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[[File:Bingham_mayo.jpg|thumb|right|302px|[[Mayonnaise]] is a Bingham plastic. The surface has ridges and peaks because Bingham plastics mimic solids under low shear stresses.]]
In [[marketing]], '''customer lifetime value''' (CLV), '''lifetime customer value''' (LCV), or '''user lifetime value''' (LTV) is a prediction of
A '''Bingham plastic''' is a [[viscoplastic]] material that behaves as a rigid body at low stresses but flows as a [[viscosity|viscous]] [[fluid]] at high stress. It is named after [[Eugene C. Bingham]] who proposed its mathematical form.<ref>E.C. Bingham,(1916) ''U.S. Bureau of Standards Bulletin'', 13, 309-353 "An Investigation of the Laws of Plastic Flow"</ref>
the net profit attributed to the entire future relationship with a customer. The prediction model can have varying levels of sophistication and accuracy, ranging from a crude [[heuristic]] to the use of complex [[predictive analytics]] techniques.


It is used as a common [[mathematical model]] of [[mud]] flow in [[drilling engineering]], and in the handling of [[slurry|slurries]]. A common example is [[toothpaste]],<ref name=Steffe>J. F. Steffe (1996) ''Rheological Methods in Food Process Engineering'' 2nd ed ISBN 0-9632036-1-4</ref> which will not be [[extruded]] until a certain [[pressure]] is applied to the tube. It then is pushed out as a solid plug.
==Origins==
One of the first accounts of it is in the 1988 book Database Marketing, and includes detailed worked examples.<ref>Shaw, R & Stone, M. (1988) Database Marketing, Gower, London</ref><ref>Shaw, R & Stone, M. (1990) Database Marketing, Wiley US Edition</ref>


==Explanation==
== Uses and Advantages ==
[[File:Bingham1a.svg|thumb|left|302px|Figure 1. Bingham Plastic flow as described by Bingham]]
Customer lifetime value has intuitive appeal as a marketing concept, because in theory it represents exactly how much each customer is worth in monetary terms, and therefore exactly how much a marketing department should be willing to spend to acquire each customer, especially in [[direct response marketing]].
'''Figure 1''' shows a graph of the behaviour of an ordinary viscous (or Newtonian) fluid in red, for example in a pipe. If the pressure at one end of a pipe is increased this produces a stress on the fluid tending to make it move (called the [[shear stress]]) and the volumetric flow rate increases proportionally. However for a Bingham Plastic fluid (in blue), stress can be applied but it will not flow until a certain value, the [[yield stress]], is reached. Beyond this point the flow rate increases steadily with increasing shear stress. This is roughly the way in which Bingham presented his observation, in an experimental study of paints.<ref>E. C. Bingham (1922) ''Fluidity and Plasticity'' McGraw-Hill (New York) page 219</ref> These properties allow a Bingham plastic to have a textured surface with peaks and ridges instead of a featureless surface like a Newtonian fluid.
[[File:Bingham2a.svg|thumb|right|302px|Figure 2. Bingham Plastic flow as described currently]]
'''Figure 2''' shows the way in which it is normally presented currently.<ref name=Steffe/> The graph shows [[shear stress]] on the vertical axis and [[shear rate]] on the horizontal one. (Volumetric flow rate depends on the size of the pipe, shear rate is a measure of how the velocity changes with distance. It is proportional to flow rate, but does not depend on pipe size.) As before, the Newtonian fluid flows and gives a shear rate for any finite value of shear stress. However, the Bingham Plastic again does not exhibit any shear rate (no flow and thus no velocity) until a certain stress is achieved. For the Newtonian fluid the slope of this line is the [[viscosity]], which is the only parameter needed to describe its flow. By contrast the Bingham Plastic requires two parameters, the '''yield stress''' and the slope of the line, known as the '''plastic viscosity'''.


The physical reason for this behaviour is that the liquid contains particles (e.g. clay) or large molecules (e.g. polymers) which have some kind of interaction, creating a weak solid structure, formerly known as a '''false body''', and a certain amount of stress is required to break this structure. Once the structure has been broken, the particles move with the liquid under viscous forces. If the stress is removed, the particles associate again.
Lifetime value is typically used to judge the appropriateness of the costs of acquisition of a customer. For example, if a new customer costs $50 to acquire (COCA, or cost of customer acquisition), and their lifetime value is $60, then the customer is judged to be profitable, and acquisition of additional similar customers is acceptable.


