GB304 Final Project Report Final 2

GenerAL bUSINESS 304

The Culver’s Case

AbstractThe major purpose for this business report is to help our clients, Russ and Vicky, choose the

best location for a new Culver’s franchise restaurant in Carbondale, Illinois, basing on comprehensive statistical analysis

Rena Huang, Yuting Yang, Yaoyao Chen, Zichun He, Tina Zhou, & Pack Zhao

[Email address]May, 10th, 2015

CONTENTS

Executive Summary........................................................................................................................... iii

Introduction........................................................................................................................................... 1

Building Business Model...................................................................................................................4

Financial Analysis..............................................................................................................................29

Recommendation.............................................................................................................................. 34

Conclusion............................................................................................................................................ 36

Appendix....................................................................................................................................... 38/-1-

Figure 1 - Handling Missing Data.................................................................................................................9

Figure 2 - Normal probability plot of the residuals for the gross sales....................................28

Figure 3 - Plot of residuals against dummy variable 2 of CFSI suitability rating of the

Culver's restaurant..........................................................................................................................................28

Figure 4 - Plot of residuals against dummy variable 1 of CFSI suitability rating of the


Figure 5 - Plot of residuals against the traffic count around the Culver's restaurant........28

Figure 6 - Plot of residuals against the population within a one-mile radius of the


Figure 7 - Predicted gross sales.................................................................................................................31

Figure 8 - Startup expenses.........................................................................................................................32

Figure 9 - Location Information.................................................................................................................35

EXECUTIVE SUMMARY

SCOPE AND OBJECTIVE

As a student-run consulting firm, we received a request from our clients, Russ

and Vicky, to make a decision of choosing a site location for a Culver's franchise

restaurant by analyzing a set of data from Culver’s restaurants and relative

financial information.

IMPORTANCE OF THE ANALYSIS

Location is one of the key factors of a restaurant’s success, but it is hard to decide

which location is the best by just looking at demographic

characteristics. Therefore we did statistical analysis of the past data and financial

analysis of other relevant information with the intention to provide the most

accurate and reliable recommendations for our clients.

PREDICTION AND RECOMMENDATION

Along with analysis of the sample data, we utilized our financial knowledge and

business acumen to do further comparisons. Based on our business prediction

model, Site C is the most profitable one, but its startup expenses exceed our

clients' budget. Considering their financial ability, we recommend our clients to

choose the second most profitable location, Site A, instead.

INTRODUCTION

Culver's is one of the various food chains in the Midwest, which provides

franchise options for individuals. Our clients want to seize this business

opportunity, but they have difficulties selecting the best site for the new

franchise restaurant among three potential locations. To help our clients choose

the most appropriate site, we analyzed the sample data retrieved from 89

current Culver’s restaurants. Besides statistical analysis, we also took other

associated costs into account for site recommendations.

CLIENTS’ PROFILES

Name: Russ (age: 64) and Vicky (age: 60)

Goal: open a Culver's restaurant

Location: Carbondale, Illinois

Workforce Preference: Young students

Post-retirement Plan: actively manage an operation for a decade or more

Financial Ability: $1.2 million to $1.5 million

Acceptable minimum annual sales: $1,000,000

GENERAL COMPANY DESCRIPTION

Culver's Frozen Custard Restaurant is a family business founded in 1984 in Sauk

City, Wisconsin. It is a fast-food restaurant that cooks meal to order individually.

After the first opening’s great success, Culver’s began to franchise restaurants

through Culver Franchising System, Inc. (CFSI). Following is the information we

found useful for our clients to consider.

Mission Statement: Every guest who chooses Culver's leaves happy.

Founding principles: Freshness and quality, hospitality and service to the

community.

Business Hours: 10:00am-10:00pm (with exceptions serving breakfast as well)

Typical food service areas:

Indoor seating

Outdoor seating

Drive-up service

Competitive Advantages:

A wide variety of entrees

ButterBurgers® that are made from fresh ground chuck and serve on a

buttered toasted bun

Three daily flavors of custard: vanilla, chocolate, and the "flavor of the

day"

Qualities Culver’s are looking for of their franchise partners:

Leadership skills to take a team of people and operate a Culver's

according to the high standards.

Energy and enthusiasm

Willing to work hard

Love people and believe that having a great heart is also good business

STATISTICAL METHODS

Our statistical methods have two parts: 1) build the business prediction model;

and 2) analyze the profitability of each site. First we chose indicating variables,

and then filled out the missing data. Next we ran regressions to find the

relationship between gross sales and those relevant variables, and ultimately

picked out the best model. Then we applied this model to predicting gross

revenues of Site A, Site B and Site C. Furthermore, we took startup costs and

operating costs into consideration to find the most appropriate location for the

new Culver's restaurant. More details are in the “Building Business Model” section

and the “Financial Analysis” section.

BUILDING BUSINESS MODEL

CHOOSING INDICATING VARIABLES

We have collected the historical data of 89 Culver's Frozen Custard

restaurants from the company, which might be useful for us to build the best

model to predict future sales in the three potential locations. These independent

variables include:

Operation years (AGE)

Cost of food (FOOD)

Cost of paper (PAPER)

Labor expenses (LABOR)

Other operating expenses (OTHER OP)

Gross revenue from sales (GSALES)

Traffic count (TRAFFIC)

Population within a one-mile radius (POP1M)

Population within a five-miles radius (POP5M)

Per capita income within a one-mile radius (PERCAP1)

Per capita income within a five-mile radius (PERCAP5)

Average number of autos per household within a one-mile radius

(AUTO1)

Average number of autos per household within a five-mile radius

(AUTO5)

Percentage of adults married within a one-mile radius (MARRIED1)

Percentage of adults married within a five-mile radius (MARRIED5)

CFSI suitability rating (SUIT)

However, not all of these variables are relevant to predict gross sales. We

decided to discard variables PAPER, LABOR, FOOD, AGE and OTHER OP first

because they were irrelevant to the location of a new restaurant.

