Reconciling and Clarifying CLV Formulas

Peter T. Fader

Bruce G. S. Hardie вЂ

March 2012



A standard component to many modern-day Marketing programs is a case or physical exercise in which college students are expected to compute client lifetime value (CLV). Commonly they are presented an average retention rate ur, an average net cashflow of $m every period (having accounted for " account maintenance” costs), and an assumed discount level d. Given these advices, they are asked to determine the lifetime value of any customer; observe, for example , Mart´ınez-Jerez and Dillon (2007) and McGovern (2007).

Although these inputs are fairly related across these types of exercises, the formula which the students are expected to use in order to complete this task will depend on which in turn CLV studying has been presented to these people.

• In the event that given Blattberg et approach. (2008) or perhaps Steenburgh and Avery (2011), they will make use of

m(1 + d)





• If presented Capon (2007), Kotler and Keller (2012), or Lehmann and Winer (2008), they will use


CLV sama dengan




• If given Ofek (2002) or Davis (2007), they will make use of






c 2012 Philip S. Fader and Bruce G. S. Hardie.


one particular


This document can be found

(In accounting for right after in notation across the over references, customer acquisition costs have been ruled out from these kinds of formulas. ) What is rather disconcerting is the fact a large number of each of our colleagues around the globe who are teaching consumer lifetime benefit in Promoting courses are unaware of the existence of these " competing” formulas and for that reason do not phone attention to the interesting and important factors that underlie these kinds of differences. With this note, we all cast light upon these types of differences and, in so doing, stimulate the need for learners to better know what they are learning (and, in some cases, for instructors to better know what they are teaching).


Learning the Different Remedies

The answer to the question which formula is the " correct” one is determined by two elements: i) whether we range from the customer's 1st payment in the calculation, and ii) whether the net cash flow associated with each period can be " booked” at the beginning or perhaps the end in the period. This leads to the three cases illustrated in Figure 1 )

Period you

Period 2


Period three or more













Case you:

Case 2:


Case 3:



Determine 1: Three CLV computation scenarios

Prior to we look at each situation, let us notice the basic statistical result to get an endless geometric series which is used in all of the three circumstances: в€ћ

kn =



, 0 < t < 1 )



• Circumstance 1: We all receive $m when the " contract” with all the customer is definitely initiated (i. e., by time t = 0). The customer renews their deal at the beginning of Period 2 with probability ur, in which case we all immediately acquire another $m, which we discount simply by 1/(1+d), and so forth. Therefore , the expected consumer lifetime value is calculated as follows: one particular 1

Provided the probabilistic nature associated with an individual's " survival” being a customer to period to, we are calculating the anticipated customer life-time value (given the various underlying assumptions) and therefore write E(CLV ), certainly not CLV. All of us strongly recommend this change of notation in all discussions and demonstrations of customer life span value.



mr 2



(1 + d) (1 + d)2

E(CLV ) = m &




3rd there’s r



which, remembering equation (4) with e = r/(1 + d),


m(1 + d)



Neglecting acquisition costs, this variety represents the expected life span value of an as-yet-to-be-acquired buyer, and is an uppr bound intended for how much we might be ready to spend to be able to acquire a fresh customer.

• Case 2: This is the identical to Case you except that we do not include the primary net inflow of cash ($m) associated with the initiation of the customer...

References: Bergerot, Paul D. and Nada I. Nasr (1998), " Customer Life-time Value: Promoting Models and Applications, ” Journal of Interactive Promoting, 12

(Winter), 17–30.

Blattberg, Robert C., Byung-Do Kim, and Jeff A. Neslin (2008), Databases

Marketing: Analyzing and Managing Customers, New york city: Springer.

Fugitif, Noel (2007), Managing Marketing in the 21st Century, Bronxvile, NY:


Davis, Steve (2007), Calculating Marketing: 103 Key Metrics Every Marketer

Needs, Singapore: John Wiley & Daughters (Asia).

Dev, Chekitan S i9000. and Laure Mougeot Stroock (2007), " Rosewood Accommodations &

Resorts: Branding to Increase Customer Earnings and Lifetime Value, ”

Harvard Business Posting HBP No . 2088 (June 15, 2007).

Fader, Peter S. and Bruce G. S. Hardie (2007), " How to Job Customer

Preservation, ” Diary of Interactive Marketing, twenty-one (Winter), 76–90.

Fader, Peter S. and Bruce G. S. Hardie (2009), " Probability Models for CustomerBase Analysis, ” Journal of Interactive Promoting, 23 (January), 61–69.

Fader, Peter S i9000. and Bruce G. S i9000. Hardie (2010), " Customer-Base Valuation in

a Contractual Setting: The Perils of Ignoring Heterogeneity, ” Marketing

Gupta, Sunil and Donald R. Lehmann (2005), Managing Buyers as Purchases, Upper Saddle River, NJ-NEW JERSEY: Wharton Institution Publishing.

Gupta, Sunil, Jesse R. Lehmann, and Jennifer Ames Stuart (2004), " Valuing

Buyers, ” Journal of Marketing Exploration, 41 (February) 7–18.

Kotler, Philip and Kevin Side of the road Keller (2012), Marketing Managing (14th

edn), Upper Saddle River, NJ-NEW JERSEY: Prentice Corridor.

Lehmann, Donald R. and Russell H. Winer (2008), Analysis pertaining to Marketing

Preparing (7th edn), New York, BIG APPLE: McGraw-Hill/Irwin.

MartВґД±nez-Jerez, F. AsВґД±s and Wayne R. Dillon (2007), " Kansai Digital Phone:

Zutto, Gaining Japan Loyalty, ” Harvard Organization School Case 9-106-006

(rev. March twenty-seven, 2007).

McGovern, Gail (2007), " Virgin Mobile USA: Pricing for the first time, ”

Harvard Business University Case 9-504-028 (rev

Ofek, Elie (2002), " Customer Profitability and Lifetime Value, ” Harvard Business School Be aware 9-503-019 (rev. August several, 2002).

Steenburgh, Thomas and Jill Avery (2011), " Marketing Evaluation Toolkit: Customer Lifetime Value Analysis, ” Harvard Business School Be aware 9-511-029