University of Wisconsin – Milwaukee
Case Study: Small Copy Shop
Introduction
In this case assignment we discuss the creation, implementation, and results of an Excel model
for understanding the feasibility of a small copy shop. Specifically, we were asked to determine
annual profit and break-even points at selected demand and capacity levels and also to graph this
data for interpretation.
Daily demands levels for this exercise were selected to be 500, 1000, 1500, and 2000 copies.
Each copy costs $0.03 to print and would sell for $0.10. Capacity is constrained by the number
of copiers rented for the shop, between 1 and 5. Each copier costs $5,000 per year to rent. Other
fixed costs amount to $400 per year. The shop is expected to be open for 365 days a year.
Part A: Determine Annual Profit
For the first part of this problem we are asked to find the annual profit for each combination of
copiers and daily demand. In order to accomplish this task we first laid out all of the inputs that
necessary for computing annual revenues and annual costs. This data is provided Figure 1. To
make the data more uniform, the yearly rental cost is also given as a daily cost, where rental cost
per copier per year is divided by days open per year. The other fixed costs category is also
computed daily. This is calculated by multiplying the other fixed costs of $400 by twelve and
then dividing by days open.
Figure 1: Inputs
Next, we noted that certain demand levels are constrained by the number of copiers. For
instance, 1 copier can print 273 pages a day, but the lowest demand level is 500 a day. Therefore,
revenues and costs are calculated at 273 pages sold. As another example, 2 copiers can print 546
pages per day; with demand of 500, the needs of customers can be fulfilled and the full revenue
level for the current demand can be calculated. However, the full potential of the two copiers will
not be reached because the demand level is lower than the potential of the equipment.
To deal with these capacity constraints, the model’s profit formula catches if demand is greater
than or less than capacity and calculates accordingly. This is achieved using an IF formula
which, in simple terms, works as follows: if available capacity is less than demand, calculate
profits of running at capacity based on the number of copiers; otherwise, calculate profits of
running at the stated demand. The full statement is as follows:
The critical difference in the two formulas in the IF statement is that the output per day is always
equivalent to either demand (i.e. 500, 1000, 1500, 2000 copies) or capacity (a multiple of 273,
based on how many copiers are rented). Thus, the formula uses the given demand level
multiplied by costs and prices to calculate profit, or it uses the output per day (273 copies)
multiplied by costs and prices to calculate profit.
Rather than calculate each of the 20 combinations of demand and number of copiers
individually, we utilize a 2-way table. Refer to Figure 2 to see how this is laid out in the Excel
model.
Figure 2
Cells F3:G6 are used to set up the 2-way table. The formula above is in cell G5, and it references
the inputs from Figure 1 and cells G3 and G4, the two of which act as “samples” for the number
of copiers and profit. To actually create the two way table, only the cells G8:K8 and G9:G12 are
populated manually. The rest of the cells, G9:K12, are calculated based on the above setup by
replacing G3 and G4 with each combination of values in G8:K8 and G9:G12, respectively.
Part B: Determine Break-Even Point
For part B we set up a table to represent the calculation for daily demand that will cause revenue
and cost to break-even with three copiers. Using the same IF statement that we used to calculate
profit in part A, we are able to calculate the breakeven point using the what-if analysis Goal
Seek. Refer to Figure 3. Cell I19 contains the IF statement from above. It references the inputs
from Figure 1 and cells I17:I18 for number of copiers and demand. In the picture, Goal Seek is
set to find the value of demand that will make profit $0, i.e. the break-even point. After running,
it calculates that demand must be about 775 pages for revenues and costs to be equal.
Figure 3
Part C: Graph and Interpret the Results
For part C we are asked to graph the profit as a function of the number of copiers for a daily
demand of 500 and 2000 and then interpret the graph. Figure 4 includes a data table that is a
snapshot of Figure 2 with only these selected demands. It uses the same formula and 2-way data
table to make the calculations. Figure 4 also shows this data in a bar graph.
Figure 4
As can be seen in the graph, the profit margin starts at the same point for one copier because
there is no differential in demand. Neither demand of 500 or 2000 can be achieved with one
copier. With two copiers the daily demand of 500 can be reached but the daily demand of 2000
cannot. Even though the daily demand of 2000 cannot be reached, it is still more profitable than
having two copiers because the potential for production is higher than 500 with 2 copiers. From
this point forward daily demand has reached its maximum potential for daily demand of 500
causing it to become more and more unprofitable with every copier following the second. The
daily demand of 2000 gradually becomes more profitable because it is achieving more and more
of its production potential. The more copiers that are rented, the more profit there is at a daily
demand of 2000. The more copiers that are rented, the more unprofitable this venture would be
with a daily demand of 500 (from 2 copiers up to 5 copiers). The daily demand is slightly more
profitable with 2 copiers than it is with one, but at no point is a daily demand of 500 profitable. A
daily demand of 2000 will start to see profits after it has reached 3 rented copiers and will
continue to increase up to 5 copiers.