Therefore, the variables that we decided to keep to further analyze are:

TRAFFIC, POP1M, POP5M, PERCAP1, PERCAP5, AUTO1, AUTO5, MARRIED1,

MARRIED5, and SUIT.

HANDLING MISSING DATA

The raw data we have contained several missing data, so we decided to handle

missing data first. For Store 11 and 71, the data for POP1M, POP5M, PERCAP1,

PERCAP5, AUTO5, AUTO1, MARRIED1, MARRIED5, and SUIT were all missing.

Considering too many data were missing for these two stores and the whole data

set was relatively big, we decided to eliminate the data of these two stores as a

whole.

Then we moved on to deal with the missing data of TRAFFIC for Store 19, 23, 39,

42, 65, 75, 82, and 83. According to the information we had, this kind of missing

data was called “missing at random”. This means the cases with incomplete data

were different from those with complete data, but the pattern of the missing data

is traceable and predictable from the known data. Therefore, we decided to deal

with these missing data using hot deck imputation method.

Hot deck imputation is a method to identify the most similar case to the case

with a missing value and substitute the most similar case's Y value for the

missing case's Y value. Based on our intuition, we figured traffic count would be

related to gross sales, population and the number of automobiles, so we sorted

the data from smallest to largest based on TRAFFIC, POP1M and AUTO5. Then

we substituted the missing TRAFFIC data with those from the cases having the

most similar values of GSALES, POP1M and AUTO5.

Figure 1 - Handling Missing Data

(The cells highlighted in yellow are missing data and those in blue are reference data.)

)

BUILDING THE MODEL FOR PREDICTION

So far we have identified the 10 relevant variables to perform further data

analysis and have handled with missing data. The relevant explanatory variables

are: TRAFFIC, POP1M, POP5M, PERCAP1, PERCAP5, AUTO1, AUTO5, MARRIED1,

MARRIED5, and SUIT.

Then we used Forward Selection Method and Backward Elimination Method to

obtain the best-fit model. Then based on the best-fit model, we would decide on

the most appropriate model in this scenario and use it to make gross sales

prediction for each site.

Forward Selection Method involves starting with no variables in the model,

testing the addition of each variable using a chosen model comparison criterion

(P-value, R Square/adjusted R Square and Standard Error in our analysis),

adding the variable (if any) that improves the model the most, and repeating this

process until none improves the model.

Backward Elimination Method involves starting with all candidate variables,

testing the deletion of each variable using a chosen model comparison criterion

(P-value, R Square/adjusted R Square and Standard Error in our analysis),

deleting the variable (if any) that improves the model the most by being deleted,

and repeating this process until no further improvement is possible.

SCATTERPLOTS WITH INTERPRETATION

Here we conducted data analysis to figure out the best model: We plotted scatter

plots between every independent variable and the dependent variable, gross

sales. Scatter plot is a type of chart that displays values for two variables for a set

of data using X and Y axes and coordinates. From a scatter plot, one can get a

basic idea of the relationship between the two variables (See the scatter plots in

Appendix).

From those scatter plots, no distinct outliers could be observed, so we would not

consider the influence of outliers in further analysis. By observing the trend of

each scatter plot, we concluded that, a positive relationship existed between

gross sales and independent variables including TRAFFIC, POP1M, POP5M,

PERCAP1, PERCAP5, AUTO1, and AUTO5. Meanwhile, both MARRIED1 and

MARRIED5 variables had a negative relationship with gross sales. As for variable

SUIT, because it is categorical data, we could not conclude its relationship with

gross sales from the scatter plot.

FINDING THE BEST FIT MODEL WITH TWO METHODS

Forward Selection Method

After looking at the general relationships between each x-variable and gross

sales, we used Forward Selection to build the Model first.

1) Simple Linear Regression between Each Independent Variable and

Dependent Variable.

By doing simple linear regression of single variables, we got the following

results:

The p-values of variables MARRIED1 and MARRIED5 are both greater

than significance level of 0.05, which indicates that these two variables have no

significant influence on GSALES. Therefore we excluded them from the relevant

independent variables. The rest eight variables all have p-values less

than 0.05, which means that they have significant influence on GSALES.

Therefore, we would take them into the next step’s analysis.

Table 1 - Simple linear regression results for single variables

Among these eight independent variables, variable TRAFFIC has the highest R

Square and the lowest standard error. Therefore, it was selected as the first

independent variable of our model.

2) Multiple Regression with Two Independent Variables.

After choosing TRAFFIC as the first variable, we combined TRAFFIC with each of

the other independent variables and ran linear regressions between the two x-

variables and gross sales. The results are shown below:

Regression with an Interaction Terms:

According to the results, the p-values of all interaction terms are greater than

0.05, which means that these interactions are not significant to explain the

dependent variable. Therefore we did not need to include these

interaction terms in our model.

Regression Model without Interaction Term:

Table 2 - P-values of the interaction terms of two x-variables

Based on the results, the regression model with independent variables

TRAFFIC and POP1M is significant and has the highest adjusted R square and

the lowest standard error, so we added the second variable POP1M to

our model.

3) Multiple Regression with Three Independent Variables.

After choosing TRAFFIC and POP1M as variables, we combined TRAFFIC

and POP1M with each of the other independent variables and ran linear

regressions between the three x-variables and gross sales. The results are shown

below:

Regression with an Interaction Term


0.05, which means that all these interactions between each two terms are

not significant to explain the dependent variable. Therefore, we did not need

to include these interaction terms in our model.

