On Estimating Current-Customer Equity Using Company Summary Data

Transcription

1 Journal of Interactive Marketing 25 (2011) On Estimating Current-Customer Equity Using Company Summary Data Phillip E. Pfeifer Darden School of Business, P.O. Box 6550, Charlottesville, VA , USA Available online 3 August 2010 Abstract This paper considers how to use company reported summary data to estimate current-customer equity, taken here to mean the sum of the customer lifetime values of the firm's current customer relationships. It offers general guidance about how to estimate retention rate and revenue per renewal when the reporting period spans multiple renewal periods (as, for example, when summary data are reported quarterly but customers pay and renew on a monthly basis). The paper goes on to show that traditional retention rate and revenue estimates based on the average number of customers are biased low when acquisition rates are low and vice versa. In addition, the paper demonstrates that monthly, quarterly, and annual models for customer lifetime value are not equivalent even though there exist annual, quarterly, and monthly retention and discount rates that are equivalent. The suggested improvements for estimating the equity of current customers are demonstrated first using a previously published illustrative example and then using company summary data from Netflix, Inc. For the illustrative example, the improvements make a substantial difference in the estimate of current-customer equity (15%and 25% for the two periods) despite being straightforward and somewhat obvious in retrospect Direct Marketing Educational Foundation, Inc. Published by Elsevier Inc. All rights reserved. Keywords: Customer lifetime value; customer equity Introduction The suggestion to view customer relationships as cash-flow generating assets of the firm dates back to Bursk (1966). Atthat time, Bursk recommended that the investment value of a customer relationship be used to guide marketing spending decisions. This investment value of a customer is akin to the concept now commonly referred to as customer lifetime value (CLV) (see Pfeifer, Haskins, and Conroy 2005, for a discussion of the definition of CLV). Although the most obvious use of CLV is to guide acquisition spending, firms also recognize that decisions about the treatment of current customers should be made based not on their immediate profit impact but rather on their impact on CLV. In keeping with this relationship focus, Blattberg and Deighton (1996) popularized the idea that the overall objective of marketing should be to maximize something they called customer equity, the sum of the lifetime values of the firm's customers. It was a short step from there to begin to view the sum of the CLVs of the firm's current customers as a component of firm value and to attempt to value firms by estimating the CLVs of its existing address: pfeiferp@virginia.edu. and yet to be acquired customers (see, for example, Gupta and Lehmann 2003; Gupta, Lehmann, and Stuart 2004). The purpose of this paper is to examine how to best use company-reported summary data to estimate the total CLVs of a firm's current customers. We will refer to the sum of the CLVs of the firm's current customers as current-customer equity (CCE). We will use the term total customer equity when we want to refer to the sum of the values of both current customers (CCE) and customers to be acquired in the future. We will refrain from using the less specific term customer equity. Gupta and Lehmann (2006) report that the term static customer equity is sometimes used for what we refer to as CCE. It is important to keep in mind that the CCE we will estimate does not include the values of future customer acquisitions and thus is but a component of firm value. By considering only the equity in the firm's existing customers, we avoid the challenges of forecasting the number of and outcomes from customers acquired in the future. Despite the fact that our estimate of CCE will not translate directly into a stock price, it will prove useful for valuation purposes in that it allows one to calculate the number and pattern of future customer acquisitions that is consistent with a current stock price. It will also prove useful as a summary performance metric that managers and investors might track over time /$ - see front matter 2010 Direct Marketing Educational Foundation, Inc. Published by Elsevier Inc. All rights reserved. doi: /j.intmar

2 2 P.E. Pfeifer / Journal of Interactive Marketing 25 (2011) 1 14 We tackle the problem of estimating CCE using readily available company-reported data because that is the task faced by outside investors. Obviously, managers inside the firm have access to richer and deeper data on their current customers, which will allow them to construct better estimates of CCE. After addressing the challenges of estimating CCE using currently reported data, we will offer suggestions on what additional data firms should report in order to improve outsiders' ability to estimate CCE. Our suggestions for how to better estimate CCE will be developed in the process of critically examining three prior attempts to estimate CCE from company summary data. The first attempt we will examine is the illustrative example used by Wiesel, Skiera, and Villanueva (2008) (hereafter referred to as WSV) to illustrate the insights to be gained by estimating CCE. The simplicity of this example allows us to see clearly their underlying assumptions and offer suggestions for improvement that substantially change the CCE estimate. The revised CCE estimate is 15% lower in period one and 25% lower in period two in their two-period example. Despite making a substantial difference in the estimated CCE, the suggestions are straightforward. They follow directly from simple assumptions about the customer relationships and will appear obvious, in hindsight, to many readers. The WSV illustrative example also raises questions of how to estimate CCE when multiple periods of data are available. We will argue that the approach used by WSV overreacts to current-period data. The other two attempts to estimate CCE we will examine are both directed toward Netflix, Inc., a company described in its 2008 annual report as follows: With more than 10 million subscribers, we are the largest online movie rental subscription service in the United States. We offer a variety of subscription