Customer Lifetime Value
Italian economist Vilfredo Pareto states that 80% of the effect comes from 20% of the causes, this is known as 80/20 rule or Pareto principle. Similarly, 80% of companies business comes from 20% customers. Companies need to identify those top customers and maintain the relationship with them to ensure continuous revenue. In order to maintain a longterm relationship with customers, companies need to schedule loyalty schemes such as the discount, offers, coupons, bonus point, and gifts.
Targeting a new customer is more costly than retaining existing customers because you don’t need to spend resources, time, and work hard to acquire new customers. You just have to keep the existing customers happy. Business analyst's accurately calculate customer acquisition cost using CLTV(Customer Lifetime Value). CLTV indicates the total revenue from the customer during the entire relationship. CLTV helps companies to focus on those potential customers who can bring in the more revenue in the future.
Customer Lifetime Value (CLTV)
"Customer Lifetime Value is a monetary value that represents the amount of revenue or profit a customer will give the company over the period of the relationship". CLTV demonstrates the implications of acquiring longterm customers compare to shortterm customers. Customer lifetime value (CLV) can help you to answers the most important questions about sales to every company:
 How to Identify the most profitable customers?
 How can a company offer the best product and make the most money?
 How to segment profitable customers?
 How much budget need to spend to acquire customers?
Calculate Customer Lifetime Value
There are lots of approaches available for calculating CLTV. Everyone has his/her own view on it. For computing CLTV we need historical data of customers but you will unable to calculate for new customers. To solve this problem Business Analyst develops machine learning models to predict the CLTV of newly customers. Let's explore some approaches for CLTV Calculation:
1) You can compute it by adding profit/revenue from customers in a given cycle. For Example, If the customer is associated with you for the last 3 years, you can sum all the profit in this 3 years. You can average the profit yearly or halfyearly or monthly, but in this approach, you cannot able to build a predictive model for new customers.
2) Build a regression model for existing customers. Take recent sixmonth data as independent variables and total revenue over three years as a dependent variable and build a regression model on this data.
3) CLTV can also implement using RFM(Recency, Frequency, Monetary) values. For more details, you can refer to my tutorial.
4) Using the following equation: CLTV = ((Average Order Value x Purchase Frequency)/Churn Rate) x Profit margin.
Customer Value = Average Order Value * Purchase Frequency

Average Order Value(AOV): The Average Order value is the ratio of your total revenue and the total number of orders. AOV represents the mean amount of revenue that the customer spends on an order.
Average Order Value = Total Revenue / Total Number of Orders

Purchase Frequency(PF): Purchase Frequency is the ratio of the total number of orders and the total number of customer. It represents the average number of orders placed by each customer.
Purchase Frequency = Total Number of Orders / Total Number of Customers

Churn Rate: Churn Rate is the percentage of customers who have not ordered again.

Customer Lifetime: Customer Lifetime is the period of time that the customer has been continuously ordering.
Customer Lifetime=1/Churn Rate

Repeat Rate: Repeat rate can be defined as the ratio of the number of customers with more than one order to the number of unique customers. Example: If you have 10 customers in a month out of who 4 come back, your repeat rate is 40%.
Churn Rate= 1Repeat Rate
CLTV Implementation in Python (Using Formula)
Importing Required Library
#import modules
import pandas as pd # for dataframes
import matplotlib.pyplot as plt # for plotting graphs
import seaborn as sns # for plotting graphs
import datetime as dt
import numpy as np
Loading Dataset
Let's first load the required Online Retail dataset using the pandas read CSV function. You can download the data from here.
data = pd.read_excel("Online_Retail.xlsx")
data.head()
InvoiceNo  StockCode  Description  Quantity  InvoiceDate  UnitPrice  CustomerID  Country  