Table 4 - P-values of the interaction terms of three x-variables

Regression Model without Interaction Terms:

According to the results, the regression model with independent variables

TRAFFIC, POP1M and AUTO5 is significant and has the highest adjust R

square and the lowest standard error, so we added the third variable, AUTO5,

to our model.

4) Multiple Regression with Four Independent Variables.

After choosing TRAFFIC, POP1M and AUTO5 as our variables, we combined

TRAFFIC, POP1M and AUTO5 with each of the other independent variables

and ran linear regressions between the four x-variables and gross sales.

The results are shown below:

Table 5 - Regression results for three x-variables

Regression Model with Interaction Terms:


0.05, which means that these interactions are not significant to explain the

dependent variable. Therefore, we did not need to include these interaction

terms in our model.

Regression Model Without Interaction Terms:

Table 6 - P-values of the interaction terms of four x-variables

Table 7 - Regression results for four x-variables

Based on the results, the regression model with independent variables

TRAFFIC, POP1M, AUTO5 and POP5M is significant and has the highest adjust

R square and the lowest standard error, so we added the

fourth variable POP5M to our model.

5) Multiple Regression with Five Independent Variables.

After choosing TRAFFIC, POP1M, AUTO5 and POP5M as our variables,

we combined TRAFFIC, POP1M, AUTO5 and POP5M with each of the other

independent variable and ran linear regressions between the five x-variables and

gross sales. The results are shown below:

Regression Model with Interaction Terms:


0.05, which means that all these interactions between each two terms are

not significant to explain the dependent variable. Therefore, we did not need

to include these interaction terms in our model.

Regression Model without Interaction Terms:

Table 8 - P-values of the interaction terms of five x-variables

According to the results, we found that each model had one or two x-

variables with p-values greater than 0.05, so no additional x-variable could be

added to our model to help explain the dependent variable. We ended our

forward selection process here.

6) Conclusion

Through the forward selection process, we were able to find a model with

independent variables TRAFFIC, POP1M, AUTO5 and POP5M to best explain the

variation in gross sales, with adjusted R square 57.02% and standard error

101764.9321.

Backward Elimination Method

We then used Backward Elimination Method to validate our model.

1) Multiple Regression with Nine Independent Variables

In the regression model with interaction terms, all the p-values of interaction

terms are greater than alpha 0.05, which indicates that there is no evidence of

interaction. We then moved on to consider model without interaction terms and

got the following results:

Based on the result, the p-values of SUIT, PERCAP1, PERCAP5 and AUTO1 are

greater than the significance level of 0.05, which means that they are

not significant in explaining the variations in the dependent variable.

As PERCAP5 has the highest p-value, being the most insignificant

predictor among these four, we excluded it from our model first.

2) Multiple Regression with Eight Independent Variables

After eliminating PERCAP5, we ran regression with the rest predictors with

interaction terms, all the p -values of interaction terms were greater than the

significance level of 0.05, which indicated there was no evidence of interaction.

Table 11 - Regression results for eight x-variables

We then moved on to consider model without interaction and got the following

results:

Based on the result, the p-values of SUIT, PERCAP1, POP5M and AUTO1 were

greater than 0.05, which meant that they were not significant to explain the

variations in dependent variable. As AUTO1 had the highest p-value, being the

most insignificant predictor, we then excluded it from our model.

3) Multiple Regression with Seven Independent Variables

After eliminating PERCAP5 and AUTO1, we ran regression with the

rest predictors with interaction terms, all the p-values of interaction terms are

greater than the significance level of 0.05, which indicates there is no evidence of

Table 12 - Regression results for seven x-variables

interaction. Then we considered model without interaction and got the following

results:

Based on the result, the p-values of SUIT, PERCAP1 and POP5M are greater than

0.05, which means that they are not significant to explain the variations in

dependent variable. Although SUIT has the highest p value, we could not exclude

this variable because only one of its dummy variable's p-value is greater than

0.05. As PERCAP1 has the second-highest p-value, being the most insignificant

predictor, we then excluded it from our model.

4) Multiple Regression with Six Independent Variables

After eliminating PERCAP5, AUTO1 and PERCAP1, we ran regression with the

rest predictors with interaction terms. All the p-values of interaction terms are

greater than alpha 0.05, which indicates there is no evidence of interaction. We

then considered model without interaction and got the following results:

Table 13 - Regression results for six x-variables

Based on the result, the p-values of two dummy variables of SUIT are

both greater than 0.05, which means that they are not significant to explain the

variations in dependent variable. Therefore, we excluded it from our model.

5) Multiple Regression with Four Independent Variables

After eliminating PERCAP5, AUTO1, PERCAP1 and SUIT, we ran regression

with the rest predictors with interaction terms.

Table 14 - Regression results for four x-variables with interaction terms

According to this result, all the p-values of interaction terms are greater than

alpha 0.05, which indicates there is no evidence of interaction. We then moved

on to consider model without interaction and got following results:

Based on the result, the significance F for the overall model and the p-value of

each independent variable are all less than 0.05, which indicates that this is our

best model with all predictors being significant. So we ended our

Backward Elimination process here.

6) Conclusion

Through the backward elimination process, we were able to find a model with

independent variables TRAFFIC, POP1M, AUTO5 and POP5M to best explain the

Table 15 - Regression results for four x-variables

variation in gross sales, with adjusted R square 57.02% and standard error

101764.9321.

FINDING THE MOST APPROPRIATE MODEL AND JUSTIFICATION

Using the Forward Selection and Backward Elimination method, we have

found the best-fit regression model with independent variables TRAFFIC,

POP1M, AUTO5 and POP5M. Then we tried to find the most appropriate model to

select location and predict gross sales based on the information we know.

Because the data of AUTO5 and POP5M of these three sites are unavailable,

we need to predict AUTO5 and POP5M for each site based on other variables in

order to use the best-fit model on these sites.

