By Norbert Schumacher, Ph.D., Director of Loyalty Research, Maritz Loyalty Marketing

Transcription

1 Customer Lifetime Value: The Type of ROI Worth Caring About By Norbert Schumacher, Ph.D., Director of Loyalty Research, Maritz Loyalty Marketing Marketing literature is rife with methodologies and theories on increasing a company s return-on-investment (ROI). Maximizing ROI is the marketer s version of bloodletting: a wholly unscientific, widely adopted practice that experts and pundits recommend without regard to the potentially damaging consequences. Instead, another more appropriate measurement option exists Customer Lifetime Value (CLV), a measurement of customers time-discounted cash flow over the lifetime. Unlike ROI, this approach aligns marketing with shareholder interests. Why ROI Is Not Enough One interpretation of ROI, particularly in the marketing context, is a general financial overview. A more defined interpretation of the term is specifically the ratio of net benefits divided by costs, which ultimately provides a sense of the rate at which expenses are turned into profits. A more literal use of ROI gives rise to multiple interpretations of the term, each springing from differing views of the details surrounding the constituents of benefits and costs. For example, are the benefits calculated after taxes or before? Are benefits and costs time-discounted? This range of choice in the definition of ROI is a red flag that the metric is more arbitrary than most marketers know or want to admit. ROI owes its popularity to a lack of knowledge merging between the disciplines of marketing and financial economics. In order to analyze a company s investments, marketing professionals and financial theorists must work together to eliminate subjective ROI measurement tools and look at alternative methods of measuring costs vs. benefits based on Net Present Value (NPV), which measures the excess or shortfall of cash flows, in present value (PV) terms, once financing charges are met. Within corporate finance, there is universal consensus that capital budgeting decisions should be measured against NPV because it is aligned with shareholder goals. Should the NPV metric be used exclusively or as an additional ingredient in a marketer s stew of other financial metrics, such as ROI, internal rate of return (IRR) and Payback Period? Because NPV, unlike ROI, IRR and Payback Period, is the metric aligned with shareholder goals, marketing managers should also use this measurement tool with their own investments. Consider a scenario where shareholders demand at least 12 percent per year compounded annually. A capital budgeter is presented with several investment options: Investment 1: Buy a fallow piece of land today for $200,000, which someone else is contracted to pay $300,000 two years from today. Investment 2: Walk across the street to pick up a $10 bill. Investment 3: Do nothing at this point. Investment 4: Buy a fallow piece of land today for $200,000, which someone else is contracted to pay $350,000 five years from today. If you recognized that the investments were ordered in decreasing order of desirability, then you were using a method similar to the NPV rule. Using the ROI rule, one might be tempted to rank the investments as follows: Investment 2 Investment 4 Investment 1 Investment 3

2 However, because Investment 4 actually destroys value, it s better to do nothing, allowing shareholders to invest in other, smarter ventures. A manager using ROI metrics would not have come to that conclusion and would have been at odds with shareholders. In addition, for many marketers, the stratospheric level of ROI for Investment 2 is a siren song, but using NPV showcases Investment 1 as the better choice. The dilemma for many marketers in making their decisions to use NPV is that many times they are in pursuit of more proximate goals, such as acquiring new customers or increasing customer loyalty and customer spend. But it is important to not lose sight of the ultimate goal because while enhancing customer loyalty, for example, is often aligned with the goals of the shareholders, there is an optimal level of customer disloyalty. Finding the optimal level of customer disloyalty involves evaluating the NPV of a customer. Raise NPV not ROI The scenario demonstrates the flawed rationale for the literal interpretation of maximizing ROI. NPV aligns shareholders interests and consistent measurements, encouraging companies to review their customers time-discounted cash flow over the lifetime. The tailored approach to this particular type of NPV statistic is the Customer Lifetime Value (CLV). It, therefore, stands to reason that analysts should estimate CLV in relation to the effectiveness of a marketing stimulus on customer behavior. For example, the choice of whether an acquisition campaign is worthwhile from the shareholders perspective rests on the actual response rate lift, CLV of the acquired customer, along with the average cost of acquisition of the customer via the campaign (i.e. the NPV of the tactic). If the average cost of acquiring a new customer exceeds CLV, then the campaign is wasteful. Wait! Avoid the Sunk Cost Fallacy In calculating CLV, as with any NPV calculation, it is important to avoid the sunk cost fallacy, which considers past cash flow. The avoidance of this common fallacy is especially important in the analysis of customer loyalty where one might be tempted to account for acquisition costs of existing customers. To estimate CLV on existing customers, however, one should only assess present and future cash flows. In other words, the lifetime in Customer Lifetime Value is somewhat misleading. Perhaps a better name for the metric that marketing professionals should focus their attention on is Future Customer Lifetime Value. Thus, the success of a loyalty tactic should be measured against changes to the remaining lifetime value of the customer. Of course, acquisition costs should have an influence on prospective customers CLV. Wouldn t it just be easier to measure something else? One common complaint with the CLV metric is the difficult task of identifying the future and long-term effects of customer behavior in terms of attrition and spend levels. In contrast, it seems plausible to measure actual customer behavior over the course of the past year or two in order to assess the financial impact of a past marketing campaign. Also, because the math involved in CLV is complex, it would be easier to measure something else. However, sweeping away the excess long-term value of an investment that doesn t fit into an arbitrarily defined timeframe is liable to cause serious under-pricing, leading to poor decisions. Though the CLV calculation can involve advanced econometric techniques and/or subtle entrepreneurial judgments, one should not shirk obligations to the shareholders by estimating something irrelevant to them.

