Lab 1 Cost and Returns Modeling (Introductory Topic)
AGEC 352
January 25, 2011
Discussion Instructions:
The Blackboard page for this course has a link to the discussion topic for this week. Be sure
to sign-in to the attendance thread.
Introduction
This lab handout will guide you through the steps in creating a simple spreadsheet model
similar to the type we have seen in class to date. The objective is to provide students with
experience in formula entry and evaluation while introducing some of the design concepts
that guide effective spreadsheet modeling technique. The lab is separated into two parts. Part
I will be used for answering questions on the lab discussion board while part II is used to
answer assignment questions.
Part I: Simple Profit Model
We’ll begin by building the simple profit evaluation model that we covered in lecture on
January 19th and 24th and then consider a couple of scenarios associated with changes to that
model. In part II, you will be provided with a partially complete spreadsheet model and
asked to fill in the missing formulas. Homework questions for this week are answered from
the completed version of the model in part II.
The relevant information for a producer is given below:
Objective:
Decision:
Maximize Profits from Sales
The producer chooses the quantity to produce and sell
Definitions:
Q = Quantity
P = Price
C = Cost
Other relevant information:
[1]
[2]
P = 25 – 0.25Q
C = 60 + 0.5Q
(Demand for the producer’s product)
(Cost function for producer)
The above information is enough to build the producer’s spreadsheet model and determine
what quantity of product she should produce and sell given her objective of maximizing
profits. Our first step is to decide how we want to organize information in the spreadsheet
to enter formulas and keep track of results. Open a blank MS Excel worksheet and we
will begin by using the first column to create a set of labels that identify all of the model
information we are going to need to collect, calculate, or report.
AGEC 352 January 25, 2011
Lab 1 Cost and Returns Modeling (Introductory Topic)
In column A of the spreadsheet in figure 1, we see that all of the variables and parameters of
the model information are identified with labels. Each section is given a heading to indicate
which function the value serves in the model, making it easy to communicate to others the
assumptions of our model, in particular that the decision maker chooses a quantity level in
order to maximize profits.
Figure 1. Model labels in column A of Excel spreadsheet
Once we have the spreadsheet arranged as in figure 1, we can begin inputting values for the
different known elements of the model. The place to begin inputting data is in the
parameters section since these values are given and never change in the model. *Note that
this means that any value meeting the definition of a parameter can never have a formula
AGEC 352 January 25, 2011
Lab 1 Cost and Returns Modeling (Introductory Topic)
entered into its cell (i.e. it should just be a data entry cell). Using the information from page 1
enter the data into cells B12 through B15.
Once we have input the parameters, we start adding the formulas for the consequence
variables. To enter a formula into Excel you mouse click inside the cell to make it active and
then type the equals sign (=). This signals to Excel that information to follow needs to be
evaluated using mathematical operations. Let’s begin in cell B9 with profits and enter the
following: =B8-B7. You can enter a cell name into an equation by either typing the name
out or clicking that cell and it will appear in the equation. Checking figure 1, this instructs
Excel to calculate the difference between cell B8 (Revenue) and B7 (Costs) to calculate the
level of profits. Note that you will not have any values that mean anything in cells until the
entire model has been entered, so don’t worry if any strange values start popping up in
different cells at this point.
Finish the model equations by entering the following formulas in the appropriate cells:
In cell B8:
In cell B7:
In cell B6:
=B3*B6
=B14 + B15*B3
=B12 + B13*B3
Save your model now renaming the sheet that you are working in “Model125.” To check
your data and formula entry, the following table indicates that when quantity is set at 21,
profits should be $ 344.25. You can use the table below to check your work by entering 21
into cell B3.
Table 1. Model values for checking work (assuming Q is set at a value of 21)
Choice Variables
Quantity
21
Consequence Variables
Price
Cost
Revenue
Profit (Objective)
19.75
70.5
414.75
344.25
Parameters
Demand Intercept
Demand Slope
Fixed Costs
Variable Costs per Unit
25
-0.25
60
0.5
Some questions will be posted on the Blackboard discussion topic for week one
based on manipulation of this small model for evaluating profits. Those questions
AGEC 352 January 25, 2011
Lab 1 Cost and Returns Modeling (Introductory Topic)
will appear at approximately 12:50 during lab session so refresh the Blackboard
discussion to see those and contribute.
Part II. Case Study for Simon Pies Company
In part II, you are provided a full case to work through. A partially completed spreadsheet is
available on the class website. The questions at the end of this section are the homework
exercises for this week. You should type your answers to the questions and submit them at
the start of class the following Monday. Only the typed questions and answers need to be
submitted though you should save all of your spreadsheet work for this class.