Make Predictions for AUTO5 and POP5M:

We considered POP5M as a dependent variable and used other known

variables as independent variables to find the best regression model to predict

POP5M.

After examining the factors including significance F<0.05, individual p

value<0.05, the highest R Square or adj R Square, and the lowest standard error,

we found that it is best to use POP1M to predict POP5M.

Then we need to predict AUTO5, we did the same process as above:

After examining the factors including significance F<0.05, individual p

value<0.05, the highest R Square or adj R Sqaure, and the lowest standard error,

we found that it is best to use TRAFFIC to predict AUTO5.

Problems if we use other known variables to predict POP5M and AUTO5:

Table 17 - Regression results for finding the best x-variables to predict AUTO5

We noticed that the R Square of the regression model between TRAFFIC and

AUTO5 is only 21.72%, which means that only 21.72% of total variations in

dependent variable AUTO 5 is explained by TRAFFIC. Due to the low R Square,

the predicted value of AUTO5 will not be very accurate. The similar situation

applied to POP5M too. In addition, the adjusted R Square for the regression

model without these two variables is 51.32%, which is only 5.7% lower than the

adjusted R Square for the best-fit model.

We thought using inaccurate data to gain only such small percentage increase in

adjusted R Square was not worthy. Last but not least, there is a parsimony rule of

selecting variables in model building: use as few X variables as

possible. Therefore, we decided to exclude the two unknown independent

variable AUTO5 and POP5M from the best-fit model we got from the model

building process, in order to be align to the rule and to avoid getting an over-

specified model.

This left us with the model that includes two variables, TRAFFIC and POP1M.

Reviewing information about variables and considering that we also have

information of SUIT of each site, which is the CFSI suitability rating about the

comprehensive site analysis, we were wondering if we could add SUIT as an

explanatory variable into this model. Therefore, we ran regression analyses with

and without the two dummy variables of SUIT to see which model would be

better. The regression models are shown below.

Because significance F and p-values of two model are both less than 0.05 (only

one p-value of SUIT is greater than 0.05. In this case, we still treated it as a

significant variable and kept it in the model), these two models are both

appropriate to make predictions for gross sales. However, considering the higher

adjusted R square and the lower standard error, the second model with SUIT as a

variable is more appropriate than the first model.

Therefore, we decided that the regression model with independent variables of

TRAFFIC, POP1M and SUIT is the most appropriate model to predict gross sales

for each site.

CHECKING RESIDUALS

After selecting the best model, we performed a residual analysis to see if the

model violated any assumptions. If any assumption was violated, we might want

to use other methods to build model, such as log transformation. These

assumptions include:

Linearity

Table 19 - Regression results using TRAFFIC, POP1M and SUIT as explanatory variables of GSALES

Independence of errors

Normality of errors

Equal variances of errors

Figure 2 - Plot of residuals against the population within a one-mile radius of the Culver's restaurant

Figure 3 - Plot of residuals against the traffic count around the Culver's restaurant

Figure 5 - Plot of residuals against dummy variable 1 of CFSI suitability rating of the Culver's restaurant

Figure 4 - Plot of residuals against dummy variable 2 of CFSI suitability rating of the Culver's restaurant

Figure 6 - Normal probability plot of the residuals for the gross sales

From these residual plots, both POP1 and TRAFFIC satisfied the four

assumptions of regression:

1) There was no apparent pattern in the residual plots; the residuals

appeared to be evenly spread above and below 0. Therefore, this

assumption was not violated.

2) When data collected over periods of time sometimes exhibit an

autocorrelation effect among successive observations. In these instances,

there is a relationship between consecutive residuals. Because the

Culver's data were collected during the same time period for each

variable, we did not need to evaluate the independence assumption.

3) According to the normal probability plot of the residuals, the data did not

appear to depart substantially from a normal distribution.

4) There did not appear to be major differences in the variability of the

residuals for different Xi values. Thus, there is no apparent violation in

the assumption of equal variance at each level of X.

Note that the residual plots for dummy variables of variable SUIT cannot be

interpreted.

CHECKING COLLINEARITY

Here we checked if multicollinearity existed. Multicollinearity is a phenomenon

in which two or more predictor variables in a multiple regression model are

highly correlated, meaning that one can be linearly predicted from the

others. When multicollinearity exists, some x-variables might do a good job at

predicting the Y variable, but these variables do not bring new information to the

regression model, therefore we want to exclude them from the model. We can

detect (Multi)Collinearity when high correlation exists between predictor

variables, when absolute value of r > 0.95.

From the table, we could see that all correlations were less than 0.95 or greater

than -0.95.Therefore we concluded that there was no collinearity between these

variables, and all of them provided new information to the regression model.

LOCATION PREDICTION

Using the model we chose, we predicted the gross revenue of each location. The

results are as following:

Gross Sales Revenue = 493758.5 + 31971.99*Better + 80487.16*Best +

36.28567*TRAFFIC + 64.3183*POP1M

Table 20 - Multicollinearity results for ten relevant variables in predicting gross sales

FINANCIAL ANALYSIS

This section focuses on financial analysis of opening the Culver's Frozen Custard

restaurant at each site. The primary goal is to find the most promising location

among Site A, Site B, and Site C by the financial estimation. To simplify our

analysis, we did not consider the time value of money and the potential growth

rate of annual sales. Additionally, we took our clients' financial ability and

profitability requirements into consideration.

GROSS SALES

We predicted the gross sales of all three sites based on the traffic count, the

population within a one-mile radius, and the CFSI suitability rating: $1,391,607

for Site A, $1,279,961 for Site B, and $1,448,375 for Site C. Our clients only

consider the site with annual sales more than $1 million. Based on our results, all

sites were favorable to our clients.