plans, with no due dates, no late fees, no shipping fees, and no pay-per-view fees. We provide subscribers access to over 100,000 DVD and Blu-ray titles plus more than 12,000 streaming content choices. Subscribers select titles at our Web site aided by our proprietary recommendation service and merchandising tools. Subscribers can receive DVDs by U.S. mail and return them to us at their convenience using our prepaid mailers. After a DVD has been returned, we mail the next available DVD in the subscriber's queue. Netflix 2008 Annual Report The first attempt was by Gupta and Lehmann (2006) (hereafter referred to as GL), and the second was by WSV. Both take advantage of the fact that Netflix reports on a quarterly basis the number of beginning and ending subscribers and the number of gross subscriber additions during the quarter. This subscribercount data makes it possible to estimate retention rates across time for use in a simple model of CLV. Our examination of these two attempts does not question the underlying assumptions of the CLV model (constant monthly retention rate and cash flow) but instead will focus on the implementation of that model given the available data. In particular we will make suggestions with respect to how to improve the estimates of retention rate and cash flow per renewal the components of the CLV model. We will also demonstrate that the quarterly model used by WSV and the annual model used by GL are not interchangeable, and neither fit the Netflix situation in which fees and churn occur monthly. A difficult challenge in estimating CCE is using past retention rate estimates to forecast the future retention outcomes of existing customers. Given that estimated retention rates varied across calendar time for Netflix, we take the opportunity to approach this (rather naively) as a time-series forecasting problem. What we find is that estimated retention rates do not behave like a random walk without drift but instead behave as if generated by a first-order autoregressive process. The implication is that one should use neither the most recent estimated retention rate (as did WSV in the illustrative example) nor an un-weighted average of past estimated retention rates (as did WSV for Netflix) as the forecast of future retention rates. Note that the sole purpose of this time-series analysis is to check whether the most recent estimated retention rate is a reasonable forecast of future rates. The time-series analysis tells us this will not work. What will work is an important research question not addressed in this paper. Certainly the beta-geometric model proposed by Fader and Hardie (2007) shows promise, but must be extended if it is to be used with the calendar (rather than cohort) reporting of customer counts. In the next section we examine critically the estimation of CCE conducted by WSV for their simple illustrative example and suggest improvements that lead to substantially lower estimates. Then we examine the general problem of using company summary data to estimate CCE and offer general suggestions with respect to estimating retention rates, revenue per renewal, and combining the two into an estimate of CCE. Throughout that section we will compare the proposed improvements to the approaches used by WSV and GL in estimating CCE for Netflix. The paper concludes with a summary and discussion of results. The WSV Illustrative Example Table 1 replicates the illustrative example found in WSV designed to highlight the importance of reporting forwardlooking customer metrics most notably a metric they called customer equity which we shall henceforth refer to as the current-customer equity (CCE). The example calculated CCE for each of two periods using reported financial and customer summary metrics (the first six rows in the table). Table 1 Illustrative example. Period 1 Period 2 Cash Flow per customer ($CF) $10 $12 Total Cash Flow $10,500 $13,800 Customers beginning (n beg ) 1,000 1,050 Customers ending (n end ) 1,050 1,150 Additions (n add ) Cancellations (n cancel ) Churn Rate Retention rate (rˆwsv ) CLVWSV $ $ CCEWSV $58, $53,864.52

3 P.E. Pfeifer / Journal of Interactive Marketing 25 (2011) As articulated by WSV, the point of this example was that it illustrates that forward-looking customer metrics provide more and, in this case, different insights than short-term metrics. Instead of congratulating management for increasing the current period's cash flow by 31.4%, investors should ask management why it created short-term value at the expense of long-term value. The implication was that because the estimated CCE was lower at the end of period two, management had destroyed firm value and that this insight was made possible through the calculation of the CCE metric. Given the importance of the conclusion stated above (imagine, for example, that you are the manager on the receiving end of the conclusions from the above analysis), we think it useful to examine critically the assumptions underlying this analysis. We undertake this examination first in the context of this simple illustrative example and then in the next section to the more general problem of using company-reported summary data to estimate CCE. Before examining assumptions, we first point out that the calculated numbers in the last four rows of Table 1 are slightly different from those reported by WSV. The reason for this is that our calculations were accomplished using Microsoft Excel without rounding or truncation. Also note that we report the results of our calculations using an unusually large number of significant figures to make it easier for readers to verify our calculations. Let us also observe two sets of relationships among the set of six input metrics. The number of cancellations equals the number of beginning customers plus the number of added customers minus the number of ending customers (100 = 1, ,050). Thus, we could use any three of these four metrics to calculate the fourth. The other relationship is that total cash flow for the period equals cash flow per customer times ending customers ($10,500 = $10 1,050). This follows under the assumption that a cash flow of $10 occurs when the firm acquires a customer and when a beginning customer renews. The total number of renewals and acquisitions necessarily equals the number of ending customers when renewal opportunities occur one period apart. Acquisition costs, which need not be proportional