Marketing Analysis Toolkit: Customer Lifetime Value Analysis

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1 REV: JANUARY 18, 2017 THOMAS STEENBURGH JILL AVERY Marketing Analysis Toolkit: Customer Lifetime Value Analysis Introduction Customers are increasingly being viewed as assets that bring value to the firm. To nurture these assets, firms focus on three customer management strategies: (1) asset acquisition attracting new customers to the firm, (2) asset maximization maximizing the value the firm extracts from each customer, and (3) asset retention retaining existing customers for the long term. Customer lifetime value (CLV) is a metric that allows managers to understand the overall value of their customer base and to evaluate how well their management strategies are working. CLV analysis allows managers to estimate the cost of acquiring a customer and to compare that to the expected benefit of that customer s business during her purchasing life. A customer s lifetime value is dependent on three different factors: The cost to acquire the customer. To acquire a customer, a firm must spend some money. Customer acquisition is generally done through marketing programs such as advertising and/or sales promotions. Managers using CLV analysis must begin their analysis by figuring out how much it costs the company to acquire each type of potential customer. The annual profits the customer generates for the firm. Profits depend on both the amount of revenue the customer delivers to the firm and the variable costs incurred by the firm in serving the customer. Every time a customer buys from the firm, the firm receives revenue from the purchase. Some customers generate more revenue than others because they purchase products at full price rather than at a discounted price, or because they purchase more expensive products within the firm s product line. Customers who purchase more frequently or who purchase in large volumes generate more annual revenue than those who are infrequent purchasers. The annual profits generated also depend on the costs the firm incurs in serving the customer. Annual profit is calculated by subtracting the total variable cost of the products the customer buys from the total revenues obtained. In CLV analysis, contribution margin (revenue variable cost) is the correct profit measure to use. 1 1 However, please note that in many marketing cases, variable costs are not known. In cases where variable costs are not known, but the cost of goods sold (COGS) is, feel free to use gross margin (Revenues COGS) as your annual profit number. See the Pricing and Profitability Analysis Marketing Toolkit (HBS No ) for a discussion of the differences between contribution margin and gross margin. Professor Thomas Steenburgh and Professor Jill Avery (Simmons School of Management) prepared this note as the basis for class discussion. Copyright 2010, 2011, 2017 President and Fellows of Harvard College. To order copies or request permission to reproduce materials, call , write Harvard Business School Publishing, Boston, MA 02163, or go to This publication may not be digitized, photocopied, or otherwise reproduced, posted, or transmitted, without the permission of Harvard Business School.

2 Marketing Analysis Toolkit: Customer Lifetime Value Analysis The number of years the customer is likely to purchase from the firm. Different customers have different purchasing lifetimes with the firm. Some customers are highly brand loyal and, once acquired, will continue to buy from the firm for many years. Other customers are less brand loyal and will buy from the firm for only a short period of time. The Basic Customer Lifetime Value Formula In its most basic form, the CLV formula is expressed as CLV = m * L AC where m is the contribution margin generated from a customer in a year (or another time period), L is the expected purchasing life of a customer (measured in years if the annual contribution margin is being used), and AC is the up-front cost of acquiring a customer. Importantly, the formula highlights the three basic forces that drive customer lifetime value. It suggests that the most valuable customers: (1) are less expensive to acquire, (2) generate more profit to the firm in each period in which they choose to be a customer, and (3) choose to be customers for longer periods of time. A numerical example should help make this relationship clear. Suppose a manager wants to estimate the customer lifetime value of Tess, a new customer to the store. The manager estimates that the store spent $20 to attract Tess, and that the store will generate $50 of profit each year, so long as Tess chooses to be a customer. Based on historical churn rates (discussed in the next section), the manager expects that the store will keep Tess as a customer for 10 years. Therefore, the manager estimates the customer lifetime value of Tess to be $50 * 10 $20 = $480. It is worth commenting on a few assumptions embodied in this formula, both of which can be relaxed if necessary. First, the formula assumes that the profits generated from a customer are the same in each period. This assumption is primarily made to simplify the math, but it is reasonable in many situations, such as when customers pay monthly installments on a contract. Second, the formula does not take the time value of money into account because it implicitly assumes that the discount rate is zero. This assumption is problematic if customer relationships endure over long periods of time, and we will show how to relax it later in the note. Some Useful Metrics for Measuring Customer Retention The first issue that arises when attempting to calculate the CLV is how to determine the expected purchasing life of a customer. Although there are many ways to do this, the most basic approach is based on the customer churn rate, a commonly tracked metric at many companies. We will discuss the relationship between the customer churn rate and the expected customer lifetime, point out some of the assumptions that are implicitly made in this approach, and call attention to some related and useful metrics that are found in practice. 2