Figure 7 - Predicted gross sales

START-UP SUMMARY

The Culver's Frozen Custard restaurant has the following start-up costs:

Initial Lease Payments and Deposits

Structure and Improvements

Equipment & Signage

Other miscellaneous Costs

Franchise Fee (15-year agreement)

Note that the items mentioned above are depreciable. The difference of the

startup expenses is only due to the initial lease payments and deposits. The

startup costs of all sites are reasonable, which is less than the maximum of

typical initial investment costs ($3,046,000). However, our clients are only able

Figure 8 - Startup expenses

to obtain $1.2 to $1.55 million from the local bank. Site C ($1,815,000) requires

more than $1.55 million to start-up, which is beyond the clients' financial

abilities.

OPERATING COSTS & ANNUAL PROFITS

The operating costs for the Culver's Frozen Custard restaurant include food

costs, paper cost, labor cost, and other operating costs. To eliminate the

differences of operating costs caused by suitability, we used the comparable

analysis to estimate each site's operating costs. Specifically, we concluded each

expense as the percentage of gross sales, and then sort the data by its suitability.

For the suitability rating of 1, the total average operating costs are 94% of the

gross sales: FOOD-31%, PAPER-4%, LABOR-30%, and OTHER OP-29%. For the

suitability rating of 2, the total average operating costs are 91% of the gross

sales: FOOD-30%, PAPER-4%, LABOR-29%, and OTHER OP-28%. As results,

annual profits of each site are as followings: $80,155 for Site A, $73,725 for Site

B, and $132,410 for Site C.

OTHER CONSIDERATIONS

We also compared those three sites using their payback periods. By dividing the

initial investment by the annual profits, we got the results: Site C (6.91 years) has

the shortest payback period. Note that the payback period of Site A (7.05 years)

is similar to Site C. Even though Site C has the highest annual profit, it has the

highest startup expenses as well.

Our clients have options to renew their franchise agreement every 10 years after

the first 15 years. We recommend that they consider the renew options if the

restaurant operates well in the first 15 years, because the more year the

restaurant operates, the less annual allocation of the start-up expenses will be.

RISKS

There are also risks for the restaurant to generate profits:

1) Workforce: if the local workforce is weak, the restaurant will probably

have higher labor expense, which will lower the annual profits.

2) Competitor: there will probably be a price competition, which will lower

the annual profits.

3) Macroeconomic: if the macroeconomics got better, costumers would

probably spend less money on fast foods, which would lower the annual

profits.

In general, based on our financial analysis mentioned above, we recommend our

clients to choose Site A. If the restaurant at Site A operates well, they can

consider either to renew the franchise agreement or to open another restaurant

at Site C. Note that our clients should pay attention to the changing

circumstances to modify their financial strategies.

RECOMMENDATION

Each site has different characteristics. The CFSI rates those three sites based on

their unique characteristics: Site A - better, Site B - better, and Site C - best. We

noticed that the suitability rates provided by the CFSI did not take our clients'

preference and goal into account. Thus, we reevaluated those three sites listed

below based on our clients' needs.

Customer Group: All sites have big potential customer bases due to their

location description. The followings shows neighboring groups for each site:

Site A: 1) high school students; 2) hospital patients and employees

Figure 9 - Location Information

Site B: drivers

Site C: 1) middle school students; 2) business office residents; 3)

shoppers

Our clients prefer to interact with young students, so both Site A and Site C are

favorable to our clients. Note that the size of each site's customer group is

unknown based on our data.

Workforce: The neighboring groups mentioned above are also indications of the

potential workforce for each site. The major workforce of each site is listed as

followings:

Site A - students

Site B - adult employees

Site C - adult employees

Our clients indicated their preference for labor force - young students. Based on

their preference, Site A is the suitable location to hire young students.

Competitor Pressure: Both Site B and Site C will face intense competitions from

other restaurants: Site B - other 3 fast food restaurants (i.e. McDonald's, A&W,

and Pizza Hut); and Site C - other restaurants at the food court. As results, Site A

has the biggest business viability.

Accessibility: One of the Culvers' competitive advantages is "a wide variety of

entrees." Site C is located within a shopping center, which reduces the likelihood

for providing the out-door seating and the drive-up service. Unlike Site C, both

Site A and Site B are able to provide in-door seating, out-door seating, and drive-

up service.

Visibility: Site A is the most visible location. Its speed limit (i.e. 30 mph) will also

help draw drivers' attentions. Site B is the second visible location. Site C is the

least.

In general, Site A is most favorable place for our clients based on the location

descriptions. Both the result from the financial analysis and the result from the

location analysis have demonstrated that Site A is the best.

CONCLUSION

In conclusion, we suggest our client to locate the new Culver's restaurant at Site

A. According to the prediction of gross sale, all of the three location are

profitable. Although Site C has the highest predicted gross sale, after taking other

start-up expenses, such as franchise fee and venue purchase fee, into

consideration, we found that locating at site C was beyond our clients' financial

abilities. On the other hand, Site A has the second highest predicted gross sale,

and it is affordable to our clients. In addition, Site A is the location that suits best

for our clients' interest. Our clients enjoy interacting with young students and

they expect to recruit students as their main labor force. Because Site A is close

to a school, this location is in our clients' favor.

For further recommendation, if the restaurant at Site A operates well, our clients

can consider either to renew the franchise agreement or to open another

restaurant.