3 Back-of-the-envelope CLV Even, the act of measuring CLV has costs to the shareholders. It often pays to rely on heuristics and back-of-the-envelope calculations, rather than a full-bore econometric expedition. The choice should be guided by the size of the marketing investment. It makes little sense to spend $50,000 to justify a $40,000 investment. of 30 percent. The cost of capital for the firm is 12 percent. The campaign has a response rate of 0.5 percent and a campaign cost of $1 per prospect. The CLV of customers, given the prospective customer is acquired, within this segment is: The simplest non-trivial customer lifetime value formula looks something like: Therefore, the expected value of the NPV of the acquisition tactic on a customer-by-customer basis is: P is the annual profitability of a customer, r is the (continuously compounded) annual discount rate (i.e. the cost of capital) and L is the expected lifetime of the customer in years. If one doesn t know L, but has the annual attrition probability, then the equivalent CLV formula takes the following form: Or more simply calculated as E[NPV]=.5% x $ $1, which is approximately $0.05 per prospective customer. Because the NPV is positive, the campaign increases shareholder value and is determined successful. It would pay to either duplicate or continue the campaign in the future. ln is the natural log function and a is the annual attrition probability. The above model for CLV is a mathematical idealization in which customers attrite in a continuous random fashion, while others yield a continuous stream of profits, in contrast to reallife situations where customers spend in lump-sum amounts. Often, this idealization is a good approximation and offers consistent results. Example 2 Suppose a loyalty program is targeted to a segment of customers, who in the absence of a program, have an annual profit of $100 per year and an annual attrition rate of 30 percent. The cost of capital for the firm is 12 percent. The proposed loyalty program costs $2 per customer per year (i.e. $2 of customer annual profit is lost in the form of rewards costs) but would decrease annual attrition from 30 percent to 27 percent. The value of a customer not enrolled in the loyalty program is: Consider the following examples to understand how CLV, or the NPV of a customer, is applied in context: Whereas, the value of a customer active within the program is: Example 1 Suppose an acquisition campaign is targeted to a segment of prospective customers who, if acquired, would have an annual profitability of $100 per year and an annual attrition probability Because $ is greater than $209.79, the program increases shareholder value and is successful. Within this segment, the CLV can be enhanced via this loyalty program.

4 Optimizing the funding rate of a loyalty program involves tradeoffs between annual customer profitability and decreased attrition. The objective for a loyalty marketing analyst should be to find the optimum fund rate maximizing CLV. This statistical exercise is tricky and involved but has a similar flavor to standard price elasticity estimation. Measuring Customer Lifetime Value The back-of-the-envelope CLV calculation assumed that we could crisply define a customer and that we knew the customer attrition rate. However, it is difficult to define customer let alone customer attrition depending on the transactional relationship of the business with the customer. To this end, Peter Fader & Bruce Hardie of Wharton School of Business and London Business School, respectively, have popularized some useful relationship distinctions: Companies have either continuous or discrete opportunities to manage relationships with customers. The relationship between a company and its customers is either on a contractual or a non-contractual basis. The common thread in distinguishing survival analysis from other types of statistical analysis is that lifetimes are positive numbers and a lifetime lends itself conceptually to a hazard rate or failure rate. Consider the principle that the mortality rate of a 10-year-old child is lower than that of either a 90-year-old or a newborn. Human mortality follows what some call a bathtub curve, an idea that mortality rates actually decrease throughout childhood, until age 10, when the mortality rates start to increase. In marketing, the lifetime of customers is not as complicated. Customer hazard rates typically follow a decreasing hazard rate, as the risk of a tenured customer s attrition is much lower than a new customer s. One other prominent feature of survival analysis is the notion of censoring. Some customer lifetime rates cannot be observed because the start of the customer s relationship with your company or the exact end is unknown. In other words, all the analyst knows is that the customer s relationship is at least as old as a certain age. Statistical software supporting the analysis of survival data includes, at a minimum, the ability to handle censored data in addition to the aforementioned hazard rate estimation. Continuous / Contractual Relationship (Credit Card) The statistical theory of measuring lifetimes when the end of a customer s interaction with your brand is unambiguous (contractual) and can occur at any time (continuous) is vast. In statistics, this body of theory is known as survival analysis. Time is the salient feature being predicted or estimated. Usually, the survival data analysis follows a generalized linear model framework, whereby the modeling of lifetimes is in the same vein as ordinary linear regression and logistic regression. The result: the length of a customer s lifetime (the dependent variable) can be predicted on the basis of independent variables. Also, creative statisticians studying the topic, as well as survival analytic software, have developed exotic frameworks, such as survival trees, neural networks and random forests, to name a few. Continuous / Non-contractual Relationship (Retail) Problems occur in the lifetime/attrition measurement story in the retail environment, where identifiable customers reveal their status as a customer through transactions, but they never officially reveal their status as non-customers.