0  536365  85123A  WHITE HANGING HEART TLIGHT HOLDER  6  20101201 08:26:00  2.55  17850.0  United Kingdom 
1  536365  71053  WHITE METAL LANTERN  6  20101201 08:26:00  3.39  17850.0  United Kingdom 
2  536365  84406B  CREAM CUPID HEARTS COAT HANGER  8  20101201 08:26:00  2.75  17850.0  United Kingdom 
3  536365  84029G  KNITTED UNION FLAG HOT WATER BOTTLE  6  20101201 08:26:00  3.39  17850.0  United Kingdom 
4  536365  84029E  RED WOOLLY HOTTIE WHITE HEART.  6  20101201 08:26:00  3.39  17850.0  United Kingdom 
Removing Duplicates
Sometimes you get a messy dataset. You may have to deal with duplicates, which will skew your analysis. In python, pandas offer function drop_duplicates(), which drops the repeated or duplicate records.
filtered_data=data[['Country','CustomerID']].drop_duplicates()
Let's Jump into Data Insights
#Top ten country's customer
filtered_data.Country.value_counts()[:10].plot(kind='bar')
<matplotlib.axes._subplots.AxesSubplot at 0x7fe677a887f0>
In the given dataset, you can observe most of the customers are from "United Kingdom". So, you can filter data for United Kingdom customer.
uk_data=data[data.Country=='United Kingdom']
uk_data.info()
<class 'pandas.core.frame.DataFrame'>
Int64Index: 495478 entries, 0 to 541893
Data columns (total 8 columns):
InvoiceNo 495478 nonnull object
StockCode 495478 nonnull object
Description 494024 nonnull object
Quantity 495478 nonnull int64
InvoiceDate 495478 nonnull datetime64[ns]
UnitPrice 495478 nonnull float64
CustomerID 361878 nonnull float64
Country 495478 nonnull object
dtypes: datetime64[ns](1), float64(2), int64(1), object(4)
memory usage: 34.0+ MB
The describe() function in pandas is convenient in getting various summary statistics. This function returns the count, mean, standard deviation, minimum and maximum values and the quantiles of the data.
uk_data.describe()
Quantity  UnitPrice  CustomerID  

count  495478.000000  495478.000000  361878.000000 
mean  8.605486  4.532422  15547.871368 
std  227.588756  99.315438  1594.402590 
min  80995.000000  11062.060000  12346.000000 
25%  1.000000  1.250000  14194.000000 
50%  3.000000  2.100000  15514.000000 
75%  10.000000  4.130000  16931.000000 
max  80995.000000  38970.000000  18287.000000 
Here, you can observe some of the customers have ordered in a negative quantity, which is not possible. So, you need to filter Quantity greater than zero.
uk_data = uk_data[(uk_data['Quantity']>0)]
uk_data.info()
<class 'pandas.core.frame.DataFrame'>
Int64Index: 486286 entries, 0 to 541893
Data columns (total 8 columns):
InvoiceNo 486286 nonnull object
StockCode 486286 nonnull object
Description 485694 nonnull object
Quantity 486286 nonnull int64
InvoiceDate 486286 nonnull datetime64[ns]
UnitPrice 486286 nonnull float64
CustomerID 354345 nonnull float64
Country 486286 nonnull object
dtypes: datetime64[ns](1), float64(2), int64(1), object(4)
memory usage: 33.4+ MB
Filter required Columns
Here, you can filter the necessary columns for calculating CLTV. You only need her five columns CustomerID, InvoiceDate, InvoiceNo, Quantity, and UnitPrice.
 CustomerID will uniquely define your customers.
 InvoiceDate help you calculate numbers of days customer stayed with your product.
 InvoiceNo helps you to count the number of time transaction performed(frequency).
 Quantity is purchased item units in each transaction
 UnitPrice of each unit purchased by the customer will help you to calculate the total purchased amount.
uk_data=uk_data[['CustomerID','InvoiceDate','InvoiceNo','Quantity','UnitPrice']]
#Calulate total purchase
uk_data['TotalPurchase'] = uk_data['Quantity'] * uk_data['UnitPrice']
Here, you are going to perform the following operations:
 Calculate the number of days between the present date and the date of last purchase from each customer.
 Calculate the number of orders for each customer.
 Calculate sum of purchase price for each customer.
uk_data_group=uk_data.groupby('CustomerID').agg({'InvoiceDate': lambda date: (date.max()  date.min()).days,
'InvoiceNo': lambda num: len(num),
'Quantity': lambda quant: quant.sum(),
'TotalPurchase': lambda price: price.sum()})
uk_data_group.head()
InvoiceDate  InvoiceNo  Quantity  TotalPurchase  