to the number of customers, are ignored in this analysis because they do not affect the lifetime values of existing customers. So we will proceed with the understanding that the firm began period one with 1,000 customers, 900 of whom renewed at some point during the period. The firm also acquired 150 new customers sometime during the period. A cash flow of $10 per customer occurred with each of the 900 renewals and 150 acquisitions. This is certainly the simplest interpretation of the illustrative example and may, in fact, be the only reasonable interpretation. In our interpretation of this illustrative example there is one renewal event per period. In other words, the reporting period is short enough so that it covers one renewal event per customer. In general this will not be the case, and the problem of estimating CCE will be more difficult. With respect to Netflix, for example, summary data are reported quarterly when renewals happen monthly. The challenges of estimating CCE when the period of reporting covers multiple renewal opportunities will be addressed in the next section of the paper. Whenever one considers a present value (and both CLV and CCE are present values), it is important to articulate the time point to which future cash flows will be discounted. Here we will proceed under the assumption that the CCE for period one is meant to be the present value of the future cash flows from the 1,050 ending customers discounted back to the end of period one. This construction of CCE is consistent with the idea that CCE is the value of the firm's existing customer relationships at the end of period one. It is also consistent with the calculation in Table 1 of CCE as number of ending customers times CLV. For the purposes of the illustrative example, we will not question the assumption that all customers face the same retention rate and deliver identical cash flows. In particular, this means that new customers face the same retention rates as returning customers. Although clearly implausible in practice, our focus here is on the estimation of CCE, even if we make this simplifying assumption. The details of the WSV estimation of period one CLV are: ˆCLV WSV = CF 1+d 1+d rˆwsv = D10 1:1 = ð1:1 0:90244Þ = D55:679: The estimated CCE of $58, is simply ending customers (1050) times the estimated CLV. Here the per-period discount rate was 0.1, implying that each period is 1 year. The calculation of CCE as the product of ending customers and CLV (of those customers) is appropriate given the simplifying assumptions outlined above. This means that our remaining attention will be directed toward the estimation of CLV given the available data and the aforementioned assumptions. We will examine critically three aspects of the calculation: (1) the receipt of the first cash flow (is it certain or subject to churn?), (2) the timing of the cash flows, and (3) the estimation of retention rate. In each of the three areas we will argue that the WSV analysis was unnecessarily optimistic. Our revised estimate of CLV will turn out to be $47.196, which translates to a revised estimate of CCE of $49, an amount more than 15% below the WSV estimate. For those interested in the absolute value of CCE, the difference between the two estimators appears substantial. We will argue that the revised estimate is more accurate. The Receipt of the First Cash Flow The original WSV approach estimated CLV using the wellknown formula for CLV in a customer retention situation (in which customers not retained are lost for good) with constant cash flows and retention rate (see, for example, Blattberg and Deighton 1996). CLV = DCF 1+d 1+d r Symbol $CF represents the cash flow received from the customer (sometimes expressed as the difference between margin and retention spending), d is the per-period discount ð1þ

4 4 P.E. Pfeifer / Journal of Interactive Marketing 25 (2011) 1 14 rate, and r is the retention rate. In this example we have $CF as $10, d=0.1, and r= as estimated by WSV from the customer-count data. The assumption underlying this CLV formula is that the firm receives the initial $CF now, with certainty. As such, it represents the present value of a customer at the time of acquisition and assuming acquisition (but ignoring acquisition spending). Or, because retention rates and cash flows are constant across time, it also represents the present value of an existing customer relationship just prior to the firm receiving a $CF cash flow; but again, assuming that the firm knows it will receive that cash flow. It is as if the customer has told the firm the check is in the mail, and the firm believes it. This certainty assumption (that the firm will receive at least one more $10 cash flow) clearly does not apply to the 1050 customers at the end of the period. These are active customers, but some of them will inevitably churn before delivering the next $10 of cash flow. A better assumption would be that the firm will receive another $10 only from those existing customers who are retained. Thus, the appropriate CLV for the existing customers is $55.679, or $ In short, the WSV analysis applied a CLV formula appropriate for new customers to existing customers. The more accurate assumption is that existing customers provide value only if successfully retained, and the initial expected cash flow is r $CF rather than $CF. The revised CCE is of the original. In other words, the WSV CCE was overstated by about 10% the churn rate. If the retention rate remains constant over time, this overstatement will not affect period-to-period comparisons. But the point of the illustrative example was that CCE changes with changing retention rates. Ignoring the effect of retention on the first cash flow leads to an understatement of the change in CCE from period one to two. Whereas the WSV estimated CCE in period two decreased 8% compared with period one, the revised estimates (after implementing all three revisions) decreased by 19% (from $49,556 to $44,336). The Timing of the Cash Flows The WSV approach makes the most optimistic assumption possible with respect to the timing of the cash flows in that it assumes the initial $10 per customer occurs at the beginning of period two. The most pessimistic timing assumption would be to assume the $10 occurs at the end of period two. Given that we do not know when each customer pays (and therefore cannot be totally accurate in accounting for the