==Definition==
Additionally, CLV is used to calculate [[customer equity]].
The material is rigid for [[shear stress]] ''τ'', less than a critical value <math>\tau_0</math>. Once the critical shear [[shear stress|stress]] (or "[[yield (engineering)|yield stress]]") is exceeded, the material flows in such a way that the [[shear rate]], ∂''u''/∂''y'' (as defined in the article on [[viscosity]]), is directly proportional to the amount by which the applied shear stress exceeds the yield stress:


:<math>\frac {\partial u} {\partial y} = \left\{\begin{matrix} 0 &, \tau < \tau_0 \\ (\tau - \tau_0)/ {\mu} &, \tau \ge \tau_0 \end{matrix}\right.</math>
Advantages of CLV:
* management of customer relationship as an asset
* monitoring the impact of management strategies and marketing investments on the value of customer assets
* determination of the optimal level of investments in marketing and sales activities
* implementation of sensitivity analysis in order to determinate getting impact by spending extra money on each customer<ref>Gary Cokins (2009). Performance Management: Integrating Strategy Execution, Methodologies, Risk and Analytics. ISBN 978-0-470-44998-1. p. 177</ref>
* optimal allocation of  limited resources for ongoing marketing activities in order to achieve a maximum return
* a good basis for selecting customers and for decision making regarding customer specific communication strategies
* measurement of customer loyalty (proportion of purchase, probability of purchase and repurchase, purchase frequency and sequence etc.)<ref>V. Kumar (2008). Customer Lifetime Value. ISBN 978-1-60198-156-1. p. 6</ref>


==Friction Factor Formulae==
==Misuses and Downsides==
In fluid flow, it is a common problem to calculate the pressure drop in an established piping network.<ref>{{Cite book| title=Chemical Engineering Fluid Mechanics. | first1=Ron | last1=Darby | publisher=Marcel Dekker | year=1996 | isbn=0-8247-0444-4| postscript=<!--None--> }}. See Chapter 6.</ref> Once the friction factor, ''f'', is known, it becomes easier to handle different pipe-flow problems, viz. calculating the pressure drop for evaluating pumping costs or to find the flow-rate in a piping network for a given pressure drop. It is usually extremely difficult to arrive at exact analytical solution to calculate the friction factor associated with flow of non-Newtonian fluids and therefore explicit approximations are used to calculate it. Once the friction factor has been calculated the pressure drop can be easily determined for a given flow by the [[Darcy–Weisbach equation]]:
===NPV vs Nominal Prediction===
:<math> \ f = \ {2 h_f g D \over L V^2}</math>
The most accurate CLV predictions are made using the [[net present value]] (NPV) of each future net profit source, so that the revenue to be received from the customer in the future is recognized at the future value of money. However, NPV calculations require additional sophistication including maintenance of a [[discount rate]], which leads most organizations to instead calculate CLV using the nominal (non-discounted) figured. Nominal CLV predictions are biased slightly high, scaling higher the farther into the future the revenues are expected from customers


where:
===Net Profit vs Revenue===
* <math>{\bold \ h_f}</math> is the frictional head loss  ([[SI units]]: m)
A common mistake is for a CLV prediction to calculate the total [[revenue]] or even [[gross margin]] associated with a customer. However, this can cause CLV to be multiples of their actual value, and instead need to be calculated as the full [[net profit]] expected from the customer.
* <math>{\bold \ f}</math> is the friction factor  ([[SI units]]: Dimensionless)
* <math>{\bold \ L}</math> is the pipe length  ([[SI units]]: m)
* <math>{\bold \ g}</math> is the gravitational acceleration  ([[SI units]]: m/s²)
* <math>{\bold \ D}</math> is the pipe diameter  ([[SI units]]: m)
* <math>{\bold \ V}</math> is the mean fluid velocity  ([[SI units]]: m/s)


