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In [[marketing]], '''customer lifetime value''' (CLV), '''lifetime customer value''' (LCV), or '''user lifetime value''' (LTV) is a prediction of
{{One source|date=April 2009}}
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==
{{Acids and bases}}
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>
In chemistry, a '''weak base''' is a [[chemical]] [[base (chemistry)|base]] that does not [[ionize]] fully in an [[aqueous solution]]. As [[Brønsted–Lowry base]]s are proton acceptors, a weak base may also be defined as a chemical base in which [[protonation]] is incomplete. This results in a relatively low [[pH]] compared to [[Base (chemistry)#Strong bases|strong bases]]. Bases range from a pH of greater than 7 (7 is neutral, like pure water) to 14 (though some bases are greater than 14). pH has the formula:
:<math>\mbox{pH} = -\log_{10} \left[ \mbox{H}^+ \right]</math>
Since bases are [[proton]] acceptors, the base receives a hydrogen ion from water, H<sub>2</sub>O, and the remaining H<sup>+</sup> [[concentration]] in the solution determines pH. Weak bases will have a higher H<sup>+</sup> concentration because they are less completely protonated than stronger bases and, therefore, more hydrogen ions remain in the solution. If you plug in a higher H<sup>+</sup> concentration into the formula, a low pH results. However, pH of bases is usually calculated using the OH<sup>-</sup> concentration to find the pOH first. This is done because the H<sup>+</sup> concentration is not a part of the reaction, while the OH<sup>-</sup> concentration is.
:<math>\mbox{pOH} = -\log_{10} \left[ \mbox{OH}^- \right]</math>


== Uses and Advantages ==
By multiplying a conjugate acid (such as NH<sub>4</sub><sup>+</sup>) and a conjugate base (such as NH<sub>3</sub>) the following is given:
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.
:<math> K_a \times K_b = {[H_3O^+] [NH_3]\over[NH_4^+]} \times {[NH_4^+] [OH^-]\over[NH_3]} = [H_3O^+] [OH^-]</math>


Additionally, CLV is used to calculate [[customer equity]].
Since <math>{K_w} = [H_3O^+] [OH^-]</math> then, '''''<math>K_a \times K_b = K_w</math>'''''


Advantages of CLV:
By taking logarithms of both sides of the equation, the following is reached:
* 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>


==Misuses and Downsides==
:<math>logK_a + logK_b = logK_w</math>
===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===
Finally, multiplying throughout the equation by -1, the equation turns into:
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===
:<math>pK_a + pK_b = pK_w = 14.00</math>
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===
After acquiring pOH from the previous pOH formula, pH can be calculated using the formula '''pH = pK<sub>w</sub> - pOH''' where pK<sub>w</sub> = 14.00.
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==
Weak bases exist in [[chemical equilibrium]] much in the same way as [[weak acid]]s do, with a '''[[base dissociation constant]] (K<sub>b</sub>)''' indicating the strength of the base. For example, when ammonia is put in water, the following equilibrium is set up:
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==
:<math>\mathrm{K_b={[NH_4^+] [OH^-]\over[NH_3]}}</math>
===Simple Ecommerce Example===
(Avg Monthly Revenue per Customer * Gross Margin per Customer) / Monthly Churn Rate


You should have something that looks like:
Bases that have a large K<sub>b</sub> will ionize more completely and are thus stronger bases. As stated above, pH of the solution depends on the H<sup>+</sup> concentration, which is related to the OH<sup>-</sup> concentration by the '''[[self-ionization constant]] (K<sub>w</sub> = 1.0x10<sup>−14</sup>)'''. A strong base has a lower H<sup>+</sup> concentration because they are fully protonated and less hydrogen ions remain in the solution. A lower H<sup>+</sup> concentration also means a higher OH<sup>-</sup> concentration and therefore, a larger K<sub>b</sub>.
$100 avg monthly spend * 25% margin / 5% monthly churn = $500 LTV <ref>http://www.quora.com/How-do-you-calculate-Customer-Lifetime-Value#</ref>


===A Retention Example===
<!-- Image with unknown copyright status removed: [[Image: basestrength.jpg]] -->
====4 Steps====
# forecasting of remaining customer lifetime in years
# forecasting of future revenues year-by-year, based on estimation about future products purchased and price paid
# estimation of costs for delivering those products
# 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.


====Inputs====
NaOH (s) (sodium hydroxide) is a stronger base than (CH<sub>3</sub>CH<sub>2</sub>)<sub>2</sub>NH (l) ([[diethylamine]]) which is a stronger base than NH<sub>3</sub> (g) (ammonia). As the bases get weaker, the smaller the K<sub>b</sub> values become.<!-- The pie-chart representation is as follows:
* '''[[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.
* purple areas represent the fraction of OH- ions formed
* '''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]].
* red areas represent the cation remaining after ionization
* '''[[Contribution margin]]'''.
* yellow areas represent dissolved but non-ionized molecules.-->
* '''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====
==Percentage protonated==
<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>:
As seen above, the strength of a base depends primarily on pH. To help describe the strengths of weak bases, it is helpful to know the percentage protonated-the percentage of base molecules that have been protonated. A lower percentage will correspond with a lower pH because both numbers result from the amount of protonation. A weak base is less protonated, leading to a lower pH and a lower percentage protonated.


