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Full text of "1-2-3 market segmentation"

BEBR 

FACULTY WORKING 
PAPER NO. 1382 



1-2-3 Market Segmentation 



Frederick W. Winter 



College of Commerce and Business Administration 
Bureau of Economic and Business Research 
University of Illinois, Urbana-Champaign 



BEBR 



FACULTY WORKING PAPER NO. 1382 
College of Commerce and Business Administration 
University of Illinois at Urbana-Champaign 
August 1987 



1-2-3 Market Segmentation 

Frederick W. Winter, Professor 
Department of Business Administration 



Digitized by the Internet Archive 

in 2011 with funding from 

University of Illinois Urbana-Champaign 



http://www.archive.org/details/123marketsegment1382wint 



ABSTRACT 
Normative segmentation is difficult because of constraints and 
cost versus revenue considerations. Lotus 1-2-3 offers a 
convenient and "manager friendly" way to select appropriate 
marketing mixes to target to various market segments. 



The author would like to thank the Procter and Gamble Company for 
their generous support to the marketing faculty at the University 
of Illinois. This grant made possible the utilization of 
equipment with which this program was developed. 



Marketers have long recognized that a market is not really- 
made up of potential customers with identical needs and wants . 
Thus, the concept of market segmentation which involves "the act 
of dividing up a market into distinct groups of buyers who might 
require separate products and/or marketing mixes" (Kotler, 1984) , 
is of major importance. 

Segmentation, as a form of aggregation, can help reduce the 
complexity of market heterogenity . Obviously it is far easier to 
consider five different market segments than 500,000 individual 
potential customers. But in practice, normative segmentation has 
remained very much an art. 

In a theoretical paper, Tollefson and Lessig (1978) report: 

Market segmentation involves two related problems: 
(1) the aggregation of potential customers into 
segments or of smaller into larger segments and (2) the 
allocation of marketing effort among a given set of 
segments. 

The actual implementation of normative segmentation has been 

difficult because : 

...in all the present approaches. . .the development of 
market segments and allocation of resources. . .are 
considered as two independent questions. In fact the 
two issues are closely intertwined. 

(Mahajan and Jain, 197 8) 

These difficulties associated with application are exacerbated if 

the market is disaggregated substantially into a large number of 

microsegments (Winter, 1984) , a trend that is likely to continue 

as firms try to out-"niche"and out-position one another. 

Cost-benefit segmentation (Winter, 1979) has shown that the 

optimum "level" of segmentation aggregation (or disaggregation) 

and resource allocation can, in fact, be solved. In cost- 



m 



benefit segmentation, the market is first disaggregated as far as 
the data allow. Next, alternative marketing mixes are selected 
for each "micro-segment." Because of a fixed cost associated 
with each mix, there is the tendency to try to offer one mix to 
multiple micro-segments in spite of the fact that revenues will 
be highest with many mixes. Thus, the balance between the high 
benefit (i.e., revenue) of many mixes and the low cost of few 
mixes. If two or more of the "micro-segments" receive the same 
mix, then, indirectly, they are aggregated. This produces a 
result which is compatible with theoretical work (Tollefson and 
Lessig, 1978) which suggests segments that respond to the same 
mix should be aggregated. It also recognizes that the number of 
mixes employed is often constrained by matters such as a budget 
(Mahajan and Jain, 1978). Winter (1979) has shown that the 
process can be solved using 0,1 integer programming (See Appendix 
I). However, 0,1 integer programming has never enjoyed great 
popularity among marketing managers. This paper will present an 
alternative to this formulation. 

It is a fact of segmentation analysis that the analyst 
rarely knows the exact response of the segments. Conjoint 
analysis, causal modelling, and other methodologies have added to 
our understanding of response; nevertheless, to a great extent, 
guesswork is involved. While this methodology cannot change 
this, the procedure can help to direct our guesswork in an 
effective manner. 

