Modeling in Excel: Direct Mail Campaign*
We use this problem to illustrate a simple Excel-based model. In the Economics course, you will be
building and analyzing more complex models.
A company is planning to print a catalog of its products and undertake a direct main campaign. The cost
of printing the catalog is $20,000 plus $0.10 per catalog. The cost of mailing each catalog (including
postage, order forms, and buying names from a mail-order database) is $0.15. In addition, the company
will include direct reply envelopes in its mailings. It incurs $0.20 in extra costs for each direct mail
envelope that is used by a customer. The average size of a customer order is $40, and the company’s
variable cost per order (due primarily to labor and material costs) averages around 80% of the order’s
value. The company plans to mail 100,000 catalogs. It wants you to develop a spreadsheet model to
answer the following questions: 1) How does a change in the response rate affect profit? 2) For what
response rate does the company break even? 3) How high does the response rate have to be to make a
profit of at least $20,000? 4) How does profit vary as a function of both the response rate and the
average order size?
To help you in modeling the problem, spreadsheet Direct Mail Campaign is attached. The spreadsheet
illustrates several principles of good Excel modeling: 1) On the left side of the spreadsheet, the inputs
are clearly laid out and identified by grey cells. Bold is used to highlight the two main types of inputs,
those associated with the mailing the catalogs and those associated with orders placed by customers
who receive the catalogs. Indentation is used when there are several inputs of the same type (variable
costs). Also, all numbers are formatted appropriately; 2) On the right side of the spreadsheet, there is a
section for a Model of Responses and a section for a Model of Revenue, Costs and Profits. Again,
bolding, indentation and appropriate formatting are used. Consider the Model of Responses. Note that
there is a separate line for response rate and number of responses. Thus, rather than directing
calculating number of responses as “numbered mailed” (cell B8) times .08, it is calculated as cell B8
times cell E4. Putting .08 directly in the formula for “number of responses” is an example of “hard
coding.” It is usually bad modeling practice to hard code variables. There are two reasons for this: 1) if
you want to see the impact of changing the response rate and you have hard-coded it, you have to find
and adjust every cell that uses response rate in a formula; and 2) if you haven’t hard coded a variable,
you can more easily examine the impact of changes in that variable, as illustrated in the analyses you
will do with this model. The Model of Revenue, Costs and Profits illustrates another good Excel
modeling principle: rather than writing one long formula to calculate total costs, each component of
total cost is calculated separately and then the components added. Though it may seem like a “pain” to
lay out all of these components, it significantly reduces the chances of errors and allows you to much
more easily check your work. Finally, note how the bottom line (“profits”) has been highlighted so you
can easily find it.
Assignment:
1) Write formulas to calculate cells E5, E8 and E10-E13. Note: profit should be $17,400. If you don’t get
this, you have most likely made a mistake in cell E12, so look at this formula particularly carefully.
2) The company is interested in examining the sensitivity of profits to the response rate. Use a Data
Table to do this (see Excel Tutorial to Improve Your Efficiency, p 24). Specifically, in cell A18, type in Bold
“Sensitivity of Profit to Response Rate”, in cell A19, type “response rate” and in cell B19 type “profit”. In
cells A21 thru A30, type 1, 2, …, 10 (type 1, then 2, then highlight the 2 numbers, move the cursor to the
lower right corner of the highlighted box and drag down until you have the 10 numbers). If these cells
are not formatted as percentages, format them. In cell B20 enter “=E14”. Before you do anything else,
go to Formulas (assuming you are using Excel 2010 or later), then Calculation Options, and make use
Automatic is checked. If you are using earlier versions of Excel, click on Tools > Options > Go to the
Calculation Sheet and make sure Automatic is checked. Now, highlight cells A20 to B30, go to the Data
tab, then What-if Analysis, then Data Table. In the column input box, enter E4 (leave the row input
blank) and then hit OK. What you are doing is telling Excel to take each number in column in A (1% to
10%), put it in cell E4, and then report the new number in cell E14 (that is, the cell referenced in cell
B20). The Data Table tells you that if the response rate is 1%, you lose $37,200; if it is 3%, you lose
$21,600, etc. If in addition to profit, you wanted to examine the effect of the response rate on total
cost, you could enter =E13 in cell C20 and, when you highlight cells for the Data Table, include cells C20
to C30.
3) From the Data Table, you can see that the breakeven point is somewhere between 5% and 6%. You
could play around with different values in this range to find the exact breakeven point, but Excel has
another tool to help you do this: Goal Seek. From What-if Analysis, select Goal Seek instead of Data
Table. To find the breakeven point, you want to find the response rate that will result in a profit of 0. In
Goal Seek terms, you want to “set cell” E14 equal “to value” 0 by “by changing cell” E4. What is the
breakeven point? Using Goal Seek, you can easily find what the response rate has to be to reach any
profit goal you establish. What does the response rate have to be to have a profit of $20,000? (Put
these answers at the bottom of the spreadsheet).
4) You can use Data Table to examine the effect of changing two inputs simultaneously on one output,
e.g., both the response rate and the average order size. To illustrate this, in cells E21 thru E30, enter 1%,
2%, …, 10%; in cells F20 thru P20, enter 30, 32, …, 50 (these are various order sizes). In cell E20 enter
=E14. Highlight cells E20 to P30 and then select Data Table from the What-if Analysis. Tell Excel to put
the column numbers (the response rates), in cell E4 and the row numbers (the average order sizes) in
cell B11. Then hit OK. The results show you profit for various combinations of average order size and
response rate.
When you have finished the Pivot Table Assignment, name a new worksheet after the Summary
worksheet called DMC. Copy the model from the Direct Mail Campaign spreadsheet and paste it onto
the new worksheet. That way you only have to submit one file, which will include the results of both
assignments.
Note: Many Excel users are unaware of Data Tables. Along with Pivot Tables (illustrated in the other
Assignment), they are among the most powerful and useful Excel tools. After you have developed a
model, Data Table allows you to quickly see how outputs vary as inputs vary over some range. They
allow you to answer a large number of what-if questions quickly and easily.
*This example is from Practical Management Science, Winston and Albright, 3rd edition, South-Western
Cengage Learning, 2009. For those of you interested in these types of models, which can be quite useful
in a wide range of business situations, QM 880: Business Analytics: Modeling in Excel is an elective
course you might consider taking. The course, which uses the Winston and Albright book, develops and
analyzes optimization and simulation models to aid managerial decision-making.