CustomerID  
12346.0  0  1  74215  77183.60 
12747.0  366  103  1275  4196.01 
12748.0  372  4596  25748  33719.73 
12749.0  209  199  1471  4090.88 
12820.0  323  59  722  942.34 
Rename the column
# Change the name of columns
uk_data_group.columns=['num_days','num_transactions','num_units','spent_money']
uk_data_group.head()
num_days  num_transactions  num_units  spent_money  

CustomerID  
12346.0  0  1  74215  77183.60 
12747.0  366  103  1275  4196.01 
12748.0  372  4596  25748  33719.73 
12749.0  209  199  1471  4090.88 
12820.0  323  59  722  942.34 
Calculate CLTV using following formula:
CLTV = ((Average Order Value x Purchase Frequency)/Churn Rate) x Profit margin.
Customer Value = Average Order Value * Purchase Frequency
1. Calculate Average Order Value
# Average Order Value
uk_data_group['avg_order_value']=uk_data_group['spent_money']/uk_data_group['num_transactions']
uk_data_group.head()
num_days  num_transactions  num_units  spent_money  avg_order_value  

CustomerID  
12346.0  0  1  74215  77183.60  77183.600000 
12747.0  366  103  1275  4196.01  40.737961 
12748.0  372  4596  25748  33719.73  7.336756 
12749.0  209  199  1471  4090.88  20.557186 
12820.0  323  59  722  942.34  15.971864 
2. Calculate Purchase Frequency
purchase_frequency=sum(uk_data_group['num_transactions'])/uk_data_group.shape[0]
3. Calculate Repeat Rate and Churn Rate
# Repeat Rate
repeat_rate=uk_data_group[uk_data_group.num_transactions > 1].shape[0]/uk_data_group.shape[0]
#Churn Rate
churn_rate=1repeat_rate
purchase_frequency,repeat_rate,churn_rate
(90.37107880642694, 0.9818923743942872, 0.018107625605712774)
4. Calculate Profit Margin
Profit margin is the commonly used profitability ratio. It represents how much percentage of total sales has earned as the gain. Let's assume our business has approx 5% profit on the total sale.
# Profit Margin
uk_data_group['profit_margin']=uk_data_group['spent_money']*0.05
uk_data_group.head()
num_days  num_transactions  num_units  spent_money  avg_order_value  profit_margin  

CustomerID  
12346.0  0  1  74215  77183.60  77183.600000  3859.1800 
12747.0  366  103  1275  4196.01  40.737961  209.8005 
12748.0  372  4596  25748  33719.73  7.336756  1685.9865 
12749.0  209  199  1471  4090.88  20.557186  204.5440 
12820.0  323  59  722  942.34  15.971864  47.1170 
5. Calcualte Customer Lifetime Value
# Customer Value
uk_data_group['CLV']=(uk_data_group['avg_order_value']*purchase_frequency)/churn_rate
#Customer Lifetime Value
uk_data_group['cust_lifetime_value']=uk_data_group['CLV']*uk_data_group['profit_margin']
uk_data_group.head()
num_days  num_transactions  num_units  spent_money  avg_order_value  profit_margin  CLV  cust_lifetime_value  

CustomerID  
12346.0  0  1  74215  77183.60  77183.600000  3859.1800  3.852060e+08  1.486579e+12 
12747.0  366  103  1275  4196.01  40.737961  209.8005  2.033140e+05  4.265538e+07 
12748.0  372  4596  25748  33719.73  7.336756  1685.9865  3.661610e+04  6.173424e+07 
12749.0  209  199  1471  4090.88  20.557186  204.5440  1.025963e+05  2.098545e+07 
12820.0  323  59  722  942.34  15.971864  47.1170  7.971198e+04  3.755789e+06 
Prediction Model for CLTV
Let's build the CLTV prediction model.
Here, you are going to predict CLTV using Linear Regression Model.
Let's first use the data loaded and filtered above.
uk_data.head()
CustomerID  InvoiceDate  InvoiceNo  Quantity  UnitPrice  TotalPurchase  month_yr  