In order to effectively analyze different market 
segments, one needs a tool that will handle a great many 
microsegments as well as a considerable number of "what ifs" on 



the part of the analyst. Lotus 1-2-3 software in conjunction 
with a microcomputer is superb in this regard. Its acceptance 
among managers is legendary and, thus, it offers a practical "on 
hands" alternative to 0,1 programming formulations. 

The process of determining each mix to be offered is 
hopelessly complex. A change of marketing mix can be expected to 
change market share (and therefore sales units), price, unit 
cost, and maybe fixed costs. Imagine being given the following 
instructions: 

"There are 10 segments out there, all of whom behave 
differently. We need you to develop the optimal 
advertising, price, distribution, and product mix. 
Bear in mind that if you want to offer different 
colors, the manufacturing setup cost is $40,000. But 
if you can get them to buy blue colored units, we can 
save $ .20 per unit. Don't spend too much on 
advertising since only segments 3, 4, and, to a lesser 
extent 8, respond at all to advertising, although 
segment 7 will respond to fear appeals. Make sure that 
if you sell units at different prices to different 
segments, then atleast the units differ in terms of 
some product f eature. . . .And, by the way, Pete Jones, 
our Sales Manager, can brief you as to the costs of 
increasing distribution." 



THE SEGMENTATION PROBLEM 
The segmentation problem is essentially quite simple: Given 
different microsegments, what marketing mix should be assigned to 
each segment, recognizing that more mixes will be more costly 
than few and that some mixes are more expensive than others? 
Furthermore, the cost of each additional mix employed must be 
compensated for by offsetting revenue increases. 

For segmentation purposes, numbers in the spreadsheet are 
the result of either inputs (that may later be subject to "what 



if" analysis) , or formulae representing values which depend upon 
other cells. The "macro" feature of 1-2-3 which permits programs 
to be written that process data or assist in cell transfer or 
movement was used extensively. Some of the macros employed in 
segmentation analysis will be discussed in Appendix II . 

The discussion of the worksheet approach to segmentation will 
proceed by describing different zones of the 1-2-3 worksheet that 
are used in determining the overall profit associated with the 
different marketing combinations. 

Early "Field" Testing 1-2-3 Segmentation 

Eleven managers of profit and non-profit organizations were 
taught to use Lotus 1-2-3 segmentation in approximately 2 hours. 
All had prior exposure to Lotus although some were more 
comfortable than others with the use of 1-2-3 . 

Once the model was described, the managers inputted best 
guess estimates of the market for one of their products/services. 

All the managers developed spreadsheets which they felt 
represented the market in which they compete. After inputting 
the status quo mix(es) which their firm currently employs, they 
then tried different mixes to develop alternative mixes to 
consider. The change in profit was noted. The expected profit 
increases varied from a low of +12.5% up to +141%. While these 
are projected, not actual results, all managers felt that real 
gains would result because of 1-2-3 segmentation. 

An illustrative problem will first be described from an in- 
depth case study on which the data in the zones is based (the 
actual data have been partially disguised) . 



An Illustrative Application 

A manufacturer of a sporting goods/recreational consumer 

good was interested in adding a new product to a current product 

line. The 1-2-3 model was used to review the marketing mix 

targeted for the market. 

The manufacturer determined the following factors to be 

relevant in terms of the effect on profit: 

Controllable exogeneous variables-price, promotional 
giveaways, weight, advertising budget, product feature 
X (unnamed to prevent disclosure of the product) , and 
number of dealers 

Uncontrollable exogeneous variables — price charged by 
competitors 

Endogeneous variables — competitive entry (and price 
charged) as well as professional use of brand. 

The controllable variables would directly affect market 
share and would also effect the endogeneous variables which, in 
turn, affect market share. For example, the weight of the 
product will not only affect the user, but the lighter the unit 
the more appeal to the professional. If the professional 
segment were to adopt the brand it would further influence the 
weekend athelete in his choice of brands. 

Many of the inputs are from company records, but many such 
as competitive prices had to be guessed. Of course it is easy to 
do a sensitivity analysis on values with subjective estimates. 

