Example 12.12

Marketing Models

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Background Information

DoItQuick is software company that sells programs to individuals for keeping track of home finances, home inventory, and other common tasks.

The company has done extensive research into its costs and revenues, and it has discovered that new customers are much less profitable on an annual basis than long-standing customers. There are several reasons for this.

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Background Information -- continued Long-standing customers tend to require less in

overhead costs, they tend to order more merchandise annually, and they help DoItQuick make money by referring new customers to the company’s products.

The company estimates that a customer who has been loyal for n years – that is has brought from the company for n consecutive years – contributes a normally distributed random amount of profit in the nth year that has mean and standard deviation as listed on the next slide.

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Background Information -- continued DoItQuick is interested in seeing how much profit a

typical customer is worth over his or her years with the company.

This depends on the probability of retention. To model retention, let r(n) be the probability that a customer who has purchased for n consecutive years does not purchase the next year.

If this occurs, we assume that the customer switches loyalty and never purchases from DoItQuick again.

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Background Information -- continued A consultant has suggested to DoItQuick that a

reasonable model of customer retention is to let r(1) = 1-p for some p between 0 and 1, and to use the equation r (n) = qr(n-1) for n>2, where q is a positive constant.

What does this model mean, and how can it and the data be used to simulate the nest personal value 9NPV) of profit over a 20-year period from a typical customer who has made his or her first purchase from DoItQuick this year? Assume an interest rate of 10% for discounting.

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Solution

The solution is broken into several parts.

First we will explain the consultant’s retention model.

Then we will fit curves to the profit data.

Finally, we will develop the simulation model and run it with @Risk.

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Explaining the Retention Model The consultant’s retention model makes sense.

First, p represents the probability that a customer who purchases this year for the first time will purchase again next year.

Then q is the fraction by which the probability of not remaining loyal changes year by year.

The company wants the r(n) values, the probabilities of losing customers, to be small, so it wants p to be large and q to be small. We will test several pairs of p and q when we run the simulation to see how these parameters affect the NPV of profit.

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Finding the Data We first use the ideas from Chapter 2 to fit equations

to the means and standard deviations.

For each, we draw a scatterplot versus year, then superimpose an appropriate trendline with Excel’s Chart/Add Trendline menu item.

As shown in the figure, a logarithmic fit of the means looks good, whereas a linear fit of the standard deviation seems appropriate.

Therefore, in the simulation model we will estimate the mean and standard deviation of profit from a customer in her nth year with the company as –23.285 + 64.941ln(n) and 5.5515 + 1.3505n, respectively.

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LOYALTY.XLS The simulation model appears on the next slide.

This file contains the model.

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Developing the Spreadsheet Model The model can be developed with the following steps.

– Inputs. Enter the inputs in the shaded cells. These include the parameter of the fitted equations for mean and standard deviation, the discount rate, and selected values of the retention parameters p and q.

– Simulation index. We will use RISKSIMTABLE to run the simulation 12 times, once for each combination of p and q. To set up the model to do this, enter the formula RISKSIMTABLE(SimIndexes) in cell B11. Then obtain the corresponding values of p and q in cells B13 and B15 with the formulas =VLOOKUP(SimIndex,LookupTable,2) and VLOOKUP(SimIndex,LookupTable,3)

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Developing the Spreadsheet Model -- continued

– Profits. We want to simulate profits from a customer for as long as the customer remains loyal to the company. To do so, first calculate the appropriate means and standard deviations in columns B and C of the simulation section with the formulas =InterceptMean+SlopeMean*LN(A21) and =InterceptStdev+SlopeStdev*A21 in cells B21 and C21, and copy them down for all 20 years. Then generate the actual profits from this customer in column D as long as the customer remains loyal. Start by generating the first-year profit in cell D21 with the formula =RISKNORMAL(B21,C21) Then for succeeding years, enter the formula =IF(OR(F21=“Yes”,D21=“”),””,RISKNORMAL(B22,C22)) in cell D22 and copy it down. The OR condition checks whether the customer has discontinued buying from DoItQuick. If so, a blank is entered. Otherwise, a normally distributed profit is generated.

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Developing the Spreadsheet Model -- continued

– Probabilities of quitting. Calculate the probabilities of quitting in column E from the retention model. To do so, enter the formula =1-PrKeepBuying1 in cell E21. Then for succeeding years, enter the formula =IF(OR(F21=“Yes”,D21=“”),”” ,RetFactor*E21) in cell E22 and copy it down.

– Quits? We keep track of the customer’s status in column F. First, enter the formula =IF(RAND( ) < E21,”Yes”,”No”) in cell F21. Then enter the formula =IF(OR(F21=“Yes”,D21=“”),””,IF(RAND( )<=E22, “Yes”, “No”)) in cell F22 and copy it down. This logic will produce several values of “No”, followed by a single “Yes” and the blanks.

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Developing the Spreadsheet Model -- continued

– Output cells. We will keep track of the NPV of profit and the number of years remaining loyal for this customer as @Risk outputs. Calculate these in cells B43 and B44 with the formulas =RISKOUTPUT( ) + NPV(DiscRate,Profits) and =RISKOUTPUT( )+COUNT(Profits). Note that the COUNT function counts nonblank cells only.

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@Risk Results

We set the number of iterations to 1000 and the number of simulations to 12.

Selected summary results appear on the next slide.

For a change, we copied and pasted the @Risk results to the spreadsheet so that we could easily see how they vary with p and q.

The bar charts of the means clearly show how large values of p and small values of q are best for the company.

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@Risk Results -- continued

By increasing the probability of keeping customers loyal, the company can make a big improvement in its bottom line.