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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
Culver's restaurant..........................................................................................................................................28
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
Culver's restaurant..........................................................................................................................................28
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
According to the results, the p-values of all interaction terms are greater than
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:
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 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:
According to the results, the p-values of all interaction terms are greater than
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
P-value Adj R^2 StdError Significance F
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
P-value Adj R^2 StdError Significance F
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
P-value Adj R^2 StdError Significance F
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
P-value Adj R^2 StdError Significance F
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
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