customer lifecycle value calulation (CLV,LCV,LTV)

clv.py

#----------------------------------------------------------
# customer lifecycle value calulation (CLV,LCV,LTV)
# python version : 2.7.10
#----------------------------------------------------------

# facilitate division
from __future__ import division

# clvBasic ----
# define clv for finite or infinite horizon(from geometric series)
# margin    : gross margin per customer(or cohort) per time period (typically a year)
# retention : retention rate for the time period(typically a year)
# discount  : discount rate(inflation accounted for)
# time      : number of time periods(typically number of years)
#             ,avg lifetime = 1/churn rate, default is zero indicating infinite horizon
# firstPay  : whether the customer pays for the first time period
# prepaid   : whether the scheme is prepaid or not
#             (note that both firstPay and prepaid cannot be False)

def clvBasic(margin
			,retention
			,discount
			,time = 0
			,firstPay = False
			,prepaid = True):
    if time == 0:
		if firstPay == False and prepaid == True:
			return margin * (retention/(1 + discount - retention))
		elif firstPay == True and prepaid == True:
			return margin * (1 + d) * (retention/(1 + discount - retention))
		elif firstPay == True and prepaid == False:
			return margin * (1/(1 + discount - retention))
		else:
			raise ValueError('Both firstPay and prepaid cannot be False.')
    else:
		if firstPay == False and prepaid == True:
			firstTerm = 0 
			begin = 1
			end = time
			return margin * sum([(retention/(1 + discount)) ** i for i in range(begin,end)]) + firstTerm
		
		elif firstPay == True and prepaid == True:
			firstTerm = margin
			begin = 1
			end = time - 1
			return margin * sum([(retention/(1 + discount)) ** i for i in range(begin,end)]) + firstTerm
		
		elif firstPay == True and prepaid == False:
			firstTerm = margin/(1 + discount) 
			begin = 1
			end = time - 1
			return margin * sum([(retention ** i)/((1 + discount) ** (i + 1)) for i in range(begin,end)]) + firstTerm
		
		else:
			raise ValueError('Both firstPay and prepaid cannot be False.')

# example (not run)
'''
clvBasic(margin = 100 \
			,retention = 0.8 \
			,discount = 0.1 \
			,time = 10 \
			,firstPay = False \
			,prepaid = True)
'''

# clvCost ----
# clv for finite horizon with contribution and retention costs
# contrib   : gross margin per customer(or cohort) per time period (typically a year)
# cost		: retention cost per time period(typically a year)
# retention : retention rate for the time period(typically a year)(1 - churn rate)
# discount  : discount rate(inflation accounted for)
# time      : number of time periods(typically number of years)
#             ,avg lifetime = 1/churn rate
# firstPay  : whether the customer pays for the first time period
# prepaid   : whether the scheme is prepaid or not
#             (note that both firstPay and prepaid cannot be False)

def clvCost(contrib
			,cost
			,retention
			,discount
			,time
			,firstPay = False
			,prepaid = True):
	if firstPay == False and prepaid == True:
		firstTerm = 0 
		begin = 1
		end = time
		conSum = contrib * sum([(retention/(1 + discount)) ** i for i in range(begin,end)]) + firstTerm
		retSum = cost * sum([((retention)**(i-1))/((1 + discount)**(i - 0.5)) for i in range(1,time)])
		return conSum - retSum
		
	elif firstPay == True and prepaid == True:
		firstTerm = contrib
		begin = 1
		end = time - 1
		conSum = contrib * sum([(retention/(1 + discount)) ** i for i in range(begin,end)]) + firstTerm
		retSum = cost * sum([((retention)**(i-1))/((1 + discount)**(i - 0.5)) for i in range(1,time)])
		return conSum - retSum
		
	elif firstPay == True and prepaid == False:
		firstTerm = contrib/(1 + discount) 
		begin = 1
		end = time - 1
		conSum = contrib * sum([(retention ** i)/((1 + discount) ** (i + 1)) for i in range(begin,end)]) + firstTerm
		retSum = cost * sum([((retention)**(i-1))/((1 + discount)**(i - 0.5)) for i in range(1,time)])
		return conSum - retSum

	else:
		raise ValueError('Both firstPay and prepaid cannot be False.')

# example (not run)
'''
clvCost(contrib = 100
		,cost = 25
		,retention = 0.8
		,discount = 0.09
		,time = 15
		,firstPay = False
		,prepaid = True)
'''