<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>,
The typical proton transfer equilibrium appears as such:


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.
:<math>B(aq) + H_2O(l) \leftrightarrow HB^+(aq) + OH^-(aq)</math>


==Simplified Models==
B represents the base.
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>
:<math>Percentage\ protonated = {molarity\ of\ HB^+ \over\ initial\ molarity\ of\ B} \times 100\% = {[{HB}^+]\over [B]_{initial}} {\times 100\%}</math>
 
In this formula, [B]<sub>initial</sub> is the initial molar concentration of the base, assuming that no protonation has occurred.
 
==A typical pH problem==
Calculate the pH and percentage protonation of a .20 M aqueous solution of pyridine, C<sub>5</sub>H<sub>5</sub>N. The K<sub>b</sub> for C<sub>5</sub>H<sub>5</sub>N is 1.8 x 10<sup>−9</sup>.
 
First, write the proton transfer equilibrium:
 
:<math>\mathrm{H_2O(l) + C_5H_5N(aq) \leftrightarrow C_5H_5NH^+ (aq) + OH^- (aq)}</math>
 
:<math>K_b=\mathrm{[C_5H_5NH^+] [OH^-]\over [C_5H_5N]}</math>
 
The equilibrium table, with all concentrations in moles per liter, is
 
{| width:75%; height:200px border="1"
|+
|-style="height:40px"
! !! C<sub>5</sub>H<sub>5</sub>N !! C<sub>5</sub>H<sub>6</sub>N<sup>+</sup> !! OH<sup>-</sup>
|-
! initial normality
| .20 || 0 || 0
|-
! change in normality
| -x || +x || +x
|-
! equilibrium normality
| .20 -x || x || x
|}
 
{| width:75%; height:200px border="1"
|-
| Substitute the equilibrium molarities into the basicity constant
| <math>K_b=\mathrm {1.8 \times 10^{-9}} = {x \times x \over .20-x}</math>
|-
| We can assume that x is so small that it will be meaningless by the time we use significant figures.
| <math>\mathrm {1.8 \times 10^{-9}} \approx {x^2 \over .20}</math>
|-
| Solve for x.
| <math>\mathrm x \approx \sqrt{.20 \times (1.8 \times 10^{-9})} = 1.9 \times 10^{-5}</math>
|-
| Check the assumption that x << .20
| <math>\mathrm 1.9 \times 10^{-5} \ll .20</math>; so the approximation is valid
|-
| Find pOH from pOH = -log [OH<sup>-</sup>] with [OH<sup>-</sup>]=x
| <math>\mathrm pOH \approx -log(1.9 \times 10^{-5}) = 4.7 </math>
|-
| From pH = pK<sub>w</sub> - pOH,
| <math>\mathrm pH \approx 14.00 - 4.7 = 9.3</math>
|-
| From the equation for percentage protonated with [HB<sup>+</sup>] = x and [B]<sub>initial</sub> = .20,
| <math>\mathrm percentage \ protonated = {1.9 \times 10^{-5} \over .20} \times 100\% = .0095\% </math>
|}
 
This means .0095% of the pyridine is in the protonated form of C<sub>5</sub>H<sub>5</sub>NH<sup>+</sup>.
 
==Examples==
* [[Alanine]],
* [[Ammonia]], NH<sub>3</sub>
* [[Methylamine]], CH<sub>3</sub>NH<sub>2</sub>], C<sub>5</sub>H<sub>8</sub>O<sub>2</sub>
 
Other weak bases are essentially any bases not on the list of [[strong base]]s.
 
==Simple Facts==
*An example of a weak base is ammonia. It does not contain hydroxide ions, but it reacts with water to produce ammonium ions and hydroxide ions.<ref>Atkins, Peter, and Loretta Jones. Chemical Principles: The Quest for Insight, 3rd Ed., New York: W.H. Freeman, 2005.</ref>
*The position of equilibrium varies from base to base when a weak base reacts with water. The further to the left it is, the weaker the base.<ref>Clark, Jim. "Strong and Weak Bases."N.p.,2002. Web.</ref>


==See also==
==See also==
[[Gompertz distribution]]
* [[Strong base]]
* [[Weak acid]]


==References==
==References==
 
{{reflist}}
<references/>


==External links==
==External links==
* [http://www.chemguide.co.uk/physical/acidbaseeqia/bases.html Explanation of strong and weak bases] from ChemGuide
* [http://bouman.chem.georgetown.edu/S02/lect16/lect16.htm Guide to Weak Bases from Georgetown course notes]
* [http://www.intute.ac.uk/sciences/reference/plambeck/chem1/p01154.htm Article on Acidity of Solutions of Weak Bases] from Intute


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#[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/]
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#[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]]


