Example 2.1
Finding a Breakeven Point
Background Information

The Great Threads Company sells hand-knit
sweaters. Great Threads is planning to print a
brochure of its products and undertake a direct mail
campaign.

The cost of printing the brochure is $20,000 plus
$0.10 a catalog. The cost of mailing each catalog is
$0.15. In addition, the company will include direct
reply envelopes in it’s mailings. It incurs $0.20 in
extra cost for each direct mail envelope that is used
by a respondent.

The average size of a customer order is $40, and the
company’s variable cost per order averages around
80% of the order’s value.
Background Information -continued

The company plans to mail 100,000 catalogs. It
wants to develop a spreadsheet model to answer the
following questions:
– How does a change in the response rate affect profit?
– For what response rate does a company break even?
– If the company estimates a response rate of 3%, should it
proceed with the mailing?
– How does the presence of uncertainty affect the usefulness
of the model?
GREATTHREADS.XLS

This file contains the completed model shown below.
GREATTHREADS.XLS -continued

Note the clear layout of the model
– The input cells are outlined and shaded and separated from
the outputs.
– There are boldfaced headings, several headings are
indented.
– Numbers are formatted appropriately.
– Text boxes to the right spell out all the range names used.
Creating the Model

To create this model, proceed through the following
steps.
– Enter heading and range names.
• Obviously we have a lot of cells, more than you might want to
enter, but you will see their value when we start entering
formulas.
– Enter input values.
• The values in the shaded cells are all given in the statement of
the problem. Enter these values and format them appropriately.
Creating the Model -- continued
– Model the responses.
• We have not specified the response rate of the mailing, so
enter any reasonable values such as 8% in the ResponseRate
cell – we will perform sensitivity on this value later on – and
enter the formula =NumMailed*ResponseRate in the
NumResponses cell.
– Model the revenues, costs and profits.
• Enter the formula =NumResponses*AvgOrder in the
Revenues cell.
• Enter the formula =FCostPrinting,
=SUM(VCostMailing)*NumMailed and
=NumResponses*(AvgOrder*VCostOrderPct+VCostEnvelo
pes) in the Cost cells (E10, E11, E12).
• Enter the formula =SUM(Costs) in the TotalCost cell, and enter
the formula =Revenue-TotalCost in the Profit cell.
Answering the Questions

Now that a basic model has been created, we can
answer the questions posed by the company.

For questions 1, we form a data table to show how
profit varies with the response rate. The table is
shown here.
Creating a Data Table

First, enter a sequence of trial values of the response
rate in column A, and enter a “link” to profit in cell B20
with the formula =Profit.

Finally, highlight the entire table range, A20:B30, and
select the Data/Table menu item to bring up the
dialog box shown here.
Creating a Data Table -continued

It should be filled in as shown to indicate that the only
input ResponseRate, is listed along a column.

When you click OK, Excel substitutes each response
rate value in column A in to the ResponseRate cell,,
recalculates the profit, and reports it in the data table.

For a final touch, we have created a scatterplot(or in
Excel’s terminology X-Y chart) of the values in the
data table.
Answering the Questions -continued

Clearly, profit increases in a linear manner as
response rate varies. More specifically, a 1%
increase in the response rate always increased profit
by $7800.

Here is the reasoning. Each 1% in response rate
results in 100,000 x 0.01=1000 more orders. Each
order yields an average revenue of $40 but incurs a
variable cost of $40 x 80% = $32 and a $0.20
envelope cost. The net gain is $7.80 per order, or
$7800 for 1000 orders.
Answering the Questions -continued

From the data table, we see that profit goes from
negative to positive when the response rate is
somewhere between 4% and 5%.

Question 2 asks for the exact breakeven point. This
could be found with trail and error but is easy with
Excel’s Goal Seek tool. Goal Seek is useful for
solving a single equation in a single unknown.

Here the equation is Profit=0, and the single
unknown is the response rate.
Answering the Questions -continued

In Excel terminology, the unknown is called the
changing cell because we are allowed to change it
to make the equation true.

To implement Goal Seek, select Tools/Goal Seek
menu item and fill in the resulting dialog box as
shown below.
Answering the Questions -continued

After clicking on OK, the ResponseRate and Profit
cells have values 5.77% and $0. In words, if the
response rate is 5.77% Great Threads breaks even.
If the response rate is greater then 5.77%, the
company makes money; otherwise, it loses money.

Question 3 asks if the company should proceed with
the mailing if the response rate is only 3%. From the
data table, the apparent answer is “no” because profit
is negative, a loss. However, like many U.S.
companies, we are taking the short term view with
this reasoning.
Answering the Questions -continued

We should realize that many customers who respond
to direct mail will reorder in the future. The company
makes $7.80 per order. If each of the respondents
ordered two or more times, say, the company would
earn 3000 x $7.80 X 2 = $46,800 more than appears
in the model, and profit would then be positive.

The moral is that we must look at long-term impact of
our decisions. However, if we want to incorporate the
long term explicitly into the model, we must build a
more complex model.
Answering the Questions -continued

Finally, question 4 asks about the impact of
uncertainty in the model. We would be kidding
ourselves to think that all model inputs are known
with certainty.

For example, the size of an order is not always $40 –
it might be, say, from $10 to $100. When there is a
high degree of uncertainty about model inputs, it
makes little sense to talk about the profit level or the
breakeven response rate.

It makes more sense to talk about the probability that
profit will have a certain value or the probability that
the company will break even.