timing of the cash flows from the existing customers), we propose a compromise that looks at cash flows as if they occur mid-period. The revised average CLV will be the original CLV multiplied by the discount ratio appropriate for mid-period cash flow: (1/1.1) 0.5 = An alternative assumption is that payment dates are uniformly distributed throughout the period. Such might be the case with Netflix given that customers pay on the day of the month they became subscribers. The discount multiplier for that situation can be shown to be d/[(1+d) ln(1+d)], which equals for d=0.1. Fig. 1. WSV expected cash flows versus revised expected cash flows. End of Period 1 for the illustrative example. Note that although this revision will again lead to a lower estimated CCE, it will reduce the CCEs of periods one and two by the same percentage and thus not affect period-to-period percentage comparisons. The combination of these first two revisions can be thought of as replacing the expected cash flow assumptions underlying Eq. (1) (which are appropriate for new customers) with a revised set of expected cash flow assumptions appropriate for existing customers as depicted in Fig. 1. The Estimation of Retention (Churn) Rate The models discussed here use retention rates and discount rates appropriate for the entire period. Given the assumed discount rate of 0.1, we will talk about that period as if it were 1 year. So the models are yearly models with one cash flow event per customer per year and one opportunity for each beginning customer to churn. The newly acquired customers, in contrast, became customers for the first time during the period. So we received $10 from each new customer in period one that was what qualified them as a customer. But those new customers, in our yearly model, have yet to face an opportunity to churn. Their first opportunity to churn will not come until period two when their second payment comes due 2. 2 The lost-for-good assumption underlying Eq. [1] means we need not distinguish whether the customer left for a competitor or completely abandoned the category. In more sophisticated models such as that of Libai, Muller, and Peres (2009), that distinction is critical. Here we refer to any non-retention event as churn.

5 P.E. Pfeifer / Journal of Interactive Marketing 25 (2011) Where the assumption that new customers are immune to (initial) churn becomes relevant is in the estimation of the churn (retention) rate. In short, since new additions did not have an opportunity to churn, they should not be included in the denominator when estimating churn rate. Our revised estimate of retention rate is the ratio of retained customers to beginning customers where the number of retained customers is the number of ending customers minus the number added. rˆrev = n end n add n beg : In period one this turned out to be (1, )/1,000, or 90%. When examining the WSV estimated retention rate, it is easier to express it as one minus the estimated churn, where WSV estimated churn in the traditional way as the ratio of number of cancellations to the average of beginning and ending customers: rˆwsv =1 n cancel ðn beg + n end Þ = 2 : Although the two estimators agree that the number of cancellations is 100, the revised estimator compares this to the 1000 beginning customers (who had the opportunity to cancel) whereas the WSV estimator compares this to 1025, the average number of customers. Because the revised estimated retention rate is slightly lower, it further reduces the estimated CCE. The Revised Estimate of CCE By way of summary, the WSV approach estimated CCE at the end of period one as the number of ending customers times the CLV of a customer calculated via Eq. (1) as the per-period cash flow times the well-known multiplier that accounts for the per-period discount rate and retention rate. 1+d CCE ˆWSV = n end ĈF 1+d rˆwsv =1; 050 D10 5:5679 =1; 050 D55:679 = D58; 462:93: We have proposed three changes designed to improve the estimate. All these changes remain true to the basic underlying assumption of identical customers with constant retention rates and constant periodic cash flows. The changes include (moving left to right in the equation below) replacing the optimistic beginning-of-period timing assumption with a more realistic mid-period assumption, multiplying by the estimated retention rate in recognition that existing customers are subject to churn, and revising our estimate of retention to recognize the fact that new customers (by definition) have no opportunity to churn prior to their first cash flow. Each of these three changes leads to a lower estimate of CCE: ˆCCE rev = n end ð 1 1+dÞ 0:5 rˆrev ĈF 1+d 1+d rˆrev =1; 050 0:9535 0:9 D10 5:5 =1; 050 0:9535 0:9 D55 =1; 050 0:9535 D49:5 =1; 050 D47:196 = D49; 556:22: Notice that revising the retention rate estimate from down to 0.9 had a relatively minor effect on CLV moving it from $55.68 to $55. Recognizing that existing customers are subject to churn has the biggest impact, reducing the CLV down to $ We lose another $2.30 when we are more realistic with respect to cash flow timing. Although straightforward and rather obvious in retrospect, the net/net of all the changes is a nontrivial reduction in estimated CCE of over 15%. Period Two Analysis Table 2 reports the revised estimates of retention (churn) rate, CLV, and CCE if the proposed revisions are applied to the data from period two. Note that the revisions reduce estimated CCE by a larger percentage in period two (about 25%) compared with period one (15%) primarily because the period two estimated retention rate was smaller. Note also that, using the revisions, the estimated percentage decrease in CCE across the two periods is more than twice (18.6%) what was reported by WSV (7.9%). Clearly the revisions make a difference not only in the absolute value of estimated CCE but also in the relative change in estimated CCE across periods. Note that the revised estimates for period two were carried out by simply applying Eq. (2) to the period two data. We did so Table 2 Illustrative Example Continued. Period 1 Period 2 Change (%) Cash Flow per customer ($CF) $10 $ % Total Cash Flow $10,500 $13, % Customers beginning (n beg ) 1,000 1, % Customers ending (n end ) 1,050 1, % Additions (n add ) % Cancellations % WSV Churn Rate % Retention rate (rŵsv) % CLVWSV $ $ % CCEWSV $58, $53, % Revised Churn Rate % Retention rate (r rev ) % CLV rev $ $ % CCErev $49, $40, % CCErev CCE WSV 84.77% 74.88% ð2þ