The laboratory exercise today involves working through the example of Simon Pies
Company. The objective of working through this example is to improve our familiarity with
the model building and implementation in spreadsheets. Thus, the example should
demonstrate the importance of model specification and organization (e.g. declaration of
parameters and incorporating them via cell references), model revision and refinement (e.g.
moving from an exogenous* to an endogenous† specification of quantity demanded), and
interpretation (e.g. using graphical methods to assess the pie price that yields maximum
profits).
Problem Statement: Simon Pies is a startup company that produces and sells apple pies
wholesale. The proprietor has identified both his objective and critical decision variables.
Objective variable: Weekly Profits
Decision variable: Pie Price
Working from the objective of earning the highest possible weekly profits, we develop the
relationship between the objective variable and decision variable. As was the case in lecture
we can create a diagram as seen in Figure 1 below. In this case it is perhaps easiest to begin
with a core accounting model to determine profits from the given data in Table 1. The basic
accounting is depicted by the arrows in Figure 1. Using the data in Table 1 and the
framework from Figure 1, we can set up our ‘core’ model in an Excel spreadsheet, as is
depicted in Table 2. See the sheet called “core” in this week’s spreadsheet. You will need to
complete the formulas as indicated in the sheet named “core.”
*
Exogenous refers to a quantity or value that is determined outside of the model solution framework. It is
taken as given and can be changed by modeler assumption.
†
Endogenous refers to a quantity of value that is determined as part of the solution to the model and cannot
be changed by the modeler without violating the consistency of the model.
AGEC 352 January 25, 2011
Lab 1 Cost and Returns Modeling (Introductory Topic)
Table 1. Data for Simon Pies Company (Accounting Model)
Base Pie Price
$ 8.00
Pies Demanded and Sold
16,000
Unit Pie Processing Cost ($ per pie)
$ 2.05
Unit Cost, Fruit Filling ($ per pie)
$ 3.48
Unit Cost, Dough ($ per pie)
$ 0.30
Fixed Cost of Operation
$12,000
Profit = Revenue (R) – Total Cost (TC)
R = Price (P) x Quantity (Q)
TC = Fixed Cost (FC) +
Processing Cost (PC) + Ingredients Cost (IC)
PC = Q x Unit Cost Processing
IC = Q x Unit Cost Filling +
Q x Unit Cost Dough
Figure 1. Model Formulation
Table 2. Core Model
SIMON PIE Co.
Decision Variable
Pie Price
Pies Demanded and Sold
$
8.00
16,000
Parameters
Unit Pie Processing Cost ($/pie)
Unit Cost, Fruit Filling ($/pie)
Unit Cost, Dough ($/pie)
Fixed Cost ($/wk)
$
$
$
$
2.05
3.48
0.30
12,000.00
Financial Results
Revenue
Processing Cost
Ingredients Cost
Overhead Cost
Total Cost
Pre-Tax Profits
$ 128,000.00
$ 32,800.00
$ 60,480.00
$ 12,000.00
$ 105,280.00
$ 22,720.00
AGEC 352 January 25, 2011
Lab 1 Cost and Returns Modeling (Introductory Topic)
Each entry in Table 2 represents a value from the base data of Table 1 or a computation of a
value (via the relationships described in Figure 1) using Excel formulas to relate the given
values. The model at this point is quite simple and has not taken long to construct. What can
we do with this simplified version? Well, the easiest thing is to begin to produce
counterfactual‡ states of the model by changing our assumptions about pie price (P) and pies
demanded and sold (Q). Let’s try two of those, first changing the values of (P, Q) to ($7.00,
20,000) and then to ($9.00, 12,000). These two counterfactuals can be carried out by copying
the ‘core’ model column into the two adjacent columns. Note that the price and quantity
assumptions have been changed in these columns already. (See the sheet “WhatIF” in this
lab’s spreadsheet).
Model Revision: Adding Economics
At the outset the wholesale price charged for pies was deemed the critical decision variable.
In the counterfactual arrangements, when we investigated what happens when the price set
for pies changed, the quantity of pies sold was also adjusted. This is because economic
principles indicate that when a higher price is charged, the quantity demanded will fall (i.e.
the demand schedule has a negative slope) The actual relationship between price and
quantity demanded for the two previous counterfactual cases was not made clear and was
given as a change in a parameter.