[[de:Customer Lifetime Value]]
[[Category:Bases]]
[[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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my blog post ipad repair hanover park In chemistry, a weak base is a chemical base that does not ionize fully in an aqueous solution. As Brønsted–Lowry bases are proton acceptors, a weak base may also be defined as a chemical base in which protonation is incomplete. This results in a relatively low pH compared to strong bases. Bases range from a pH of greater than 7 (7 is neutral, like pure water) to 14 (though some bases are greater than 14). pH has the formula:

pH=−log10[H+]

Since bases are proton acceptors, the base receives a hydrogen ion from water, H2O, and the remaining H+ concentration in the solution determines pH. Weak bases will have a higher H+ concentration because they are less completely protonated than stronger bases and, therefore, more hydrogen ions remain in the solution. If you plug in a higher H+ concentration into the formula, a low pH results. However, pH of bases is usually calculated using the OH- concentration to find the pOH first. This is done because the H+ concentration is not a part of the reaction, while the OH- concentration is.

pOH=−log10[OH−]

By multiplying a conjugate acid (such as NH4+) and a conjugate base (such as NH3) the following is given:

Ka×Kb=[H3O+][NH3][NH4+]×[NH4+][OH−][NH3]=[H3O+][OH−]

Since Kw=[H3O+][OH−] then, Ka×Kb=Kw

By taking logarithms of both sides of the equation, the following is reached:

logKa+logKb=logKw

Finally, multiplying throughout the equation by -1, the equation turns into:

pKa+pKb=pKw=14.00

After acquiring pOH from the previous pOH formula, pH can be calculated using the formula pH = pKw - pOH where pKw = 14.00.

Weak bases exist in chemical equilibrium much in the same way as weak acids do, with a base dissociation constant (Kb) indicating the strength of the base. For example, when ammonia is put in water, the following equilibrium is set up:

Kb=[NH4+][OH−][NH3]

Bases that have a large Kb will ionize more completely and are thus stronger bases. As stated above, pH of the solution depends on the H+ concentration, which is related to the OH- concentration by the self-ionization constant (Kw = 1.0x10−14). A strong base has a lower H+ concentration because they are fully protonated and less hydrogen ions remain in the solution. A lower H+ concentration also means a higher OH- concentration and therefore, a larger Kb.


NaOH (s) (sodium hydroxide) is a stronger base than (CH3CH2)2NH (l) (diethylamine) which is a stronger base than NH3 (g) (ammonia). As the bases get weaker, the smaller the Kb values become.

Percentage protonated

As seen above, the strength of a base depends primarily on pH. To help describe the strengths of weak bases, it is helpful to know the percentage protonated-the percentage of base molecules that have been protonated. A lower percentage will correspond with a lower pH because both numbers result from the amount of protonation. A weak base is less protonated, leading to a lower pH and a lower percentage protonated.

The typical proton transfer equilibrium appears as such:

B(aq)+H2O(l)↔HB+(aq)+OH−(aq)

B represents the base.

Percentageprotonated=molarityofHB+initialmolarityofB×100%=[HB+][B]initial×100%

In this formula, [B]initial is the initial molar concentration of the base, assuming that no protonation has occurred.

A typical pH problem

Calculate the pH and percentage protonation of a .20 M aqueous solution of pyridine, C5H5N. The Kb for C5H5N is 1.8 x 10−9.

First, write the proton transfer equilibrium:

H2O(l)+C5H5N(aq)↔C5H5NH+(aq)+OH−(aq)
Kb=[C5H5NH+][OH−][C5H5N]

The equilibrium table, with all concentrations in moles per liter, is

C5H5N C5H6N+ OH-
initial normality .20 0 0
change in normality -x +x +x
equilibrium normality .20 -x x x
Substitute the equilibrium molarities into the basicity constant Kb=1.8×10−9=x×x.20−x
We can assume that x is so small that it will be meaningless by the time we use significant figures. 1.8×10−9≈x2.20
Solve for x. x≈.20×(1.8×10−9)=1.9×10−5
Check the assumption that x << .20 1.9×10−5≪.20; so the approximation is valid
Find pOH from pOH = -log [OH-] with [OH-]=x pOH≈−log(1.9×10−5)=4.7
From pH = pKw - pOH, pH≈14.00−4.7=9.3
From the equation for percentage protonated with [HB+] = x and [B]initial = .20, percentageprotonated=1.9×10−5.20×100%=.0095%

This means .0095% of the pyridine is in the protonated form of C5H5NH+.

Examples

Other weak bases are essentially any bases not on the list of strong bases.

Simple Facts

  • An example of a weak base is ammonia. It does not contain hydroxide ions, but it reacts with water to produce ammonium ions and hydroxide ions.[1]
  • The position of equilibrium varies from base to base when a weak base reacts with water. The further to the left it is, the weaker the base.[2]

See also

References

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External links

  1. ↑ Atkins, Peter, and Loretta Jones. Chemical Principles: The Quest for Insight, 3rd Ed., New York: W.H. Freeman, 2005.
  2. ↑ Clark, Jim. "Strong and Weak Bases."N.p.,2002. Web.
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