===Laminar flow===
===Segment Inaccuracy===
An exact description of friction loss for Bingham plastics in fully developed laminar pipe flow was first published by Buckingham.<ref>Buckingham, E. (1921). "on Plastic Flow through Capillary Tubes". ''ASTM Proceedings'' '''21''': 1154–1156.</ref> His expression, the ''Buckingham-Reiner'' equation, can be written in a dimensionless form as follows:
Opponents often site the inaccuracy of a CLV prediction to argue they should not be used to drive significant business decisions. For example, major drivers to the value of a customer such as the nature of the relationship are often not available as appropriately structured data and thus not included in the formula.
:<math> \ f_L = \ {64 \over Re}\left[1 + {He\over 6 Re} - {64\over3}\left({He^4\over {f_L}^3 Re^7}\right)\right]</math>


where:
===Comparison with Intuition===
* <math>{\bold \ f_L}</math> is the laminar flow friction factor  ([[SI units]]: Dimensionless)
More, predictors such as specific [[demographics]] of a customer group may have an effect that is intuitively obvious to an experienced marketer, but are often omitted from CLV predictions and thus cause inaccuracies in certain customer segments.
* <math>{\bold \ Re}</math> is the [[Reynolds number]]  ([[SI units]]: Dimensionless)
* <math>{\bold \ He}</math> is the Hedstrom number  ([[SI units]]: Dimensionless)


The [[Reynolds number]] and the Hedstrom number are respectively defined as:
==Effects on Business Practices==
:<math> \mathrm{Re} = {D {\ V} \over {\nu_\infty}} </math>, and
Its use as a marketing metric tends to place greater emphasis on customer service and long-term customer satisfaction, rather than on maximizing short-term sales.


:<math> \mathrm{He} = {\ D^2 {\tau_o} \over {\rho{\nu_\infty}^2}} </math>
==Predictive Models==
===Simple Ecommerce Example===
(Avg Monthly Revenue per Customer * Gross Margin per Customer) / Monthly Churn Rate


where:
You should have something that looks like:  
* <math>{\bold \rho}</math> is the mass density of fluid  ([[SI units]]: kg/m<sup>3</sup>)
$100 avg monthly spend * 25% margin / 5% monthly churn = $500 LTV <ref>http://www.quora.com/How-do-you-calculate-Customer-Lifetime-Value#</ref>
* <math>{\bold \ \nu_\infty}</math> is the kinematic [[viscosity]] of fluid  ([[SI units]]: m²/s)


===Turbulent flow===
===A Retention Example===
Darby and Melson developed an empirical expression that determines the friction factor for turbulent-flow regime of Bingham plastic fluids, and is given by:<ref name=Darby>Darby, R. and Melson J.(1981). "How to predict the friction factor for flow of Bingham plastics". ''Chemical Engineering'' '''28''': 59–61.</ref>
====4 Steps====
:<math> \ f_T = \ {10^a} \ {Re^{-0.193}} </math>
# forecasting of remaining customer lifetime in years
where:
# forecasting of future revenues year-by-year, based on estimation about future products purchased and price paid
* <math>{\bold \ f_T}</math> is the turbulent flow friction factor  ([[SI units]]: Dimensionless)
# estimation of costs for delivering those products
* <math> \ a = -1.378\left[1 + 0.146{\ e^{-2.9\times {10^{-5}}}Re}\right] </math>
# calculation of the net present value of these future amounts<ref>Lynette Ryals (2008). Managing Customers Profitably. ISBN 978-0-470-06063-6. p.85</ref>
Forecasting accuracy and difficulty in tracking customers over time may affect CLV calculation process.


==Approximations of the ''Buckingham-Reiner'' equation==
====Inputs====
Although an exact analytical solution of the ''Buckingham-Reiner'' equation can be obtained because it is a fourth order polynomial equation in ''f'', due to complexity of the solution it is rarely employed. Therefore, researchers have tried to develop explicit approximations for the ''Buckingham-Reiner'' equation.
* '''[[Churn rate]]''', the percentage of customers who end their relationship with a company in a given period.  One minus the churn rate is the '''retention rate'''.  Most models can be written using either churn rate or retention rate.  If the model uses only one churn rate, the assumption is that the churn rate is constant across the life of the customer relationship.
* '''Discount rate''', the [[cost of capital]] used to discount future revenue from a customer.  Discounting is an advanced topic that is frequently ignored in customer lifetime value calculations.  The current [[interest rate]] is sometimes used as a simple (but incorrect) proxy for [[discount rate]].
* '''[[Contribution margin]]'''.
* '''Retention cost''', the amount of money a company has to spend in a given period to retain an existing customer.  Retention costs include customer support, billing, promotional incentives, etc.
* '''Period''', the unit of time into which a customer relationship is divided for analysis.  A year is the most commonly used period.  Customer lifetime value is a multi-period calculation, usually stretching 3–7 years into the future. In practice, analysis beyond this point is viewed as too speculative to be reliable.  The number of periods used in the calculation is sometimes referred to as the model '''horizon'''.