As economists, we know that we should model the quantity of pies sold as a function of the
price of pies. Fortunately, we have a function that we can incorporate via a formula in our
spreadsheet. This leads to the quantity of pies demanded and sold being changed from an
exogenous variable in our model to an endogenous variable. The linear equation representing pie
demand is given below in terms of P and Q. Here we see that the intercept of the equation is
48,000 (the amount of pies that would be consumed in the market if pies were free) and that
the slope is 4,000, such that every dollar increase in price reduces the demanded quantity by
4,000 pies. The linear demand curve represented by this equation is presented below as
Figure 2.
Q pies  48,000  4,000 P pies
‡
‘Counterfactual’ is a term we will use to indicate that we are taking a model that is assumed to represent an
equilibrium and by changing an exogenous variable, produce alternative values for the endogenous variables.
This is sometimes referred to as “What If?” analysis.
AGEC 352 January 25, 2011
Lab 1 Cost and Returns Modeling (Introductory Topic)
Demand Schedule
30,000.00
25,000.00
24,000.00
20,000.00
20,000.00
16,000.00
15,000.00
12,000.00
10,000.00
8,000.00
5,000.00
4,000.00
0.00
$5.00
$6.00
$7.00
$8.00
$9.00 $10.00 $11.00 $12.00
Figure 2. Linear Demand Schedule for Simon Pies
Table 3 provides the revised model with the linear demand formula modeled in the
spreadsheet and the altered categorization of parameters and variables. Notice that now the
values of the demand equation appear as parameters and Q (i.e. Pies Demanded and Sold)
appears as an endogenous variable determined by the model. Table 3 can be found in the
sheet “Add_Demand_Schedule” in your spreadsheet for this lab.
Table 3. Revised Model with Quantity Demanded Endogenous
SIMON PIE Co.
Decision Variable
Pie Price
Parameters
Unit Pie Processing Cost ($/pie)
Unit Cost, Fruit Filling ($/pie)
Unit Cost, Dough ($/pie)
Fixed Cost ($/wk)
Equation Coefficients
Intercept
Slope (Linear)
Physical Results
Pies Demanded and Sold
Financial Results
Revenue
Processing Cost
Ingredients Cost
Overhead Cost
Total Cost
Pre-Tax Profits
$
8.00
$
$
$
$
2.05
3.48
0.30
12,000.00
48,000
-4,000
16,000.00
$ 128,000.00
$ 32,800.00
$ 60,480.00
$ 12,000.00
$ 105,280.00
$ 22,720.00
AGEC 352 January 25, 2011
Lab 1 Cost and Returns Modeling (Introductory Topic)
Having added the demand function that relates P and Q, the pie price variable can now be
changed in isolation so that we can compute the solution for profits for any price we input
to the model without having to guess at what quantity demanded should be. The revised
model is copied in adjacent cells of the spreadsheet and the range of prices (in 1$
increments) from $6 to $11 is evaluated. Taking these model results and the X-Y scatter-plot
available in MS Excel’s chart wizard, we can begin economic interpretation of the results
with regard to the objective of maximizing weekly profits. Plotting the prices on the x-axis,
and the endogenous variables of Profits, Revenue, and Total Cost on the y-axis, we can
assess the profit maximizing decision to make in terms of pie price. The chart below should
appear in the sheet “Chart_Financial_Results” once you complete the demand formulas in
“Add_Demand_Schedule.”
$160,000.00
$140,000.00
$120,000.00
$100,000.00
$80,000.00
$60,000.00
$40,000.00
$20,000.00
$$6.00
$7.00
$8.00
$9.00
$10.00
$11.00
$(20,000.00)
Pre-Tax Profits
Revenue
Total Cost
Figure 3. Interpretation of Model for Prices from $6 to $11
Model Revision: Adding Economics and Statistics
The Simon Pies manager indicates that the profit projections from the model are not
working correctly. The manager has identified his processing cost formula as the problem
area. The data in Table 4, and graphed in Figure 4 represent the processing cost projections
and actual observed data for pie processing.