The remainder of the paper will describe the major zones of 



the worksheet by use of the illustrative example, above. The 
data shown in the illustrative problem are for one time period, 
the ending period. Later a procedure to consider the worksheet 
over multiple time periods will be discussed. 



ZONES OF THE WORKSHEET 
The Summary Zone: The Results Section 

The Summary Zone in Exhibit 1 can be called the "results" 
zone since decisions in other zones will produce "results" such 
as market shares, unit costs, fixed costs, and the criterion 
variable, total profit (in the lower left corner of the Summary 
Zone) . Note that the results in the total market column are 
simply the summation of results in individual micro-segments (up 
to 12 micro-segments are allowed) . 

Inputs to the Summary Zone by the manager are segment names, 
segment proportions, total number of consumers in the market, and 
the purchase rates of the different segments. Furthermore, the 
user can specify fixed or unit costs associated with transactions 
with a particular segment. For example, if one segment is 
geographically distant from others, there may be some particular 
transportation costs which must be incurred. All other values 
shown in the worksheet are formulae driven by inputs to other 
parts of the worksheet. 

The total size of the market targeted by the case study 
sponsor was expected to include 30,000 potential consumers 
divided between the various segments. Of those who would not be 
expected to buy the competitive product lines, the following 



segments were thought to exist: the weekend athlete who buys by 
mail, the weekender who buys from a dealer, the serious 
competitor who buys by mail, the serious user who buys from a 
dealer, and the professional. The purchase rate was expected to 
vary between .25 and (meaning purchases varying between once 
every four years) to once every year. Dealer margins were added 
to segment specific costs. 

Because the company already had an existing product line, it 
was necessary to consider two atypical segments: purchasers who 
would normally buy company brand X, and purchasers who would 
normally buy company brand Y. When this is modelled, these "loyal" 
segments (CUST X and CUST Y in the worksheet) will have costs 
associated with them that reflect the contribution margin for the 
firm's current products ($80 and $75 for X and Y respectively). 
In this way, if the new product gains some of the loyal markets, 
it must have a margin great enough to more than overcome the 
margin of the existing line. If not then "cannibalization" will 
cost the firm profit. 

The Cost Zone: Cost Assignments 

Cost-benefit segmentation clearly showed that a proliferation 
of marketing mixes can add greatly to the cost of the marketing 
program. In the Cost Zone (Exhibit 2), these costs are input. 
The first entry is base cost which represents the fixed and unit 
costs associated with production of a "base" unit. Fixed overhead 
can be considered but was not by the case study manufacturer. 

For each marketing mix component, any additive value (added 
to the base) associated with the mix is input. Note that some 



costs, such as advertising, are primarily fixed while others, 
such as weight can involve a combination — unit cost which 
reflects procurement and manufacturing and fixed cost 
incorporating set up time and administrative costs, for example. 

The model can consider the evolution of costs over time. A 
column is available for reduction in unit costs associated with 
experience. A value of 10% would, for example suggest that unit 
costs will drop 10% with each doubling of volume. In the sample 
problem the experience factor was expected to be 5%. In this 
case, experience was not a major factor, but in other studies it 
has resulted in a lower initial cost to both reduce competitive 
sales but also to drive down the experience curve more rapidly. 

Another column is available to model in a one-time fixed 
costs, such as that associated with purchase of special equipment, 
etc. 

Inputs to the cost zone come from the analyst. Columns not 
described such as cumulative units are used for calculation 
purposes. As far as outputs, the appropriate unit costs go into 
the unit cost row of the Summary Zone, for the respective 
assigned mix. Assigned fixed costs go into the total profit 
calculation, also in the Summary Zone. 