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

5 Marketing Analysis Toolkit: Customer Lifetime Value Analysis Continuing with the previous example, recall that the store spent $20 to acquire Tess and expected a $50 annual contribution margin from her so long as she was a customer. The churn rate of fashionconscious shoppers is 10% per year. We might choose to calculate Tess s CLV in two ways: Using the second expression, we would simply plug the values into the formula and find that Tess s customer lifetime value is $50 /.1 $20 = $480. The store spends $20 to acquire Tess and expects to receive $500 in contribution margin from her over time. The first expression is more complex, but it gives us insight into the assumptions that are being made in the formula. Using the retention rate for fashion-conscious shoppers, we assume that the probability that Tess has a relationship with the store in period t is equal to (RR) t-1. Thus, Tess s expected contribution margin is: Year Calculation Expected Contribution Margin 1 $50 * 1 $50 2 $50 * 1 *.90 $45 3 $50 * 1 *.90 *.90 $ $50 * 1 *.90 *.90 *.90 $ $50 * 1 *.90 *.90 *.90 *.90 $32.81 t $50 * (.90) t-1 Expanding this out in an Excel spreadsheet (which you should do as an exercise), we find that the expected contribution margin in Year 25 is $3.99 and in Year 50 is $0.29. If we go far enough into the future, the probability that Tess will still maintain a relationship with the store becomes very small, and therefore her expected contribution margin beyond that point is small too. We can simply sum the annual series of expected contribution margins over a long time horizon to approximate her expected contribution margin. Doing so, we would find that Tess is expected to generate $ of contribution margin in the first 25 periods and $ of contribution margin in the first 50 periods. Although this formula is more complex, it explicitly shows how much of the expected contribution margin is being generated in periods far into the future. We might worry about this if these values are large. Would we really expect Tess to be a customer 50 years in the future? If so, how much do we trust the assumptions of our model to make these predictions? Furthermore, shouldn t we be concerned about the time value of money? Incorporating the Time Value of Money into CLV Analysis The simple CLV formulas previously discussed ignore a very important financial fact: that money received today is more valuable than money received in the future, given that the firm can take money received today and invest it to generate interest income. Here is a brief summary of the time value of money and its formula. 5

6 Marketing Analysis Toolkit: Customer Lifetime Value Analysis The present value (the value today) of a stream of cash flows that will be received in the future is calculated as follows: PV = FV t 1 + i ( ) t 1 where t represents the period (measured in years or months), FV t is the value of each cash flow at time t in the future, and i is the firm s annual discount rate, also called the hurdle rate, or opportunity cost of capital. This represents the annual interest rate the firm could obtain by investing the cash. We can think about the annual contribution margins that a customer will generate over his or her expected lifetime as a series of cash flows that extend into the future. Thus, we can use the present value formula to help us discount those cash flows back to a present value by incorporating the time value of money into our CLV formulas. This yields a more advanced CLV formula: 2 CLV = m * RR t 1 AC 1+ i ( ) t 1 In this formula, the term m * RR t 1 ( 1+ i) t 1 represents the discounted expected contribution margin from a customer in period t. This CLV formula is equivalent to the more basic CLV formula if the discount rate is assumed to be 0 (i.e., if a dollar tomorrow is just as valuable as a dollar today). As before, summing the discounted expected contribution margins across the years in the customer s lifetime yields the simpler expression: 1 + i CLV = m * 1 + i RR AC Again, the benefit of using this form of the formula is that it is easier to calculate. Let us return to the example one last time to incorporate the idea of the time value of money. Recall that the store spent $20 to acquire Tess and expected a $50 annual contribution margin from her so long as she was a customer. The churn rate of fashion-conscious shoppers is 10% per year. Further assume that the firm s discount rate is 12% per year. 2 Gupta and Lehmann (2005) present a slightly different version of this formula. In their derivation, they assume that it is possible for a customer to end the relationship in the first period. This would change the expected lifetime calculation. 6

7 Marketing Analysis Toolkit: Customer Lifetime Value Analysis If we simply plug the values into the previous formula, we find that the CLV is $50 * ([1 +.12]/[ ]) $20 = $ if we incorporate the time value of money into our analysis. This compares to $480 if we do not. We can arrive at the same number by calculating each year s expected contribution margin and then summing across the series. According to the discounting formula, we should discount the expected contribution margin in period t by the factor 1/(1 + i) t-1. Given a discount rate of 12%, the discount factor in year 1 is 1, in year 2 is 1/(1 +.12) =.893, in year 3 is 1/(1 +.12) 2 =.797, and so on. The discounted expected contribution margin becomes much smaller in the future due to the time value of money. In the second period, the contribution margin is $50 if Tess chooses to remain a customer, the expected contribution margin is $45 since Tess may decide to end the relationship, and the discounted expected contribution margin is $40.18 considering that Tess may decide to end the relationship and money in the future is worth less than money today. The table below summarizes these quantities for the first five years of the store s relationship with Tess: Year Expected Contribution Margin Discount Factor Discounted Expected Contribution Margin 1 $ $ $ $ $ $ $ $ $ $20.85 t $50 * (.90) t-1 1/(1 + i) t-1 The table shows that the high discount rate significantly affects the calculation of Tess s CLV. By the fifth year, the difference between her expected contribution margin with and without discounting is $32.81 $20.85 = $ Given the discounting, there is very little difference between the CLV calculated using an infinite time horizon ($234.55) and the CLV using just the first 25 years of the relationship ($233.47). We leave these calculations as an exercise. Calculating Customer Lifetime Value for a Market Segment Managers can use CLV to calculate the lifetime value of different market segments. For example, managers can assess whether women are more profitable customers than men, whether customers who purchase from the firm over the Internet are more profitable customers than those who purchase through retail stores, or whether customers in the United States are more profitable than customers in Brazil. These types of calculations can help managers decide which market segments to target. Managers can compute and compare the customer lifetime value of an average customer in a market segment, or they can use the CLV of the average customer in a market segment and the size of the market segment to calculate the lifetime value of all customers in the market segment. CLV (market segment) = CLV of an average customer * number of customers in segment 7

