# Customer Lifetime Value

This is the continuation of the previous Market Analytics blog. In this post, we will cover Customer Lifetime Value.

CLV combines several of the previous ideas we have discussed and extends them to create a monetary value for each of your clients. The blog entries of this series may be found here:

- Market Segmentation
- Recommender Systems
- Market Basket Analyses
- Customer Churn
- Customer Lifetime Value (this one!)

**Introduction**

Customer lifetime value goes a step further than churn rate prediction. It uses retention (i.e. the inverse of churn) and a “discount” factor, which accounts for the decreasing value of future money to predict the expected monetary value that a customer will generate over the entire period of the relationship with your company.

CLV per period is then defined as:

Where:

- Retention Rate = 1 – Churn Rate
- Discount Rate is the decrease in monetary value of future cash flow. This factor in accounts for the general idea (even beyond the idea of inflation) that money in the future is worth less than money now.
- Margin is the gross profit expected per period, which is equal to the present value divided by the discount rate

Notice that CLV is defined as a multiple of the margin. The multiplier in turn is simply determined by how likely clients are retained in the model of a leaky bucket. When the retention rate is 0, the CLV is also zero, when the retention rate is 1, CLV is the total gross profit.

If all factors on the right-hand side are assumed constant for simplicity, with a large pool of customers and retention rate relatively high, we see that the total CLV for multiple periods will just be the number of periods multiplied by the CLV per period as expected.

Typically, the furthest we look ahead in lifetime values is 5-10 years into the future, with anything beyond that deemed too speculative to consider.

Using the cumulative CLV over multiple periods (years), we will typically find a bell-curve for the distribution of profitability.

Not only does this statistic gives an upper limit on the amount you should spend trying to capture a particular client, it also allows you to determine which clients will give you the most value to pursue and how to increase the value of existing clients.

By using recommendation systems and market segmentation, we can improve the profitability of each client, shifting more clients to the high profit regime. We can also more efficiently target low-profit customers by determining if this is due to a high churn rate or simply low spending, and much more!

Let us take a look at a common example.

**Retention Example**

Let’s take a look at a particular example. For this, we need to create a model for:

- Forecasting the remaining lifetime (in years) of clients
- An estimation of the future revenues (by year) per client
- Estimations for the costs
- Computation of the net present value of all future amounts.

The remaining lifetime can be predicted using the retention rate computed in a manner discussed in our previous blog (churn).

Future revenues per year can be computed using typical supervised learning approaches, using demographic and/or raw purchase and behavioral data of clients, or can even be estimated by unsupervised customer segmentation models (segmentation models).

Costs can be estimated per customer using standard accounting techniques or via machine learning methods.

And finally, the discounted rate, can be estimated using company specific information.

The final result for CLV over *n*-years is then given as the sum per year:

Where as before:

- r is the yearly retention rate
- d the yearly discount rate
- GC is the yearly gross contribution per customer
- M is the retention cost per customer per year

This formula is exactly how you would expect. If we take the retention cost to be zero, we are left with simply the weighted sum of revenue you expect due to customer loss and discounting.

Let’s visualize the customer lifetime values of clients that have fixed values for everything except the one variable labelled - where the default values are GC=$100, M=5, R=0.95 and d=0.05.

We have the following cumulative sum for the year-on-year value:

The red lines are varying M, the yellow varying R, the green varying d and the blue varying GC, with all else fixed. The black line is the default values mentioned above.

Similarly, just plotting the raw year-on-year value per year:

These are slightly busy figures but let’s step through the various scenarios that are most typical.

The red dashed line, where M=5, R=0.95 and d=0.05, shows a steady increase of value as you sum up the first 10 years. Such a scenario that shows only small discounting is reflected in the near straight line.

In terms of year on year projected value, the green line with the retention rate is 0.5, shows the most interesting shape. This is basically just the halving of the projected value per year as given by the formula.

Each curve represents a possible scenario for your clients. The Customer Lifetime Value with a 10 year horizon is just the value at year 10. Thus, with the relevant predictions and estimations made, each client you have will have their own value that can be used to make true business decisions.

**Final Thoughts**

Customer lifetime value is an easy concept to grasp; allowing for good understanding of your customer base, while providing a quantitative metric that each of your clients is worth in monetary value. However, it requires careful understanding of the underlying models – making use of predictions on Churn rates, expected revenue, and costs generated by clients.

This completes our Market Analytics series. The previous blog posts can be found here:

- Market Segmentation
- Recommender Systems
- Market Basket Analyses
- Customer Churn
- Customer Lifetime Value (this one!)

Anomaly detection is a common problem that can be solved using machine learning techniques. Simple density based algorithms provide a good baseline for such projects, and can be used to solve a variety of problems from defect detection in manufacturing to network attacks in IT.