The Response Zone; Segment Response 

The Response Zone (Exhibit 3) indicates the segments' market 
share responses to different marketing mixes. The figures shown 
for each segment are similar to dummy variable regression 
coefficients. An intercept term is also included. The model of 
market share is: 



EMSj = blj xlj + b2j x2j + b3j x3j +... 
where: 

EMSj = expected share realized in segment j 

bij = response coefficients; bij represents the effect of 
mix level i on segment j 

xij =0,1 dummy variables; equal to 1 if marketing mix 
level i is directed to segment j , otherwise 

However, Lotus 1-2-3 is very flexible and its formulae could 
easily handle nonlinear models of market share. The dummy 
variable methodology is simple to implement and understand. Both 
discrete variable and nonlinear relationships can easily be 
modelled. If formulae were substituted for scale values, 
interactions could be modelled as well. 

Early field testing of the worksheet indicated that many 
worksheet inputs were straight-forward and generally known or 
obtainable with little trouble. The inputs that presented the 
most difficulty were the response coefficients. In particular, 
the intercept value was difficult for the managers to understand. 
One method that helped enormously was to input zero for the 
coefficient for the present marketing mix (labelled "base" in the 
worksheet it might represent current price, level of 
advertising, etc. ) . If this is done, the intercept can be 
interpreted as the current (or expected) market share in each 
segment. Although some of these market shares had to be guessed, 
the total market share (Column 1 of the Summary Zone) was 
generally known and this facilitated the estimation of the 
segment components. Once the zero base was established, other 
mix coefficients were deviations around this zero value (e.g., 



the coefficient for a decreased advertising level would be 
negative and increased advertising would have a positive 
coefficient) . 

The response zone of the illustrative problem reflects the 
feeling that the professional is not a likely to be a purchaser 
of this product unless the weight is significantly reduced. It 
was felt that the market share in the professional market could 
positively impact the serious and weekend competitor and 
therefore we see "professional penetration" affecting other 
segments. 

In the illustrative problem, a straightforward guess of 
response zone coefficients produced initial values for market 
share (with various mix adjustments) that management felt were 
unobtainable. Because of this one of the options available in the 
program was used to statistically estimate coefficients using 
subjective management judgments of market share. 

This statistical estimation procedure utilizes an orthogonal 
design written into the Lotus worksheet which presents managers 
with different components of the marketing mix, and the user 
provides the expected share. (See Exhibit 4 for one of 16 
different mix combinations from the sample problem) . A 
regression was then fit to the responses and the coefficients 
then represent starting inputs to the Response Zone (Lotus 1-2-3 
Version 2 has a regression capability) . Management felt that 
these new coefficients represented a more valid picture of the 
market and only small modifications were made to the regression- 
derived values. 



10 



The market share of the Summary Zone is constrained between 
the values of and 1. Other than these limits, the response 
values of Zone 2, in conjunction with the assignments of the Mix 
Zone (to be described) determine the market share in each 
segment . 

Simulation and the Probability of Response Zone 

There exist a number of circumstances where a variable that 
affects market share may be operational in one period but not in 
another. In the example problem, the entry of a new competitor 
would affect market share if it were in effect. Therefore, it is 
desireable to allow a variable to probabilistically be included 
or excluded from the system. 

Exhibit 5 shows the "Probability of Response Zone" which 
tracks the status (e.g. included or excluded) or each variable. 
The first column represents the starting status. "1" means 
the variable is included and "0" means excluded. The next two 
columns represent the probability of inclusion given currently 
excluded or included respectively. The last column is the status 
for the period being considered. 

There are two ways in which probability can be considered. 
If the user inputs "1" for the number of simulations desired, 
the variable will be considered in a expected value mode. Thus 
the current status for a variable will be : 

Current status=previous status X probability of in given in 
+ (1-previous status) X probability of in given out 



This new current status is then multiplied by cost and respon 



se 



11 



coefficients and, therefore, is included in the summary zone. 

A second option is to do a Monte Carlo type of simulation 
(accessed by indicating a number greater than 1 when the pre- 
programmed macro asks for the number of desired simulations) . If 
the second column has a value of .6, for example, a to 1 
uniformly distributed random number (available in Lotus) will 
decide whether the next current status will be "in" (random 
number between and .6) or "not in" (random number greater than 

its response coefficients affect market share. If the next 
period status is "in", then the probability of staying in given 
already in will determine the next period status. 