===Swamee-Aggarwal Equation===
====Model====
The ''Swamee Aggarwal'' equation is used to solve directly for the Darcy–Weisbach friction factor ''f'' for laminar flow of Bingham plastic fluids.<ref>Swamee, P.K. and Aggarwal, N.(2011). "Explicit equations for laminar flow of Bingham plastic fluids". ''Journal of Petroleum Science and Engineering''. {{doi|10.1016/j.petrol.2011.01.015}}.</ref> It is an approximation of the implicit ''Buckingham-Reiner'' equation, but the discrepancy from experimental data is well within the accuracy of the data.
<ref>Berger, P. D. and Nasr, N. I. (1998), Customer lifetime value: Marketing models and applications. Journal of Interactive Marketing, 12: 17–30. {{doi|10.1002/(SICI)1520-6653(199824)12:1<17::AID-DIR3>3.0.CO;2-K}}</ref>:
The ''Swamee-Aggarwal'' equation is given by:
:<math> \ f_L = \ {64 \over Re}  + {10.67 + 0.1414{({He\over Re})^{1.143}}\over {\left[1 + 0.0149{({He\over Re})^{1.16}}\right]Re  }}\left({He\over Re}\right)</math>


===Danish-Kumar Solution===
<math>\text{CLV}  = \text{GC} \cdot \sum_{i=0}^n \frac{r^i}{(1+d)^i} - \text{M} \cdot \sum_{i=1}^n \frac{r^{i-1}}{(1+d)^{i-0.5}}</math>,
Danish ''et al.'' have provided an explicit procedure to calculate the friction factor ''f'' by using the Adomian decomposition method.<ref>Danish, M. ''et al.'' (1981). "Approximate explicit analytical expressions of friction factor for flow
of Bingham fluids in smooth pipes using Adomian decomposition method". ''Communications in Nonlinear Science and Numerical Simulation'' '''16''': 239–251.</ref> The friction factor containing two terms through this method is given as:
:<math> f_L = \frac{K_1 + \dfrac{4 K_2}{\left( K_1 + \frac{K_1 K_2}{K_1^4 + 3 K_2}\right)^3}}{1+ \dfrac{3 K_2}{\left(K_1 + \frac{K_1 K_2}{K_1^4 + 3 K_2}\right)^4}}</math>
where:
:<math> \ K_1 = \ {16 \over Re} + {16 He \over 6{Re^2}}</math>, and
:<math> \ K_2 = \ - {16 {He^4} \over 3{Re^8}}</math>


==Combined Equation for friction factor for all flow regimes==
where <math>\text{GC}</math> is yearly gross contribution per customer, <math>\text{M}</math> is the (relevant) retention costs per customer per year (this formula assumes the retention activities are paid for each mid year and they only affect those who were retained in the previous year), <math>n</math> is the horizon (in years), <math>r</math> is the yearly retention rate, <math>d</math> is the yearly discount rate.
===Darby-Melson Equation===
In 1981, Darby and Melson, using the approach of Churchill<ref>Churchill, S.W. (1977). "Friction factor equation spans all fluid-flow regimes". ''Chemical Engineering'' '''Nov. 7''': 91–92.</ref> and of Churchill and Usagi,<ref>Churchill, S.W. and Usagi, R.A. (1972). "A general expression for the correlation of rates of transfer and other phenomena". ''AIChE Journal'' '''18(6)''': 1121-1128.</ref> developed an expression to get a single friction factor equation valid for all flow regimes:<ref name=Darby/>
:<math> \ f = \ {\left[{f_L}^m + {f_T}^m\right]}^{1\over m}</math>
where:
:<math> \ m = \ 1.7 + {40000\over Re} </math>


Both ''Swamee-Aggarwal'' equation and the ''Darby-Melson'' equation can be combined to give an explicit equation for determining the friction factor of Bingham plastic fluids in any regime. Relative roughness is not a parameter in any of the equations because the friction factor of Bingham plastic fluids is not sensitive to pipe roughness.
==Simplified Models==
It is often helpful to estimate customer lifetime value with a simple model to make initial assessments of customer segments and targeting. Possibly the simplest way to estimate CLV is to assume constant and long-lasting values for contribution margin, retention rate, and discount rates, as follows <ref>Adapted from "Customer Profitability and Lifetime Value," HBS Note 503-019</ref>:
 