AGEC 352 January 25, 2011
Lab 1 Cost and Returns Modeling (Introductory Topic)
Table 4.Pie Processing Costs Actual and Projected
Simon Pie Cost Data
Pie Numbers Processing Cost (actual) Processing Cost (predicted)
6,000 $
10,100.00 $
12,300.00
8,000 $
11,200.00 $
16,400.00
10,000 $
16,500.00 $
20,500.00
12,000 $
24,600.00 $
24,600.00
14,000 $
32,400.00 $
28,700.00
16,000 $
41,100.00 $
32,800.00
18,000 $
45,300.00 $
36,900.00
20,000 $
55,100.00 $
41,000.00
22,000 $
59,900.00 $
45,100.00
$70,000.00
$60,000.00
$50,000.00
$40,000.00
$30,000.00
$20,000.00
$10,000.00
$0
5,000
10,000
Processing Cost (actual)
15,000
20,000
25,000
Processing Cost (predicted)
Figure 4. Plot of Processing Costs (Actual and Predicted)
From Table 4 and Figure 4 it is observed that the cost predictions for low quantities are
over-predicted and predictions for high quantities are under-predicted using the current cost
formula. Using statistics in the form of a fitted trend-line through the actual data points and
the equation for the trend-line, we can improve the formula for processing costs of pies.
This is the procedure performed with the result presented below as Figure 5.
AGEC 352 January 25, 2011
Lab 1 Cost and Returns Modeling (Introductory Topic)
Fitted Processing Cost Equation
$70,000.00
$60,000.00
y = 3.375x - 14339
R2 = 0.9863
$50,000.00
$40,000.00
$30,000.00
$20,000.00
$10,000.00
$0
5,000
10,000
Processing Cost (actual)
15,000
20,000
25,000
Linear (Processing Cost (actual))
Figure 5. Fitting a Trend-line for Processing Costs
As before, we can introduce this new equation into the spreadsheet model by adding the
parameters of the processing cost equation and removing the parameter for Unit Processing
Cost of pies. This is shown in Table 5 below.
Table 5. Revised Model with Fitted Processing Cost Equation
SIMON PIE Co.
Decision Variable
Pie Price
$
9.00
Parameters
Unit Cost, Fruit Filling ($/pie)
Unit Cost, Dough ($/pie)
Fixed Cost ($/wk)
$
$
$
3.48
0.30
12,000.00
Equation Coefficients
Demand Equation
Intercept
Slope (Linear)
Processing Cost Equation
Intercept
Slope
Physical Results
Pies Demanded and Sold
Financial Results
Revenue
Processing Cost
Ingredients Cost
Overhead Cost
Total Cost
Pre-Tax Profits
48,000
-4,000
-14,339
3.375
12,000.00
$ 108,000.00
$ 26,161.00
$ 45,360.00
$ 12,000.00
$ 83,521.00
$ 24,479.00
AGEC 352 January 25, 2011
Lab 1 Cost and Returns Modeling (Introductory Topic)
So, our process of model implementation has gone through two phases of revision from the
initial setup phase which was based on an accounting model. We added the equation
specifying the demand relationship as well as the improved processing cost based on
historical data for different levels of pie production. This is a theme that will recur
throughout all our model building exercises. The lesson is that it is important to start from a
simple framework and then allow performance of the model, judgment regarding the results,
and knowledge of economic principles to guide you through the process of arriving at a
finished product by adding more complex relationships or formulas as needed.
The homework questions on the next page use the Simon Pies model. Type your answers
and submit the assignment at the beginning of class next Monday. Feel free to post any
questions you have on this week’s Blackboard discussion topic.
AGEC 352 January 25, 2011
Lab 1 Cost and Returns Modeling (Introductory Topic)
Assignment 1 Due Date: January 31, 2011
Name:
1. In Figure 1 (Part II) of this handout, we mapped the model in words and symbols using a
diagram to represent model relationships. Describe the addition we need to make to the diagram
in Figure 1 when we change the quantity of pies demanded and sold (Q) to a variable that
depends on the price charged?
2. In Figure 3 above, three schedules are plotted for Revenue, Costs, and Profits. The plot for
profits can be used to find the correct price to charge by finding the highest point it reaches.
Describe how would you find the highest profit using this graph if it only had revenue and costs
plotted?
3. Assume that the manager of Simon Pies Co. chooses $9.00 as the price to set. Using the
worksheet Sens.Analysis.9dollars in the Laboratory 2 Spreadsheet discuss how sensitive profits
are to this choice of price. (In other words, how do changes in the price around the $9.00 level
affect profits the company earns and do profits increase or decrease when the price changes?).
4. Using the spreadsheet model (and the graphs in the spreadsheet) what would the new profit
maximizing price be if the slope of the demand curve was increased to -3,600? Explain this
change. (Note: Use the worksheet Add_Demand_Schedule for this question and change the
slope parameter for all columns).
5. Assume the demand curve slope is again -4,000. What is the new profit maximizing price when
fixed costs are increased by 100 percent to $ 24,000? What is the new profit level? Explain this
change.
AGEC 352 January 25, 2011