5 One flawed construction is to arbitrarily declare a customer as attrited if he has not participated in a recent transaction. For example, if a customer, on average, transacts twice a year, but hasn t made a transaction in the past year, he perhaps can be defined as attrited. But, this is a perilous approach for an important reason: the chance, under standard assumptions, that a two-purchase-per-year customer will not make a transaction in any given year-long period is exp(-2) = 13.5 percent. In other words, this approach is systematically prone to confuse lowfrequency customers with attrited customers. A better approach in defining attrition in this environment is to abandon rigid distinctions in customer attrition and adopt a flexible notion, where customer attrition is described in terms of probabilities. Unfortunately, this approach turns measuring customer lifetimes from the advanced subject of survival analysis into something much more complicated. The seminal approach to this type of attrition/survival modeling is the Pareto / Negative Binomial Distribution model by David Schmittlein, Donald Morrison and Richard Colombo. It gives a very systematic, logical and sensible answer to the following questions: What is my attrition rate? How likely is it that a given customer is going to make a transaction (given attrition and purchase frequency)? The challenge is that in contrast to the classical survival models, the continuous opportunity/non-contractual model is not well supported by software. The construction of the statistical model involves manual development of a very complex likelihood function involving somewhat exotic functions that don t typically appear on a calculator. Discrete / Non-contractual (Prescriptions, Event Attendance) The discrete/non-contractual setup also is complicated and requires statistical software to accommodate the model. The simplest approach is to assume all customers conduct a transaction at every known time (e.g. prescription refill) with probability p. With probability (1-p), the customer takes his business elsewhere, but remains a customer because he will possibly make a transaction in the future. Similarly, one assigns a probability to represent the probability of attrition; therefore, 1- is the probability that the customer is still a customer at any discrete period of time. Because all events are categorical (e.g. attrited/non-attrited) the modeling of times is an easily managed geometric distribution. The probability that a customer is attrited, given recent events, is easy to derive via Bayes Theorem, a probability theory that relates conditional probability. In order to clarify measuring the lifetimes of non-contractual customers, consider a customer in a discrete setting who makes a purchase (e.g. fills a prescription at a pharmacy) with probability p, with a chance of customer attrition at any period. Suppose the last two prescriptions were not filled because the customer filled it elsewhere. Is the customer willing to refill in the future (active) or unwilling to fill in the future (attrited)? Note that, in this example, p, or the probability he will refill the next time, is akin to the notion of frequency, whereas the phrase last two is akin to the notion of recency. Here is the answer: The generalization of this formula to values of customer recency other than two is: and etc. These fuzzy customer attributes defining customers as customers probabilistically are important. Marketing managers contemplating a mail piece, for example, would certainly first want to know if a customer really still is a customer and therefore should have interest in these

6 quantities. Another critical use is in the determination of the expected number of future purchases given values of customer recency. The longer the time span since the last purchase, the more certain one can be that the customer has attrited thereby reducing the expectation of number of future purchases. This is key in determining customer lifetime value. Paul Berger, Bruce Weinberg and Richard Hanna advocate a variation of this approach that assumes all customers probabilities of purchase p and attrition rates are different across customers. In this case, the heterogeneity is usually introduced via a Beta distribution across both parameters. As Beta functions are introduced, the model becomes considerably more complicated. However, it is still possible to implement this model via Excel. This variation, incidentally, generalizes the hazard rate, which is flat in the previous example (i.e. tenured customers attrite at the same rate as new customers) to the more realistic decreasing hazard rate (where tenured customer decrease at a lower rate than new customers). Discrete / Contractual Relationship (Insurance Policy) This probability model is simpler than the discrete/noncontractual, as we assume that a customer cannot miss a discrete transaction without declaring him attrited. Similar to the previous calculation, it is assumed that attrition falls under a geometric distribution and introduces customer heterogeneity via a Beta distribution. This model can be fitted via Excel, and the customer attrition rates/lifetimes are inferred. The Last Word It is misguided to cling to the unscientific goal of maximizing ROI in the literal sense. Instead, managers should embrace NPV, which translates into examining investments from the standpoint of changes to CLV. The dominance of NPV in financial economics demonstrates the importance of CLV within marketing. However, while building a business case for a marketing initiative around CLV is not simple, the rewards are well worth the investment. ML / Maritz Inc.