0  17850.0  20101201 08:26:00  536365  6  2.55  15.30  Dec2010 
1  17850.0  20101201 08:26:00  536365  6  3.39  20.34  Dec2010 
2  17850.0  20101201 08:26:00  536365  8  2.75  22.00  Dec2010 
3  17850.0  20101201 08:26:00  536365  6  3.39  20.34  Dec2010 
4  17850.0  20101201 08:26:00  536365  6  3.39  20.34  Dec2010 
Extract month and year from InvoiceDate.
uk_data['month_yr'] = uk_data['InvoiceDate'].apply(lambda x: x.strftime('%b%Y'))
uk_data.head()
CustomerID  InvoiceDate  InvoiceNo  Quantity  UnitPrice  TotalPurchase  month_yr  

0  17850.0  20101201 08:26:00  536365  6  2.55  15.30  Dec2010 
1  17850.0  20101201 08:26:00  536365  6  3.39  20.34  Dec2010 
2  17850.0  20101201 08:26:00  536365  8  2.75  22.00  Dec2010 
3  17850.0  20101201 08:26:00  536365  6  3.39  20.34  Dec2010 
4  17850.0  20101201 08:26:00  536365  6  3.39  20.34  Dec2010 
The pivot table takes the columns as input, and groups the entries into a twodimensional table in such a way that provides a multidimensional summarization of the data.
sale=uk_data.pivot_table(index=['CustomerID'],columns=['month_yr'],values='TotalPurchase',aggfunc='sum',fill_value=0).reset_index()
sale.head()
month_yr  CustomerID  Apr2011  Aug2011  Dec2010  Dec2011  Feb2011  Jan2011  Jul2011  Jun2011  Mar2011  May2011  Nov2011  Oct2011  Sep2011 

0  12346.0  0.00  0.00  0.00  0.00  0.00  77183.60  0.00  0.00  0.00  0.00  0.00  0.00  0.00 
1  12747.0  0.00  301.70  706.27  438.50  0.00  303.04  0.00  376.30  310.78  771.31  312.73  675.38  0.00 
2  12748.0  1100.37  898.24  4228.13  1070.27  389.64  418.77  1113.27  2006.26  1179.37  2234.50  10639.23  2292.84  6148.84 
3  12749.0  0.00  1896.13  0.00  763.06  0.00  0.00  0.00  0.00  0.00  859.10  572.59  0.00  0.00 
4  12820.0  0.00  0.00  0.00  210.35  0.00  170.46  0.00  0.00  0.00  0.00  0.00  343.76  217.77 
Let's sum all the months sales.
sale['CLV']=sale.iloc[:,2:].sum(axis=1)
sale.head()
month_yr  CustomerID  Apr2011  Aug2011  Dec2010  Dec2011  Feb2011  Jan2011  Jul2011  Jun2011  Mar2011  May2011  Nov2011  Oct2011  Sep2011  CLV 