6 6 P.E. Pfeifer / Journal of Interactive Marketing 25 (2011) 1 14 simply to mimic the approach taken in WSV in which the CLV and CCE estimates at the end of period two were based solely on period two metrics. If that is what one wants to do, then we would recommend using the proposed revisions. At the end of period two, however, we have two periods of data upon which to forecast the future cash flows from existing customers. In period one, observed churn (revised) was 10%. In period two, observed churn (revised) was 19%. The question the modeler must answer is what churn estimate should be applied (at the end of period two) toward all future periods. The WSV answer to that question was 19%. We think that is too high. We think that period-to-period observed churn will not behave like a random walk without drift (in which the best prediction of tomorrow's value is the current value) especially in this illustrative example with its small number of customers and dramatic dip in estimated retention. We expect that a better estimator of period-three churn will not ignore the data from period one. These same comments apply to cash flows per customer. Just because average cash flow per customer was unusually low in the current period, for example, does not mean we should revise our expectations down to that level for all future periods. This use of current-period churn and cash flow metrics to estimate CCE produces CCE estimates that will vary from period to period to the extent that observed churn and cash flow estimates vary from period to period. We would argue that these estimated CCEs will vary more wildly than the actual (unknowable) CCE values. In addition, we should be concerned about encouraging managers to pay attention to the CCEs estimated in this manner (using only current-period data). If our conjecture is correct that the estimated CCEs overreact to current noisy results, then management attempts to improve these measures will be misguided and harmful to actual firm value. To demonstrate the sensitivity of estimated CCE to currentperiod results, we calculate what estimated CCE would have been if one additional customer had canceled during period two. If the suggestion is to evaluate management using the estimated CCE metric, the change in that metric reflects the firm value managers lost if one customer unexpectedly leaves. It is but a small step to conclude that this change in estimated CCE also represents the amount of money management can afford to spend to prevent the customer from canceling. But whereas traditional thinking would say that CLV is the appropriate limit on retention spending, the calculated change in estimated CCE (if there had been 1149 ending customers instead of 1150) turns out to be much higher $214 using the revised estimate of CCE and $236 using the WSV estimate of CCE. The numbers are so high because the lost customer changes the estimated churn rate for period two, which then gets extrapolated to all future periods. With more customers (here there are only 1150), losing one would not have such a big effect on estimated churn. But the other source of the problem is extrapolating the current churn rate into the infinite future. That approach has merit only if churn rates across time follow a random walk without drift. In the next section we will examine the time series of estimated retention rates for Netflix, Inc., to see how reasonable the random walk without drift assumption is. Estimating the Equity of Existing Customers Using Company Summary Data We turn now to the more general question of how to estimate CCE using summary data typically reported by companies, and will use Netflix, Inc., as our archetypal example. As mentioned above, what makes the general problem more difficult than the illustrative example is that the reporting period is (typically) longer than the period between payments/retention. Netflix reports financial results and customer counts on a quarterly basis, for example, whereas payments and retention occur monthly. 3 Let k be the number of retention events per reporting period. We will say that the reporting period covers k periods, where period refers to the time between retention events. For Netflix, k will equal 3 because data are reported quarterly and retention is assumed to happen monthly. When using annual data, k will be 12 if retention occurs monthly, 4 if retention occurs quarterly, and 1 if retention occurs yearly. With respect to customer counts, let n 0 be the number of customers at the beginning of the reporting period, n k be the number of customers at the end of the reporting period, and A be the number of gross additions per period. (Netflix reports gross additions for the quarter. Thus, A will be gross additions divided by 3. Given that it is not reported during the quarter the new customers were acquired, we assume they were acquired uniformly out of necessity.) With respect to financial results, let $REV be the total revenue from customers during the reporting period. We recognize that it is the present value (at the time of the renewal) of the after-tax cash flow consequences of each renewal that is required in the construction of CLV and CCE. One needs to consider taxes if CCE will be compared with the current market value of the firm. If some of the cash flow consequences of a renewal come after the timing of the renewal, the present value of those cash flows are what gets include in $CF. This all means that $CF in Eq. (1) (repeated below for the convenience of the reader) CLV = DCF 1+d ð1þ 1+d r should be referred to more properly as the present value of the after-tax cash flows associated with each successful renewal (in general, then, $CF will depend on d). We focus here on how to assign total revenue during the period to the customer activity of that period under the assumption that the present value of the 3 Netflix customers pay monthly and may cancel at any time. Because churn is possible at each month in a customer's lifetime, it seems reasonable to start with the assumption that retention/churn happens monthly. Clearly this monthly model of customer retention does not have to be correct, particularly in light of the assumption of constant retention rate. How to use quarterly data to estimated CE in situations where monthly retention rates are not constant is a subject for future research.

