep="\t")


# Rename to simply names
att2 <- att[,2:9]
rnames <- c("rev","cost","mar","nsub","churn")
rownames(att2) <- rnames
colnames(att2) <- 1:8

# CLV - Infinite
d <- 0.01
rev <- 1000000*att2[1,]
cost <- 1000000*att2[2,]
mar <- 1000000*att2[3,]
nsub <- 1000*att2[4,]
rr <- 1-att2[5,]
#arpu <- rev/nsub
CLV <- mar * rr / (1+d-rr)
CLV_sub <- (mar/nsub) * rr / (1+d-rr)
rownames(CLV_sub) <- "CLV per subscriber"
CLV
CLV_sub

# CLV - Finite
d <- 0.01
rev <- 1000000*att2[1,]
cost <- 1000000*att2[2,]
mar <- 1000000*att2[3,]
nsub <- 1000*att2[4,]
rr <- 1-att2[5,]
#arpu <- rev/nsub
CLV_fin <- 0
CLV_fin_sub <- 0
for (i in 1:12){
	CLV_q <- mar*( rr^i /((1+d)^i) )
	CLV_fin <- CLV_fin + CLV_q
	CLV_q_sub <- (mar/nsub)*( rr^i /((1+d)^i) )
	CLV_fin_sub <- CLV_fin_sub + CLV_q_sub
}
CLV_fin_sub

		

# Number precision, to the 323rd decimal point
pre <- c(1e-322,1e-323,1e-324)