The Seven Step Model
1) Problem Definition
Would opening a copy shop bring in a positive annual profit? By using the information provided
for the given problem, the profit would have to be sufficient enough to sustain a business and
operate at an efficient rate.
2) Data Collection
Our data collection plan used a two way table to configure the cost of running multiple copiers
per day at different expected rates of demand. While using the information provided, we can
analyze and calculate the projected profit for running each copier based on the demand.
3) Model Development
Daily Costs:
To help formulate the model structure, we broke down the provided data into daily expected
outcomes. When one copier is to be used at a rented price of $5,000 for a year at 365 days, the
daily rental cost comes to be $13.70.The maximum output in one day is found by taking 100,000
copies divided by 365 days. This allows for each copier to produce a maximum of 273 copies per
day. The maximum variable cost per day to run one copier is found by taking 273 copies times
$0.03 per copy. While this comes out to be $8.19 there is still a monthly fixed cost that needs to
be addressed to run the store. We took our estimated monthly fixed cost of $400.00 and
multiplied it by 12 then divided by 365 to find a daily fixed cost rate. This total came to be
$13.15 per day. By taking the daily fixed cost, maximum variable cost, and rental cost per day;
we can find the total cost per day with one copier being used comes out to be $35.04. If the daily
fixed cost is not included then the projected cost for one copier being used per day at a maximum
output will be $21.89.
Daily Sales:
In order to calculate the daily sales total, we multiplied our projected daily demand times $0.10
per copy being sold. For example if the daily demands was 500 then, the daily sales would be
$50.00. In order for the demand to be met, an additional copier would be required if the demand
exceeded the maximum output from a single copier. With the example given for a demand of
500, 2 copiers would need to be ran in order to meet the daily demand quota because each copier
can only produce a maximum of 273 copies per day.
Daily Profits:
In order to find our daily profits per copier being used in a single day, the daily demand was put
into the following intervals: 500, 1000, 1500, and 2000. If more than one copier was ran per day
the cost would be found by taking $35.04 and adding $21.89 per additional copier if it was being
ran at a maximum output of 273 copies per day. However, if the copier or additional copier was
not being ran at maximum output of 273 copies the cost would be found by taking the number of
copies being ran times the cost of $0.03 per copy plus the daily cost of $13.70 for each copier
being rented. This is not to forget that the fixed cost per day of $13.15 must be included in the
final daily cost analysis. Then to find the profit based off each demand interval set you would
subtract your sales from your daily costs.
Model Inputs:
Inputs consisted of variable costs, fixed costs, and days of operation per year. This data was
provided, although it was necessary to divide the numbers in to daily values.
4) Model Verification
To confirm our formula set in the data table was correct, several calculations from Figure 2 were
spot checked and calculated by hand to verify that our profit formula was correct.
5) Optimization and Decision Making
In this step, we focused on determining two things: demand needed to break-even for each
number of copiers, and the maximum annual profit for each number of copiers.
As with part B, we used Goal Seek to determine the break-even point. We determined that for 1
or 2 copiers, it is impossible to break-even; the output per copier is too low to cover fixed costs.
For 3 to 5 copiers, the break-even points are shown in Figure X below.
Figure 5
With this information, our first recommendation is to only open a copy shop with at least 3
copiers and only if expected daily demand is on average at least 775 pages. Otherwise, the shop
will not be profitable.
The last row of Figure 5 calculates the break-even demand as a percentage of the capacity. To
break-even, demand needs to be between 85% and 95% of capacity. This number decreases as
more copiers are used. This is because the fixed costs are more spread out. This means that more
copiers are better- assuming that the demand is there.
We noted that the question asks to project profit up to demand of 2000. To have capacity for this
demand, 8 copiers would be needed. If this demand is expected, or if it is even just the upper
bound, we strongly recommend considering renting a sixth and possibly seventh copier.
6) Model Communication to Management
For a better understanding of the formulas being used within our spreadsheet analysis, the Figure
6 below portrays how daily profits can be calculated. The daily profits are calculated by taking
the daily sales minus the daily costs. Depending upon the number of copiers being ran and
projected demand being used. Each variable input attributes towards the projected daily profit
being calculated, because a copier has a maximum output of 273 copies per day, a second copier
would be needed if the total demand exceeded that amount.
Figure 6
7) Model Implementation
Implementation of the model would involve creating a user-friendly front-end. The two-way
table offers a simple way to visualize the differences in profit of the combinations of demand and
number of copiers. However it does not simply offer a way to extend the number of copiers or
modify demand levels. A combination of macros and UserForms could provide sandbox
environment where the user can change inputs and immediately see the resulting outputs. This
method also has the advantage of allowing the designer to hide key formulas and data tables,
preventing the user from accidentally breaking the model.