7 P.E. Pfeifer / Journal of Interactive Marketing 25 (2011) after-tax cash flow consequences of a renewal are a known function (constant across time) of the revenue associated with the renewal. The challenges of going from revenue per renewal to the present value of after-tax cash flows from a renewal involve questions of timing (Netflix, for example, is in the enviable position of receiving revenue prior to paying many of the costs associated with that revenue), tax effects (DVDs are a capital expenditure for Netflix that are amortized for tax purposes), and cost attribution. As one example of how to meet those challenges, GL converted their estimated revenue to estimated after-tax cash flow using a multiplier of (1 0.38) ( ) where 0.38 was the assumed tax rate, was the gross margin, and accounted for other variable costs. Both the gross margin and variable cost percentages were derived from company operating statements for the most recent reporting period. Finally we will assume that both retention and revenue are constant across both customers and periods. In other words, we invoke all the assumptions underlying model Eq. (1). Estimating Retention If there are n 0 customers at the start of the reporting period, A customers are acquired each period, and r is the per-period retention rate that applies to all customers, then it can be shown that the number of customers at the end of the reporting period will be given as n k = n 0 r k + A S k ; where S k =1+r+r 2 + +r k 1 =(1 r k )/(1 r) for r 1. Eq. (3) follows directly from the assumption of constant retention rate and constant customer acquisitions of A per period. Eq. (3) is a kth order polynomial in r for which we will not provide a closed-form solution. We will refer to the r that solves Eq. (3) for given n 0, n k, A, and k as the revised estimated retention rate, rˆrev. Note that if k=1, this general model is consistent with the illustrative example considered earlier. With k=1, we can solve Eq. (3) for rˆrev to obtain rˆrev = ðn 1 AÞ = n 0. This is equivalent to (n end n add )/n beg, our earlier expression. In contrast, the traditional estimate of retention rate starts with an estimate of churn as the ratio of cancellations to the average number of customers over the period (often implemented as the midrange between beginning and ending customer counts). Although sometimes this churn estimate for the reporting period is converted to a per-period estimate by simply dividing by k, we will assume the conversion is accomplished more appropriately as follows: ð3þ with this traditional estimate is that it uses a simple arithmetic average in the denominator of the churn calculation when, in fact, the number of customers at risk of churning changes in a predictable way within the reporting period. In general, the larger is the reporting period (k), the more severe the consequences of using this traditional estimate of retention as opposed to the revised estimate given by Eq. (3). In extreme cases involving high churn rates and long reporting periods, it is even possible for the number of canceling customers to exceed the arithmetic average number of customers, in which case the traditional estimate of retention is undefined. Fig. 2 charts monthly retention rate estimates based on quarterly data (k=3) as a function of A for a situation in which there were 1000 beginning customers and the actual retention rate was The three estimates charted are the revised estimate (which equals 0.96 to no one's surprise), the traditional estimate, and a Netflix estimate. We discuss the Netflix estimate because it appears to have been used by Gupta and Lehmann (2006). On a quarterly basis, Netflix reports monthly churn defined as customer cancellations in the quarter divided by the sum of beginning subscribers and gross subscriber additions, divided by three months (Netflix, 2006). The equation for the Netflix estimated monthly retention rate (based on quarterly data) is as follows: rˆnetflix =1 n 0 +3A n 3 n 0 +3A = 3: As we noted before, dividing cancellations by the sum of beginning and added customers leads to an underestimation of churn because customers added during the period do not face as many opportunities to churn as do beginning customers. (See Weil, 2007, for additional commentary on this point.) Dividing by three (rather than raising the corresponding retention rate to the 1/3 power) also leads to an underestimation of churn rˆ = " # 1 n ð 1 k Þ 0 + k A n k n 0 + n k : 2 Notice that if k=1, this traditional estimator is equivalent to the WSV retention rate estimate used in their illustrative example and in their examination of Netflix. The problem Fig. 2. Monthly retention rates estimated from quarterly data. (1000 beginning customers, actual retention rate of 0.96).