Appendix

Scatter Plots

The P-value of All the Models with and without Interaction Terms

Two independent variables

w/o interaction w/ interactionIntercept 0.43348 0.40838TRAFFIC 7.80E-11 0.06915PERCAP1 0.9735 0.35657INTERACTION 0.35622

w/o interaction w/ interactionIntercept 0.46665 0.7826TRAFFIC 1.40E-11 0.19668PERCAP5 0.76497 0.70195INTERACTION 0.71604

w/o interaction w/ interactionIntercept 0.37269 0.09544TRAFFIC 1.20E-10 0.07114AUTO1 0.23231 0.08876INTERACTION 0.1111

w/o interaction w/ interactionIntercept 0.01908 0.09005TRAFFIC 6.90E-09 0.11049AUTO5 0.01159 0.08357INTERACTION 0.13908

w/o interaction w/ interactionIntercept 0.05081 0.603399681TRAFFIC 0.00011 0.357418767POP1M 0.00057 0.783023942INTERACTION 0.901200161

w/o interaction w/ interactionIntercept 0.394738756 0.47211TRAFFIC 8.12381E-11 0.11211POP5M 0.799642004 0.62557INTERACTION 0.60635

TRAFFIC+AUTO5 P-value

TRAFFIC+AUTO1 P-value

TRAFFIC+POP1M P-value

TRAFFIC+POP5M P-value

TRAFFIC+PEPCAP5 P-value

TRAFFIC+PEPCAP1 P-value

Three independent variables

Four independent variables

w/o interaction w/ interactionIntercept 1.36E-02 0.498090689TRAFFIC 3.38E-03 0.848364022POP1M 2.91E-05 0.697357523POP5M 1.53E-02 0.222223963AUTO5 3.67E-03 0.483820834TRAFFIC*POP1M 0.575456565TRAFFIC*POP5M 0.701585147TRAFFIC*AUTO5 0.795198863POP1M*POP5M 0.253422815POP1M*AUTO5 0.777626544POP5M*AUTO5 0.188947803

TRAFFIC+POP1M+AUTO5+POP5M P-value

w/o interaction w/ interactionIntercept 1.81E-02 0.289156326TRAFFIC 1.41E-03 0.462728048POP1M 2.22E-04 0.427426298PERCAP1 1.20E-01 0.659558869AUTO5 4.79E-03 0.289654461TRAFFIC*POP1M 0.134770616TRAFFIC*PERCAP1 0.781645695TRAFFIC*AUTO5 0.457229181POP1M*PERCAP1 0.408255822POP1M*AUTO5 0.402860714PERCAP1*AUTO5 0.609579772

P-valueTRAFFIC+POP1M+AUTO5+PERCAP1

w/o interaction w/ interactionIntercept 0.033645144 0.195178326TRAFFIC 0.002536461 0.82575383POP1M 0.000631115 0.288784438PERCAP5 0.762702408 0.67600922AUTO5 0.012028211 0.20348482TRAFFIC*POP1M 0.411658102TRAFFIC*PERCAP5 0.790606502TRAFFIC*AUTO5 0.858837358POP1M*PERCAP5 0.549976945POP1M*AUTO5 0.261645024PERCAP5*AUTO5 0.705505216

P-valueTRAFFIC+POP1M+AUTO5+PERCAP5

w/o interaction w/ interactionIntercept 0.032969686 0.827276931TRAFFIC 0.002426639 0.998040148POP1M 6.40E-04 0.102712404AUTO5 0.022918172 0.632378294AUTO1 0.620808936 0.848592375TRAFFIC*POP1M 0.248765666TRAFFIC*AUTO5 0.236354568TRAFFIC*AUTO1 0.054019416POP1M*AUTO5 0.023192554POP1M*AUTO1 0.033882256AUTO5*AUTO1 0.613311427

TRAFFIC+POP1M+AUTO5+AUTO1 P-value

Five independent variables

w/o interaction w/ interactionIntercept 0.008036855 0.588517217TRAFFIC 0.002120117 0.935748923POP1M 1.55358E-05 0.966227731POP5M 0.022599451 0.231623635AUTO5 0.181806146 0.583749639PERCAP1 0.001758453 0.99698645TRAFFIC*POP1M 0.90967747TRAFFIC*POP5M 0.680892133TRAFFIC*AUTO5 0.93056395TRAFFIC*PERCAP1 0.877853946POP1M*POP5M 0.260062713POP1M*AUTO5 0.938137001POP1M*PERCAP1 0.372762671POP5M*AUTO5 0.220951299POP5M*PERCAP1 0.844453844AUTO5*PERCAP1 0.963257698

TRAFFIC+POP1M+AUTO5+POP5M+PERCAP1 P-value

w/o interaction w/ interactionIntercept 0.013769273 0.432126455TRAFFIC 0.003527195 0.64843858POP1M 3.19406E-05 0.780363724POP5M 0.016246984 0.255628541AUTO5 0.811993476 0.454411787PERCAP5 0.003886997 0.385625986TRAFFIC*POP1M 0.416473029TRAFFIC*POP5M 0.664258255TRAFFIC*AUTO5 0.611119175TRAFFIC*PERCAP5 0.991194099POP1M*POP5M 0.3389989POP1M*AUTO5 0.859479362POP1M*PERCAP5 0.650267147POP5M*AUTO5 0.227048849POP5M*PERCAP5 0.735902116AUTO5*PERCAP5 0.40368779

TRAFFIC+POP1M+AUTO5+POP5M+PERCAP5 P-value

w/o interaction w/ interactionIntercept 0.013220237 0.435918536TRAFFIC 0.003310179 0.661902071POP1M 3.22391E-05 0.227489821POP5M 0.016179132 0.516589135AUTO5 0.009917151 0.299045728AUTO1 0.642402171 0.586221726TRAFFIC*POP1M 0.757787423TRAFFIC*POP5M 0.629680089TRAFFIC*AUTO5 0.13536717TRAFFIC*AUTO1 0.06031056POP1M*POP5M 0.330263026POP1M*AUTO5 0.108121193POP1M*AUTO1 0.060704469POP5M*AUTO5 0.992942165POP5M*AUTO1 0.200376619AUTO5*AUTO1 0.372894793