In the application discussed the probability of competitive 
entry was felt to be .90. Note, however, that the entries can be 
formulae instead of numbers. Thus the probability of competitive 
entry can be based on the price level (or some other variable 
that affects competitive entry) . 

The Mix Zone: Mix Assignments 

The Mix Zone (Exhibit 6) represents the marketing mixes that 
have been assigned to the various segments (microsegments) . 
Therefore, it represents the zone where the manager tries 
alternative "what if" mixes and observes the effect on profit in 
the results zone (continually displayed using Lotus' title 
feature) . For example, one might want to consider a high-priced 
product with a special product feature to the serious segment and 
a lower-priced product with an inferior feature to the weekend 
athlete. In contrast, advertising is spent and directed at all 
segments. However, because of media exposure, persuasability, 

12 



etc., some segments will respond more than others to this 
advertising. 

One column of the Mix Zone allows an override of individual 
assignments ("u" or "d" specification) ; this allows the analyst 
to observe the effect of profitability of a treatment that is 
common to all segments (i.e. undifferentiated marketing). When 
this is done, the individual segment treatments have a "NOT APPL" 
designation (meaning that individual treatments are "not 
applicable") . In this way, the effect of special targeted mixes 
which offer the promise of more revenue ("d" for differentiated) 
can be compared with less costly mixes which offer identical 
treatments to all segments ("u" for undif ferentited) . 

All numbers in the Mix Zone are input by the user, and, 
together with the response numbers of the Response Zone, market 
share for each segment is determined, displayed, and used further 
in the Summary Zone. The program allows interpolation for 
intervally-scaled variables, and, thus, the cost and 
response components contributions to the summary zone may be 
subject to interpolation. Furthermore, the program warns the user 
when levels are selected which are outside the upper and lower 
limits for each variable. 

Dynamic Modelling 

As the discussion indicated, it may be desireable to consider 
the worksheet over multiple time periods. Because of this, the 
program is set up to cycle through consecutive time periods. One 
option is to go through time periods where pre-programmed 
formulae change the values. For example, the formula 



30000* ( (1.07) C PERIOD) will increase a value of 30,000 (e.g. 
market size) by 7% every year (or whatever the duration of one 
time period) . Alternatively, the user can select the option to 
intervene on a period by period basis and change elements of the 
worksheet prior to proceeding. 

Throughout the cycles, the profit figures are calculated and 
stored. Present values are then calculated (Exhibit 7 for the 
case study) . 

Advanced Modelling Options 

A number of advanced modelling features including simulation 
and dynamic modelling using formulae instead of constants for 
cell entries have already been discussed. To supplement this two 
other "mini-zones" are available on the worksheet (Exhibits 8 and 
9) . The random number zone will simply generate random numbers 
from a uniform or normal distribution with specified parameters. 
This can be helpful in introducing noise or randomness in cost, 
mix or other zones of the worksheet. 

The lagged variable zone will track variables of interest 
through three lagged time periods. In the illustrative problem, 
note that the variable in the mix zone that represents 
professional penetration really a "formula" and is equal to the 
cell that tracks the one-period lagged market share in the 
professional segment (Exhibit 9) . Professional penetration then, 
in turn, affects market shares of the weekend, serious, and loyal 
customer segments via the response coefficients. 

This particular case indicates further why a dynamic 
analysis is particularly important. While it may not be 



±L 



^MB^^H« 



worthwhile to market to professionals in a one period time 
horizon, the value is clearly seen over multiple time periods, 
because of the professional impact on the amateur. In other 
applications, low price strategies could be considered that gain 
early experience curve effects and/or discourage competitive 
entry. 

Case Study Results 

In the case study described (Mix Zone appears in Exhibit 6) , 
the firm was able to increase its expected three year profit by 
14%, when compared to what was previously felt to be the best 
mix. The better mix was achieved by not increasing the number of 
dealers and by changing the weight of the product to 9 from the 
originally-planned weight of 10 (with the exception of 
professionals who will receive the professional model with weight 
of 8) . 