8 8 P.E. Pfeifer / Journal of Interactive Marketing 25 (2011) 1 14 (overestimation of retention). The end result (as shown in Fig. 2) is that the Netflix estimated monthly retention rate is biased high for all reasonable levels of acquisition activity. The traditional retention estimate, however, is biased low at low rates of acquisition, high at high rates of acquisition, and just right at somewhere in the middle. This may provide some comfort to those using the traditional estimate. To see how the three estimators compare when applied to historical Netflix quarterly data, please refer to Table 3 and the corresponding chart in Fig. 3. The Netflix estimate is consistently the highest, and the traditional estimate is consistently the lowest. At Netflix's historical acquisition rates, it appears the traditional estimate tracks the revised estimate closely albeit consistently lower. Time-Series Analysis of Estimated Retention Rate Recall from the opening section of this paper that in their illustrative example, WSV used the retention rate from the most recent period in Eq. (1) to estimate CCE. This is conceptually equivalent to using the most recent retention rate as the forecast of all future retention rates. We pointed out that this is only appropriate if the time series of retention rates was a random walk without drift. In their estimation of Netflix CCE, WSV replaced the quarterly retention rate [in the CLV formula] with the mean of Fig. 3. Monthly retention rates estimated from quarterly Netflix data. the corresponding retention rates for the previous four quarters. So when estimating Netflix CCE, WSV used a fourperiod moving average to forecast future churn (retention). What is consistent between the two examples is that both forecasted churn rates were based on the trailing year of data. The GL forecast of monthly churn used in Eq. (1) to estimate Netflix CCE at the end of 2005 was given without explanation as 4.3%. This happens to be the Netflix churn estimate for quarter 3 of Netflix also reported churn for 2005 to be 4.5% calculated as the un-weighted average of the reported Table 3 Netflix subscriber counts (000 s) and estimated retention rates. Monthly retention rate estimated from quarterly data Quarter Year Beginning Subscribers Additions Ending Subscribers Revised Traditional Netflix % 90.23% 93.29% % 89.20% 92.78% % 90.85% 93.69% % 91.55% 94.19% % 92.40% 94.39% % 92.98% 94.79% % 93.65% 95.24% % 93.44% 95.33% % 92.46% 94.41% % 92.44% 94.36% % 94.12% 95.55% % 93.19% 94.96% % 93.97% 95.27% % 94.55% 95.75% % 94.86% 96.01% % 94.63% 95.86% % 94.62% 95.69% % 94.69% 95.80% % 95.09% 96.09% % 94.41% 95.58% % 94.35% 95.39% % 94.84% 95.81% % 94.95% 95.92% % 95.11% 96.08% % 94.87% 95.79% % 94.79% 95.75% % 94.68% 95.76% , % 94.67% 95.78%

9 P.E. Pfeifer / Journal of Interactive Marketing 25 (2011) churn rates for the four quarters of So although it appears GL based their forecast of churn on Netflix churn estimates, we cannot be certain what forecasting method was used. We turn now, briefly, to the question of how to use the time series of historical revised retention rates to forecast future retention rates. In particular, we are interested in if it is best to use the trailing observation, the moving average of several trailing observations, or some other method when forecasting retention rate. As always, a time-series analysis approach is naïve and subject to many valid criticisms. (For example, early retention rates are more variable than later rates because they are based on fewer customers a fact our time-series analysis will ignore. It also may easily be the case that the underlying process generating these rates has changed at some point in the history of Netflix.) Let us be clear that forecasting the future retention outcomes of current customers is a very difficult task. It is a task, however, that one must accomplish in order to estimate CCE. The purpose of our time-series analysis is not to suggest that it is a preferred method for forecasting future retention outcomes for the reasons given above. A model such as the shifted-beta-geometric (see Fader and Hardie 2007) shows promise, but must be extended to be used with the calendar (rather than cohort) customer counts reported by Netflix and others. The purpose of the time-series analysis is limited to the question of whether it is at all reasonable to use the most recent estimated retention rate (as did WSV in the illustrative example) or a moving average of past estimated rates (as did WSV for Netflix) as a forecast of all future retention rates. Table 4 gives the sample autocorrelation function of the 28- observation retention rate time series (revised estimates). The geometric decay is characteristic of an AR(1) time-series process. Fitting the AR(1) model using ordinary regression produced the results in Table 5 and residuals with sample autocorrelation function given in Table 6. None of the sample autocorrelations in Table 6 are significantly different from zero, which suggests the AR(1) model is appropriate for this retention rate time series. The implications are that retention rates at Netflix do not behave like a random walk without drift, but instead have shown a tendency to regress to a mean. What this indicates with respect to forecasting is that we should neither extrapolate the Table 4 Sample autocorrelation Revised Retention Rates. Number of Values 28 Standard Error Lag # Lag # Lag # Lag # Lag # Lag # Lag # Sample Autocorrelations greater than two standard errors away from zero are given in bold. Table 5 AR(1) regression results. Summary Multiple R-Square Adjusted StErr of R R-Square Estimate Degrees of Sum of Mean of F-ratio ANOVA table Freedom Squares Squares Explained Unexplained E-05 Coefficient Standard t-value p-value Regression table Error Constant Lag1(Retention) b last rate into the foreseeable future nor use an un-weighted average of past rates. The s-step ahead point forecast from the AR(1) model is given as ˆr rev ðt + sþ = a 1 bs 1 b + bs ˆr rev ðtþ whereˆr rev ðtþ is the revised estimated retention rate for period T (the trailing period), a is the estimated regression intercept, and b is the estimated regression coefficient. The double hat on the point forecasts reflects the idea that this is a time-series point forecast of a future estimate of an underlying retention rate. These point forecasts decay geometrically (with decay parameter b) from the trailing retention rate to an eventual mean of a/ (1 b). Here a/(1 b) turns out to be , and the series of point forecasts made at the end of the first quarter of 2009 will decay ever so slightly from the current retention rate of down to At the end of quarter one of 2009, the forecasts from the AR(1) behave very similarly to the forecasts for a random walk without drift because the trailing observation happened to be close to the estimated long-run mean. The AR (1) forecasts would have been very different from those from a random walk without drift, however, had the trailing retention rate been far away from Thus the intuition we expressed with respect to forecasting retention for the illustrative example is consistent with the empirical behavior of the Netflix churn rates. Given that the observed churn rate in the illustrative example changed dramatically from period one to two (from 10% to 19%), the Table 6 Sample autocorrelations AR(1) residuals. Number of values 27 Standard Error Lag # Lag # Lag # Lag # Lag # Lag #