TRAFFIC+POP1M+AUTO5+POP5M+AUTO1 P-value

All Adjusted R square and Standard Error in Forward Selection

One independent variable R^2 StdError TRAFFIC 0.45190 115602.52613

POP1M 0.43087 117799.65984 POP5M 0.09197 148794.30237 PERCAP1 0.09037 148925.41929 PERCAP5 0.05351 151912.59198 AUTO1 0.11404 146975.20269 AUTO5 0.24093 136043.50349 MARRID1 0.02077 154517.73000 MARRID5 0.02142 154466.84955 SUIT 0.33622 127972.87754

Two independent variables Adj R^2 StdError TRAFFIC+POP1M 0.513267 108303.4 TRAFFIC+POP5M 0.43928 116243.8

TRAFFIC+PERCAP1 0.438855 116287.8 TRAFFIC+PERCAP5 0.439448 116226.4 TRAFFIC+AUTO1 0.448354 115299.4 TRAFFIC+AUTO5 0.480083 111934.5

TRAFFIC+SUIT 0.47344 112647.3

Three independent variables Adj R^2 StdError TRAFFIC+POP1M+POP5M 0.529113 106525.8

TRAFFIC+POP1M+PERCAP1 0.511616 108486.9 TRAFFIC+POP1M+PERCAP5 0.50751 108942.1 TRAFFIC+POP1M+AUTO1 0.515217 108086.3 TRAFFIC+POP1M+AUTO5 0.543671 104866.3

TRAFFIC+POP1M+SUIT 0.532763 106112.2

Four independent variables Adj R^2 StdError TRAFFIC+POP1M+AUTO5+POP5M

0.57026291

3 101764.932

1 TRAFFIC+POP1M+AUTO5+PERCAP1

0.551634574

103947.1981 TRAFFIC+POP1M+AUTO5+PERCA

P5 0.53862201

3 105444.799

2 TRAFFIC+POP1M+AUTO5+AUTO1 0.539490538

105345.5047 TRAFFIC+POP1M+AUTO5+SUIT 0.55776336

3 103234.317

All Adjusted R square and Standard Error in Backward Elimination

TRAFFIC+POP1M+AUTO5+POP5M+PERCAP1+PERCAP5+AUTO1+SUIT

P-value Adj R^2 StdError Significance F

Intercept 0.026856118 0.57907521 100716.1188 3.61E-13 SUIT--1 0.21286813 　　　 SUIT--2 0.038320033 　　　 TRAFFIC 0.040929748 　　　 POP1M 5.80345E-05 　　　 POP5M 0.059731892 　　　

PERCAP1 0.144033811 　　　 PERCAP5 0.984763695 　　　 AUTO5 0.008492431 　　　 AUTO1 0.64802495 　　　

TRAFFIC+POP1M+AUTO5+POP5M+PERCAP1+AUTO1+SUIT


Intercept 0.025873201 0.584469701 100068.6585 8.61489E-14 SUIT--1 0.199058924 　　　 SUIT--2 0.032483762 　　　 TRAFFIC 0.039616272 　　　 POP1M 4.83363E-05 　　　 POP5M 0.058019786 　　　

PERCAP1 0.08320902 　　　 AUTO5 0.006966252 　　　 AUTO1 0.62939005 　　　

TRAFFIC+POP1M+AUTO5+POP5M+PERCAP1+SUIT


Intercept 0.026496734 0.588494882 99582.80379 2.13327E-14 SUIT--1 0.203929082 　　　 SUIT--2 0.032431055 　　　 TRAFFIC 0.040363014 　　　 POP1M 4.33066E-05 　　　 POP5M 0.056125081 　　　 AUTO5 0.002632807 　　　

PERCAP1 0.079199368 　　　

TRAFFIC+POP1M+AUTO5+POP5M+PERCAP1+SUIT


Intercept 0.044007842 0.577371846 100919.6979 1.98104E-14 SUIT--1 0.279323383 　　　 SUIT--2 0.070466957 　　　 TRAFFIC 0.048119601 　　　 POP1M 0.000098001 　　　 POP5M 0.032096495 　　　 AUTO5 0.007179133 　　　

TRAFFIC+POP1M+AUTO5+POP5M


Intercept 0.013610014 0.570262913 101764.9321 3.27079E-15 TRAFFIC 0.003382438 　　　 POP1M 0.000029141 　　　 POP5M 0.015300094 　　　 AUTO5 0.003668162 　　　

Regression Analysis of the Final Model

SUMMARY OUTPUT

Multiple R 0.744644163R Square 0.55449493

Adjusted R Square 0.532762975Standard Error 106112.2087Observations 87

ANOVAdf SS MS F Significance F

Regression 4 1.14918E+12 2.87296E+11 25.51518901 9.51338E-14Residual 82 9.23304E+11 11259800825

Total 86 2.07249E+12

Coeffi cients Standard Error t Stat P-value Lower 95% Upper 95%Intercept 493758.5078 167123.8924 2.954445955 0.004087076 161295.8474 826221.1682

1 31971.98741 30955.05052 1.032852051 0.304709787 -29607.46903 93551.443852 80487.15826 34575.50525 2.327866438 0.022383888 11705.46405 149268.8525

TRAFFIC 36.28566855 13.98095071 2.595364885 0.011192846 8.473103848 64.09823325POP1M 64.31830078 18.93507811 3.396780324 0.001053908 26.65039851 101.9862031

Regression Statistics

Residual Plots

Collinearity Matrix

Collinearity TRAFFIC POP1M POP5M PERCAP1 PERCAP5 AUTO5 AUTO1 MARRIED1 MARRIED5 SUITTRAFFIC 1POP1M 0.6838116 1POP5M 0.4234277 0.6406478 1