<math>\text{CLV} = \text{GC} \cdot (\frac{1+d}{1+d-r})</math>
 
==See also==
[[Gompertz distribution]]


==References==
==References==
{{reflist}}


{{DEFAULTSORT:Bingham Plastic}}
<references/>
[[Category:Materials]]
 
[[Category:Non-Newtonian fluids]]
==External links==
[[Category:Viscosity]]
 
[[Category:Offshore engineering]]
#[https://www.custora.com/home/customer_lifetime_value custora.com/home/customer_lifetime_value]
#[http://www.mineful.com/customer-retention-roi-calculator.html Free customer lifetime value calculator]
#[http://www.kaushik.net/avinash/analytics-tip-calculate-ltv-customer-lifetime-value/ kaushik.net/avinash/analytics-tip-calculate-ltv-customer-lifetime-value/]
#[http://ariegoldshlager.posterous.com/recommend-reading-customer-lifetime-value-pot ariegoldshlager.posterous.com/recommend-reading-customer-lifetime-value-pot]
#[http://www.quora.com/Turki-Fahad/Great-Stuff/How-do-you-calculate-Customer-Lifetime-Value quora: How-do-you-calculate-Customer-Lifetime-Value]
 
{{DEFAULTSORT:Customer Lifetime Value}}
[[Category:Marketing]]
[[Category:Consumer behaviour]]


[[bs:Binghamova plastika]]
[[de:Customer Lifetime Value]]
[[de:Bingham-Fluid]]
[[es:Valor del tiempo de vida del cliente]]
[[fa:پلاستیک بینگهام]]
[[fr:Valeur vie client]]
[[fr:Fluide de Bingham]]
[[it:Lifetime value]]
[[nl:Bingham plastic]]
[[pl:LTV (marketing)]]
[[zh:宾汉流体]]
[[pt:Lifetime value]]

Revision as of 04:36, 12 August 2014

In marketing, customer lifetime value (CLV), lifetime customer value (LCV), or user lifetime value (LTV) is a prediction of the net profit attributed to the entire future relationship with a customer. The prediction model can have varying levels of sophistication and accuracy, ranging from a crude heuristic to the use of complex predictive analytics techniques.

Origins

One of the first accounts of it is in the 1988 book Database Marketing, and includes detailed worked examples.[1][2]

Uses and Advantages

Customer lifetime value has intuitive appeal as a marketing concept, because in theory it represents exactly how much each customer is worth in monetary terms, and therefore exactly how much a marketing department should be willing to spend to acquire each customer, especially in direct response marketing.

Lifetime value is typically used to judge the appropriateness of the costs of acquisition of a customer. For example, if a new customer costs $50 to acquire (COCA, or cost of customer acquisition), and their lifetime value is $60, then the customer is judged to be profitable, and acquisition of additional similar customers is acceptable.

Additionally, CLV is used to calculate customer equity.

Advantages of CLV:

  • management of customer relationship as an asset
  • monitoring the impact of management strategies and marketing investments on the value of customer assets
  • determination of the optimal level of investments in marketing and sales activities
  • implementation of sensitivity analysis in order to determinate getting impact by spending extra money on each customer[3]
  • optimal allocation of limited resources for ongoing marketing activities in order to achieve a maximum return
  • a good basis for selecting customers and for decision making regarding customer specific communication strategies
  • measurement of customer loyalty (proportion of purchase, probability of purchase and repurchase, purchase frequency and sequence etc.)[4]

Misuses and Downsides

NPV vs Nominal Prediction

The most accurate CLV predictions are made using the net present value (NPV) of each future net profit source, so that the revenue to be received from the customer in the future is recognized at the future value of money. However, NPV calculations require additional sophistication including maintenance of a discount rate, which leads most organizations to instead calculate CLV using the nominal (non-discounted) figured. Nominal CLV predictions are biased slightly high, scaling higher the farther into the future the revenues are expected from customers

Net Profit vs Revenue

A common mistake is for a CLV prediction to calculate the total revenue or even gross margin associated with a customer. However, this can cause CLV to be multiples of their actual value, and instead need to be calculated as the full net profit expected from the customer.

