# Marketing Analysis Toolkit: Customer Lifetime Value Analysis

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3 Marketing Analysis Toolkit: Customer Lifetime Value Analysis Let s begin with a few definitions: The churn rate (CR) is defined as the percentage of customers who end their relationship with the company in a given period. The churn rate is typically defined at the segment level, and it is implicitly assumed that all individuals in that segment have the same probability of ending the relationship. The churn rate is typically tracked either by year or by month. The retention rate (RR) is a related metric that measures the percentage of customers who continue their relationship with the firm in a given period. By definition, RR = 1 CR The survival probability (s) is the probability that a customer has a relationship with a firm during a given period. It is typically assumed to be 1 in the period in which the customer joins the firm. In each subsequent period, a customer may choose to end the relationship with the firm, so the survival probability is modeled as decreasing over time. The series of survival probabilities are useful in CLV analysis because they are needed to determine the expected contribution margin in a given period. The series of survival probabilities are commonly determined by using the retention rate as a proxy for the probability that a customer leaves in a given period. If we assume that the retention rate does not change over time, we can determine the series of survival probabilities by assuming that: (1) The probability that a customer has a relationship with the firm in the first period is 1. (2) The probability that a customer has a relationship in the current period is equal to the probability that the customer had a relationship with the firm in the previous period multiplied by the probability that the customer does not end the relationship in the current period (the retention rate). This implies that: s 1 = 1 s 2 = s 1 * RR s 3 = s 2 * RR s t = RR t 1 The expected purchasing life (L) is the number of periods that a customer is expected to continue the relationship with the firm. If we assume that: (1) the churn and retention rates do not change over time, and (2) it is possible for a customer to remain with the firm over an infinite time horizon, then the following relationships hold between the expected purchasing life, churn rate, and retention rate: 3

4 Marketing Analysis Toolkit: Customer Lifetime Value Analysis L = 1 CR = RRt 1 An example helps make these ideas concrete. Suppose Tess is a fashion-conscious shopper who is brand loyal. We know the customer churn rate of the fashion-conscious segment is 10% per year. Thus, the retention rate of the fashion-conscious segment is 90% (1 10%) per year. If we assume that all fashion-conscious shoppers have the same chance of ending the relationship in a given period (so the segment churn rate can be interpreted as the probability that Tess herself stops being a customer) and that the customer churn rate does not change over time, we can easily compute Tess s survival probabilities for all subsequent years and her expected purchasing life. By definition, the probability that Tess is a customer in year 1 is 1. The probability that Tess is a customer in year 2 is the probability that Tess is a customer in year 1 multiplied by the probability that Tess continues the relationship in any given period: s 2 = 1 *.9 =.9. By similar logic, the probability that Tess is a customer in year 3 is s 3 =.9 *.9 =.81, in year 4 is s 4 =.81 *.9 =.729, and so on. Tess s expected purchasing life is L = 1/.1 = 10 years. CLV Expressed in Terms of Survival Probabilities To make the contribution of each future period clear, the CLV formula is commonly expressed in terms of survival probabilities: CLV = ( m * s t ) AC where m and AC are as previously defined, t represents the period (month or year), and s t is the probability that a customer maintains a relationship with the firm in period t, The term m * s t is equivalent to the expected contribution margin generated by the customer in period t. It accounts for the possibility that the customer may either choose to end the relationship in the current period or has already chosen to do so in a previous period. If we are willing to assume that the churn and retention rates do not vary over time, we can write: CLV = ( m * RR t 1 ) AC Summing this over all time periods yields the simple formula: CLV = m CR AC Both expressions are useful in their own way. The first has the advantage of explicitly showing the expected contribution margin in each period, whereas the second is easier to calculate. 4