8 Marketing Analysis Toolkit: Customer Lifetime Value Analysis Using CLV Analysis to Guide Marketing Decision Making Marketers use CLV analysis to inform many different kinds of marketing decisions. The primary decision areas where CLV analysis is helpful are outlined below: To decide which type of customer (or customer segment) would be more profitable to target. When marketing resources are constrained, marketers often need to prioritize which customer segments to target with marketing activity. CLV analysis can help make this decision by illuminating the profitability of different segments. Marketers who are prioritizing their marketing spending can focus on segments with higher CLVs than segments with lower CLVs. To decide when to scale up or scale down marketing expenditures for a particular customer. CLV is also useful when allocating marketing resources across customers. Many marketers use a tool called the customer profitability pyramid to rank their customers by their CLV. Customers who have the highest CLV go into the top tier and are labeled platinum. These are the customers in whom the marketer wants to invest and these are often the customers who receive special concierge levels of service. Below the platinum level come customers who are labeled gold and silver. These customers, although less profitable than the platinum customers, still return a positive CLV to the firm and thus are worth serving. However, the marketer may consider scaling up marketing expenditures toward customers in the higher tiers, while scaling down marketing expenditures toward customers in the lower tiers. To decide when to fire a customer. The lowest level in the customer profitability pyramid is for lead customers, customers with a negative CLV. These customers do not contribute incremental profitability to the firm, perhaps because they purchase infrequently, they purchase low-margin products, and/or they have high costs-to-serve. Sometimes firms decide to fire their lead customers as a way of increasing profitability. For example, American Express paid customers $300 to end their relationship with the firm, to disentangle itself from customers with high risk of defaulting on their credit card debt. Sprint/Nextel canceled the service contracts of 1,000 of its cell phone subscribers because they called customer service for help too often, driving up their cost-to-serve. Running CLV analysis can help marketers determine which customers are no longer contributing positive value to the firm, so that they can be considered as candidates for firing. To decide how much to spend to acquire a new customer, retain an existing customer, or try to cross-sell or up-sell additional products to existing customers. CLV analysis can guide marketing spending decisions pertaining to customer acquisition programs, customer satisfaction programs, customer retention or loyalty programs, and cross-selling or up-selling programs. Understanding the CLV of a particular customer (or customer segment) gives a marketer a sense of how much she should spend on marketing to that customer. Let us consider the example of Amy. Amy is a prospect for a cell phone company. She is projected to generate $100 per year in profits and stay with the company for three years. o Customer acquisition. Firms should not spend more than the CLV of a potential customer to acquire that customer. The cell phone company should be willing to spend up to $300 to acquire Amy. Why? Because Amy will generate ($100 * 3) = 8

9 Marketing Analysis Toolkit: Customer Lifetime Value Analysis $300 in profits for the firm over her lifetime as a customer. If it costs more than $300 to acquire Amy, the firm should not target her with marketing efforts. o o Customer retention. Firms use loyalty programs or programs designed to increase customer satisfaction to improve retention. They also use long-term contracts and switching charges to increase the stickiness of the customer relationship, making it harder for a customer to defect to the competition. Firms should not spend money on retention programs unless the resulting increase in retention results in a CLV that is high enough to cover the cost of the investment. If the cell phone company launches a loyalty program that it projects will increase Amy s loyalty to the company, causing her to stay with the company for five years (instead of three), then the firm should be willing to spend the difference between Amy s projected CLV with the loyalty program ($100 * 5) and Amy s current CLV ($100 * 3), which equals $200 to execute the loyalty program. Customer margin expansion. Firms try to up-sell existing customers to highermargin products or cross-sell them additional products to increase the revenues they receive from them while they are customers. Firms can also expand customer margins by encouraging customers to use self-service operations to reduce the firm s cost of serving them. Firms should not invest in up-selling or cross-selling activities unless the resulting increase in profits from the sale of these products results in a CLV that is high enough to cover the cost of the investment. Thus, understanding CLV allows a manager to know how much money to expend on acquiring, serving, or retaining a customer. The fundamental decision rule is to invest if the projected increase in a customer s CLV as a result of running the marketing program is greater than the cost of the marketing program. References Gupta, Sunil, and Donald R. Lehmann. Managing Customers as Investments: The Strategic Value of Customers in the Long Run (Philadelphia: Wharton School Publishing, 2005). 9