0  12346.0  0.00  0.00  0.00  0.00  0.00  77183.60  0.00  0.00  0.00  0.00  0.00  0.00  0.00  77183.60 
1  12747.0  0.00  301.70  706.27  438.50  0.00  303.04  0.00  376.30  310.78  771.31  312.73  675.38  0.00  4196.01 
2  12748.0  1100.37  898.24  4228.13  1070.27  389.64  418.77  1113.27  2006.26  1179.37  2234.50  10639.23  2292.84  6148.84  32619.36 
3  12749.0  0.00  1896.13  0.00  763.06  0.00  0.00  0.00  0.00  0.00  859.10  572.59  0.00  0.00  4090.88 
4  12820.0  0.00  0.00  0.00  210.35  0.00  170.46  0.00  0.00  0.00  0.00  0.00  343.76  217.77  942.34 
Selecting Feature
Here, you need to divide the given columns into two types of variables dependent(or target variable) and independent variable(or feature variables). Select latest 6 month as independent variable.
X=sale[['Dec2011','Nov2011', 'Oct2011','Sep2011','Aug2011','Jul2011']]
y=sale[['CLV']]
Splitting Data
To understand model performance, dividing the dataset into a training set and a test set is a good strategy.
Let's split dataset by using function train_test_split(). You need to pass 3 parameters features, target, and test_set size. Additionally, you can use random_state as a seed value to maintain reproducibility, which means whenever you split the data will not affect the results. Also, if random_state is None, then random number generator uses np.random for selecting records randomly. It means If you don't set a seed, it is different each time.
#split training set and test set
from sklearn.cross_validation import train_test_split
X_train, X_test, y_train, y_test = train_test_split(X, y,random_state=0)
Model Development
First, import the Linear Regression module and create a Linear Regression object. Then, fit your model on the train set using fit() function and perform prediction on the test set using predict() function.
# import model
from sklearn.linear_model import LinearRegression
# instantiate
linreg = LinearRegression()
# fit the model to the training data (learn the coefficients)
linreg.fit(X_train, y_train)
# make predictions on the testing set
y_pred = linreg.predict(X_test)
# print the intercept and coefficients
print(linreg.intercept_)
print(linreg.coef_)
[208.50969617]
[[0.99880551 0.80381254 1.60226829 1.67433228 1.52860813 2.87959449]]
How Well Does the Model Fit the data?
In order to evaluate the overall fit of the linear model, we use the Rsquared value. Rsquared is the proportion of variance explained by the model. Value of Rsquared lies between 0 and 1. Higher value or Rsquared is considered better because it indicates the larger variance explained by the model.
from sklearn import metrics
# compute the R Square for model
print("RSquare:",metrics.r2_score(y_test, y_pred))
RSquare: 0.9666074402817512
This model has a higher Rsquared (0.96). This model provides a better fit to the data.
Model Evaluation
For regression problems following evaluation metrics used (Ritchie Ng):
 Mean Absolute Error (MAE) is the mean of the absolute value of the errors.
 Mean Squared Error (MSE) is the mean of the squared errors.
 Root Mean Squared Error (RMSE) is the square root of the mean of the squared errors.
# calculate MAE using scikitlearn
print("MAE:",metrics.mean_absolute_error(y_test,y_pred))
#calculate mean squared error
print("MSE",metrics.mean_squared_error(y_test, y_pred))
# compute the RMSE of our predictions
print("RMSE:",np.sqrt(metrics.mean_squared_error(y_test, y_pred)))
MAE: 595.0282284701234
MSE 2114139.8898678957
RMSE: 1454.0082151995896
RMSE is more popular than MSE and MAE because RMSE is interpretable with y because of the same units.
Pros and Cons of CLTV
CLTV helps you to design an effective business plan and also provide a chance to scale your business. CLTV draw meaningful customer segments these segment can help you to identify needs of the differentdifferent segment.
Customer Lifetime Value is a tool, not a strategy. CLTV can figure out most profitable customers, but how you are going to make a profit from them, it depends on your strategy. Generally, CLTV models are confused and misused. Obsession with CLTV may create blinders. Companies only focus on finding the best customer group and focusing on them and repeat the business, but it’s also important to give attention to other customers.
Conclusion
Congratulations, you have made it to the end of this tutorial!
In this tutorial, you have covered a lot of details about Customer Lifetime Value. You have learned what customer lifetime value is, approaches for calculating CLTV, implementation of CLTV from scratch in python, a prediction model for CLTV, and Pros and Cons of CLTV. Also, you covered some basic concepts of pandas such as groupby and pivot table for summarizing selected columns and rows of data.
Hopefully, you can now utilize CLTV concept to analyze your own datasets. Thanks for reading this tutorial!
If you would like to learn more about analyzing customer data in Python, take DataCamp's Customer Analytics & A/B Testing in Python course.
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