Management continues to debate the outcome of the program 
and other management participants will input best guesses to the 
program. The exercise was felt to be very helpful in indicating 
where additional data were required and where the solution is 
insensitive to different inputs. Plans to extend the analysis to 
other products of the company have already been made. 

USING 1-2-3 
There are a number of major benefits associated with using 
the special 1-2-3 worksheet for market segmentation. First and 
most important is the ability to change mix assignments (in the 
Mix Zone) and observe the effect of market share, sales, and 



15 



profitability in the Summary Zone. The results of the current 
mix employed can be easily compared to a large number of other 
mixes. 

The method used can structure the analyst's thinking. 
Managers are forced to think about various segments — segments 
which truly respond differently to different marketing stimuli. 
In segmentation, if one were to use bases that are inappropriate, 
then each segment will respond similarly (and therefore equal to 
the aggregate market) , and differentiation in terms of marketing 
mixes will yield no additional profit over and above the best 
aggregated mix. 

Another benefit is that management is forced to incorporate 
costs and the cost structure of the different mixes into their 
thinking. This, traditionally has been a weakness of marketing 
managers. Finally, the procedure helps to point out unknowns and 
graphically demonstrate the sensitivity of profit to these 
unknowns . 

Although the 0,1 programming solution of Appendix I is more 
elegant, 1-2-3 segmentation permits the modelling of real-world 
complexities such as non-linear cost functions, multiple time 
periods and the dynamic response of the market, and competitive 
reaction. While many analytical solutions or programming 
solutions are more elegant, few methods can offer the realism of 
a sophisticated worksheet such as that described. 

LIMITATIONS AND CONCLUSIONS 
Some features not explicitly discussed are described in 
Appendix II. These greatly enhance the usefulness of the 



16 



approach. Nevertheless, the model recommended has a number of 
limitations, most of which can be easily overcome with simple 
modification. All in all, 1-2-3 segmentation would appear to 
contain realistic models of the market and revenue and cost 
behavior resulting from the direction of marketing mixes to the 
segments of the market. The form is "manager friendly" since 1- 
2-3 has many enthusiastic followers among marketing managers. 
Various features of 1-2-3 including macros and graphing should 
assist use and presentation of the results. 



17 



REFERENCES 

Kotler, Philip, Market of Management Analysis, Planning, and 

Control , Englewood Cliffs, NJ: Prentice Hall, 1984, 
Mahajan, Vijay and Arun K. Jain (1978), "An Approach to Normative 

Segmentation," Journal of Marketing Research , 15 (August), 

338-34 
Tollefson, John 0. and V. Parker Lessig (1978), "Aggregative 

Criteria in Normative Segmentation Theory, " Journal of 

Marketing Research , 15 (August), 346-355. 
Winter, Frederick W. (1979), "A Cost-Benefit Approach to Market 

Segmentation," Journal of Marketing , 43 (Fall), 103-111. 
Winter, Frederick W. (1984), "Market Segmentation: A Tactical 

Approach," Business Horizons, (January-February), 57-63. 



APPENDIX I 
0,1 Programming Formulation of the Segmentation Problem 

We can consider overall profit Z as: 
Z= Xij GPij - wj FCj 

or: 

Z= Xij (Ni Cj Di Pij) - wjFCj 



subject to: 



where: 



Xij -wj < for all i f j 
Xij=0,l 



Xij =0,1 assignment variable. If 1 it indicates 
marketing mix j is assigned to segment i. 

wj = 1 if marketing mix j has been assigned to 
atleast one segment, otherwise 

GPij =gross profit before fixed costs associated with 
offering marketing mix j to segment i 

Ni =number of consumers in segment i 

Cj contribution margin which is the price 

associated with marketing mix j minus the cost 
associated with mix j 

Di =per capita demand of product class by segment i 
consumers 

Pij =probability of brand (defined by mix j) purchase 
by members of segment i 

FCj =fixed costs associated with offering mix j 






APPENDIX II 
Macros and Special Features of 1-2-3 Segmentation 

1. Initialization Macro 

After the user responds that he would like the initialization 
procedure, the program queries the analyst with regard to the 
relevant marketing mix variables and the levels described (up to 
eight mix variables of four levels are allowed) . 