Segment Inaccuracy

Opponents often site the inaccuracy of a CLV prediction to argue they should not be used to drive significant business decisions. For example, major drivers to the value of a customer such as the nature of the relationship are often not available as appropriately structured data and thus not included in the formula.

Comparison with Intuition

More, predictors such as specific demographics of a customer group may have an effect that is intuitively obvious to an experienced marketer, but are often omitted from CLV predictions and thus cause inaccuracies in certain customer segments.

Effects on Business Practices

Its use as a marketing metric tends to place greater emphasis on customer service and long-term customer satisfaction, rather than on maximizing short-term sales.

Predictive Models

Simple Ecommerce Example

(Avg Monthly Revenue per Customer * Gross Margin per Customer) / Monthly Churn Rate

You should have something that looks like: 

$100 avg monthly spend * 25% margin / 5% monthly churn = $500 LTV [5]

A Retention Example

4 Steps

  1. forecasting of remaining customer lifetime in years
  2. forecasting of future revenues year-by-year, based on estimation about future products purchased and price paid
  3. estimation of costs for delivering those products
  4. calculation of the net present value of these future amounts[6]

Forecasting accuracy and difficulty in tracking customers over time may affect CLV calculation process.

Inputs

  • Churn rate, the percentage of customers who end their relationship with a company in a given period. One minus the churn rate is the retention rate. Most models can be written using either churn rate or retention rate. If the model uses only one churn rate, the assumption is that the churn rate is constant across the life of the customer relationship.
  • Discount rate, the cost of capital used to discount future revenue from a customer. Discounting is an advanced topic that is frequently ignored in customer lifetime value calculations. The current interest rate is sometimes used as a simple (but incorrect) proxy for discount rate.
  • Contribution margin.
  • Retention cost, the amount of money a company has to spend in a given period to retain an existing customer. Retention costs include customer support, billing, promotional incentives, etc.
  • Period, the unit of time into which a customer relationship is divided for analysis. A year is the most commonly used period. Customer lifetime value is a multi-period calculation, usually stretching 3–7 years into the future. In practice, analysis beyond this point is viewed as too speculative to be reliable. The number of periods used in the calculation is sometimes referred to as the model horizon.

Model

[7]:

,

where is yearly gross contribution per customer, is the (relevant) retention costs per customer per year (this formula assumes the retention activities are paid for each mid year and they only affect those who were retained in the previous year), is the horizon (in years), is the yearly retention rate, is the yearly discount rate.

Simplified Models

It is often helpful to estimate customer lifetime value with a simple model to make initial assessments of customer segments and targeting. Possibly the simplest way to estimate CLV is to assume constant and long-lasting values for contribution margin, retention rate, and discount rates, as follows [8]:

See also

Gompertz distribution

References

  1. ↑ Shaw, R & Stone, M. (1988) Database Marketing, Gower, London
  2. ↑ Shaw, R & Stone, M. (1990) Database Marketing, Wiley US Edition
  3. ↑ Gary Cokins (2009). Performance Management: Integrating Strategy Execution, Methodologies, Risk and Analytics. ISBN 978-0-470-44998-1. p. 177
  4. ↑ V. Kumar (2008). Customer Lifetime Value. ISBN 978-1-60198-156-1. p. 6
  5. ↑ http://www.quora.com/How-do-you-calculate-Customer-Lifetime-Value#
  6. ↑ Lynette Ryals (2008). Managing Customers Profitably. ISBN 978-0-470-06063-6. p.85
  7. ↑ Berger, P. D. and Nasr, N. I. (1998), Customer lifetime value: Marketing models and applications. Journal of Interactive Marketing, 12: 17–30. 21 year-old Glazier James Grippo from Edam, enjoys hang gliding, industrial property developers in singapore developers in singapore and camping. Finds the entire world an motivating place we have spent 4 months at Alejandro de Humboldt National Park.
  8. ↑ Adapted from "Customer Profitability and Lifetime Value," HBS Note 503-019

External links

  1. custora.com/home/customer_lifetime_value
  2. Free customer lifetime value calculator
  3. kaushik.net/avinash/analytics-tip-calculate-ltv-customer-lifetime-value/
  4. ariegoldshlager.posterous.com/recommend-reading-customer-lifetime-value-pot
  5. quora: How-do-you-calculate-Customer-Lifetime-Value

de:Customer Lifetime Value es:Valor del tiempo de vida del cliente fr:Valeur vie client it:Lifetime value pl:LTV (marketing) pt:Lifetime value

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