10 10 P.E. Pfeifer / Journal of Interactive Marketing 25 (2011) 1 14 appropriate forecasts of future churn rates will decay from 19% down toward some (impossible to determine given only two data points) long-run mean if churn rates in the illustrative example are mean reverting as are those of Netflix. On the other hand, the observed behavior of Netflix churn rates gives no support to the idea that the best forecast of future churn/retention is an un-weighted average of past rates. The most recent rate deserves more weight than those in the more distant past. Estimating Revenue Per Renewal As mentioned earlier, we proceed under the assumption that $CF in Eq. (1) is a known function of revenue per renewal ($RPR), and that function is constant across time. The remaining challenge in estimating CCE from company summary data is to estimate $RPR from $REV, the total revenue from customers during the reporting period. Note that it is revenue per (successful) renewal that Eq. (1) requires as opposed to revenue per customer. If a customer paying $18 per month renewed twice during the quarter and then canceled, the total revenue from that customer was $36 during the reporting period. Although the average revenue from the customer was $12 per month, in Eq. (1) we need to use the average of $18 per successful renewal. To convert $REV to average revenue per renewal requires an accounting of the number of renewals that occurred during the reporting period. Under the assumptions of uniform customer acquisitions, the number of acquisitions and renewals during the reporting period are given as follows: acquisitions = A k renewals = n 0 r S k + A r 1 r ð4þ ðk S k Þ: ð5þ The total number of transactions (defined as acquisitions and renewals) during the reporting period can be written as: transactions = n 0 r S k + A 1 ðk r S k Þ: 1 r In a situation where acquisitions and renewal revenues are reported separately, estimated $RPR can be calculated as $REV (from renewals) divided by the number of renewals calculated using Eq. (5) upon substituting rˆrev for r. In a situation where acquisitions and renewals generate identical revenues, $RPR can be estimated as $REV divided by number of transactions calculated using Eq. (6) upon substituting rˆrev for r. In situations in which revenue per acquisition is either known or a known fraction of revenue per renewal (if the firm offers a 50% discount to new subscribers, for example), then $RPR can be estimated using Eqs. (4) and (5) and some simple algebra. In situations where it is known only that revenue per acquisition is different from $RPR, it will not be possible to generate separate estimates from a single period of reporting data. ð6þ In situations where customers pay different rates (as is the case with Netflix), the proposed estimate of $RPR is built upon an assumption that rate paid is unrelated to propensity tochurn(andonecanusetheaverage rate paid in the context of the model). Of course, if propensity to churn varied with rate paid (which it almost certainly does, especially when comparing free trial memberships to the higher prices paid by satisfied, heavy-using customers), Eq. (1) would not apply. As was the case with retention rate, the revised estimate RPRrev described above is more accurate than traditional estimates because it accounts for the pattern of acquisition and retention within the reporting period. An example of a traditional estimate is the Netflix metric average monthly revenue per paying subscriber, which is akin to the more common ARPU (average revenue per user). Netflix calculates its metric as $REV (for the quarter) divided by the average of beginning and ending paying subscribers, divided by three months. Three features of the Netflix average revenue metric deserve comment. First, the metric takes advantage of the fact that Netflix reports beginning and ending paying customers (in addition to total customers). Although Netflix reports gross additions during the quarter, it does not report how many paying customers were acquired. This means we cannot model the within-quarter behavior of paying customers because we know only beginning and ending counts. And although we have modeled the churn/retention behavior of total customers, we know we cannot ignore the distinction between paying and nonpaying when it comes to estimating revenues and costs. Gupta and Lehmann (2006) did ignore the distinction and applied the Netflix reported average monthly revenue per paying customer to the ending count of total customers. WSV also used ending total customers as their basis for calculating CCE and estimated customer cash flow as a rolling four-quarter average of average cash flow per quarter per customer without mentioning a distinction between paying and nonpaying customers. Second, the average for the quarter is divided by three to reach a monthly figure. Whereas dividing by three was not appropriate when working with churn rates, it is appropriate here as monthly revenues do add together to get quarterly revenue. Finally, the average is calculated as total revenue divided by the midrange between beginning and ending customer counts. Just as was the case with the traditional and Netflix churn estimates, this is not as accurate as it could be because it ignores the number of renewals involved in the path between beginning and ending customer counts. As was the case with churn, when acquisition rates are low, this traditional estimate of average (monthly) revenue per user is too low, and when acquisition rates are high, the estimate is too high. To see this, consider 1,000 beginning customers and a retention rate of With no customer acquisitions, the firm will end up with customers at the end of the quarter and enjoy 2,766.3 successful renewals. The correct average $RPR will be $REV divided by 2, Because the average number of customers is