PERCAP1 0.4436024 0.4600323 0.387156 1PERCAP5 0.3098713 0.2481092 0.1951778 0.6132598 1AUTO5 0.466031 0.3518318 0.3219075 0.4066712 0.2902353 1AUTO1 0.3691286 0.2764955 0.2490518 0.3162532 0.0761126 0.6798959 1

MARRIED1 -0.146772 -0.0442296 0.0848045 -0.0874612 0.0806431 -0.1110432 -0.0689627 1MARRIED5 -0.195277 -0.2368674 -0.1413524 -0.1719712 -0.0875225 -0.0489086 -0.0697864 -0.0900383 1

SUIT 0.6327749 0.4938176 0.2351384 0.4333737 0.4078884 0.370709 0.2984209 0.0178559 -0.1848175 1

Site Information

Site Price LocationPosted

Speed LimitNearby Notes

A 410,000$ in a residental area on a mainstreet

30 mph

Within Walking Distance:- a high school- a small grocery store- a hospital

B 480,000$ off a freeway ramp on theedge of Carbondale

45 mph

A Frontage Road- 2 gas stations w/ conveniencestores- a McDonald's- an A&W- a Pizza Hut

1) the frontage road runs to thecounty road leading to thefreeway ramp2) the frontage road has aspotlight to make access easier

C 760,000$ at the far end of Carbondale'snew shopping center

N/A

A Shopping Center:- a food court (including aBaskin-Robbins ice creamshop)Within Waling Distance:- a middle school- business offi ces housing(about 100 employees)

access from:1) the street that runs past theshopping cenrer and dead endsabout a block beyond Site C2) the end of the shoppingcenter itself

Predicted Gross Sales Revenue

15,000 5,000 1 1,391,60716,000 2,700 1 1,279,96117,000 4,000 2 1,448,375

TRAFFIC POP1M SUIT (1) Predicted GSales (2)

A B C 1,150,000 1,200,000 1,250,000 1,300,000 1,350,000 1,400,000 1,450,000 1,500,000

Predicted Gross Sales

Startup Funding

Startup CostsA B C

Initial Lease Payments and Deposits 410,000$ 480,000$ 760,000$ Structure and Improvements 600,000 600,000 600,000

Equipment & Signage 300,000 300,000 300,000 Miscellaneous Costs 100,000 100,000 100,000 Franchise Fee (15 yr) 55,000 55,000 55,000

Total 1,465,000 1,535,000 1,815,000

Renew Franchise Agreement (10 yr) 30,000 30,000 30,000

Organization Budget - Example

Numbers of Personnel

A B COwners 2 2 2General Manager (1) 1 1 1Assistant Manager (2) 2 2 2Team Member (3) 52 52 52Total (4) 57 57 57

Site

Personnel Plan -Yearly

A B COwners - - - General Manager (1) 37,158 37,158 37,158 37,158 Assistant Manager (2) 69,278 69,278 69,278 34,639 Team Member (3) - - - Total (4) 106,436 106,436 106,436

Site Salaries perperson

Comparable Analysis

Comparable Analysis (Suit-1) Comparable Analysis (Suit-2)Food Paper Labor Other OP Food Paper Labor Other OP

32% 4% 30% 32% 30% 3% 28% 27%32% 4% 35% 28% 31% 4% 31% 31%31% 4% 32% 30% 30% 4% 30% 28%31% 4% 31% 30% 32% 4% 30% 32%32% 4% 33% 30% 31% 4% 30% 31%32% 3% 29% 31% 30% 3% 30% 28%33% 4% 30% 30% 31% 3% 29% 29%31% 4% 31% 30% 29% 4% 28% 28%32% 3% 31% 29% 30% 4% 30% 29%30% 4% 30% 29% 31% 4% 26% 29%29% 3% 26% 28% 31% 4% 29% 27%30% 3% 25% 27% 29% 3% 27% 25%31% 3% 29% 29% 31% 4% 31% 29%32% 4% 30% 28% 31% 4% 31% 30%32% 4% 33% 30% 30% 4% 30% 29%30% 4% 30% 28% 27% 3% 25% 26%31% 4% 32% 29% 30% 4% 28% 26%30% 4% 30% 29% 28% 3% 26% 28%31% 4% 29% 31% 32% 3% 29% 28%31% 5% 32% 30% 29% 3% 28% 27%30% 4% 29% 29% 30% 4% 30% 29%29% 4% 29% 28% 31% 4% 32% 29%31% 4% 30% 29% 29% 3% 29% 27%31% 4% 30% 29% 29% 4% 28% 27%

30% 4% 29% 28%Variable Cost 94% 31% 4% 31% 30%

35% 4% 29% 28%28% 3% 25% 28%28% 3% 26% 28%28% 3% 26% 27%30% 4% 29% 28%

Variable Cost 91%

Annual Profit

Initial InvestmentA B C

Franchise Fee 55,000$ 55,000$ 55,000$ Start-up Costs 100,000 100,000 100,000 Site 410,000 480,000 760,000 Total 565,000$ 635,000$ 915,000$

Renew Franchise Agreement (10 yr) 30,000$

Annual ProfitA B C

Predicted GSales (1) 1,391,607$ 1,279,961$ 1,448,375$ Food (2) (430,900) (396,330) (436,847)

% of Gsales 31% 31% 30%Paper (3) (53,004.49) (48,752.04) (51,822.65)

% of Gsales 4% 4% 4%Labor (420,519) (386,782) (417,426)

% of Gsales 30% 30% 29%Other Operating Costs (4) (407,028) (374,373) (409,870)

% of Gsales 29% 29% 28%Total Annual Profit 80,155 73,725 132,410

Total ProfitsTotal Profits after () yr A B C

10 236,554 102,246 409,100 15 637,330 470,870 1,071,150 25 1,408,884 1,178,116 2,365,250 35 2,210,438 1,915,363 3,689,350

Documents

GB304 Final Project Report Final 2