2. Interpolation Feature 

If the analyst specifies four levels of an intervally-scaled 
variable as $10MM, $20MM, $30MM, and $40MM f for example, the 
effect of $18MM on sales and costs will be interpolated. The 
program also warns the user when variable levels selected outside 
the permissable range are being used. 

3 . Movement Macros 

The program employs a number of macros that facilitate 
movement around the diverse worksheet. " Alt-Z", for example, 
put a zone menu up that facilitates movements between zones. 
"Alt-M" displays the main menu. 

4. Formula Feature 

The formula feature allows the user to select a linear, 
exponential or s-shaped formula for inclusion in any cell. In 
addition to the independent variable specification, the user must 
indicate parameter values. The graphing feature is available to 
view the relationship prior to actual "imprinting" in a cell. 



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EXHIBIT 5 



Start Prob in Prob in prev ZONE 2 ALT.MKT MIXES 
Status given outgiven in status cur StatusINTERCEPT. 
1111 1 Price 

229 
239 
259 
269 
1111 1 Promo Giveawa 

nothing 
A 
B 

A+B 
1111 1 Weight 

8 

9 

10 

1111 1 Prof. Penetra 



0.1 

0.2 

0.4 

1111 1 Adv$ 

5000 

10000 

15000 

20000 

1111 1 Feature X 

no 
yes 



111 1 Current Comp Pr 

220 
260 
290 

0.9 0.95 0.95 0.9475 New Comp Pric 

220 
260 
290 

111 1 Number Dealer 

200 
300 
400 
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cu 
cu 

< 



E- 
O 

z 



o —. 

•J 

CU 

cu 

< 



Eh 

o 

Z 



O J 
Cu 

CU 

< 



Eh 

o 

z 



CU 

cu 
< 



E- 
O 

z 



in 

CN 



O 
CN 
CN 



O 
CN 



E 

c 

-»H 



X 

2 



O J 

cu 
cu 

< 

Eh 

O 

z 



O J 
Cu 
CU 

< 



Eh 

o 

z 



O J 
CU 

Cu 

< 



Eh 

o 

z 



O J 
CU 
CU 

< 



Eh 
O 

z 



o — . 
•J 
cu 
cu 

< 

E- 

O 

z 



O J 

cu 
cu 

< 

Eh 
O 

z 



cu 

CU 

< 



Eh 
O 

z 



o 

o 



o 
o 

CN 



O 

o 
m 



E 
C 



x 

X 



o 

CU 



I 



9) 

u 

3 

<0 
0) 



0) 

o 
kl 

CU 



I 



01 

z 



EXHIBIT 7 



SIMULATION RUN 




1 


2 


TIME PERIOD 






CASH FLOWS 


1 


$330, 


699 





2 


$350, 


714 





3 


$355, 


886 





4 










5 










6 










7 










8 










9 










10 










NET PRES VALUE 


$725, 


,0 87 


$0 













$0 



EXHIBIT 8 



RANDOM NUMBERS 
if NORMAL distrib."n n SIGMA= MEAN= 



if UNIFORMd 


is 


trib. 


"u" 


LOW= 


HIGH= 


RN 


#1 






u 


0.1 


1.1 


0.939 


#2 






u 


0.2 


1.2 


0.498 


#3 






u 





1 


0.414 


#4 






n 


50 


100 


143.798 


#5 






n 


1 


5 


5.869 


#6 






u 






0.000 


#7 






u 






0.000 



EXHIBIT 9 

LAGS SECTION 
Var t (formula) t-1 t-2 t-3 
prof, penetr 0.25 0.25 0.15 0.00