Exploring Misconceptions in Retailing
Using a local example to endeavour to make financial mathematics relevant for business students can lead
to a greater understanding of the misconceptions that are likely to exist in the minds of the general public.
A major retailer of home ware has been attracting customers recently with a deal giving the customer 30
months to pay with no interest and a 6-month period of deferment. It is surprising to find how many
misconceptions there are amongst students as to the effect on the different parties involved when a
customer takes advantage of this deal.
This example provides an excellent way to discuss the roles of the parties involved and to quantify the
costs. In this paper after showing the calculations involved, the assumptions that have to be made and the
impact of those assumptions on the final analysis, I will present some initial findings that will show the
extent of the misconceptions amongst students. The need to acquaint business students with this
information will be immediately apparent. However the implication that the general public might be
equally unaware of what is happening cannot be avoided.
Introduction
The teaching episode that prompted this study arose from an attempt to explore an advertisement
appearing regularly on television, in newspapers and in material distributed in mailboxes. Fig 1 is a
copy of the advertisement used for this paper. It will be known that the details of the sort of deal
this retailer offers does vary from month to month, however, the different versions are isomorphic
to the deal that is the subject of this paper.
Fig 1:The advertisement that is the basis for the numerical calculations in this paper
The question students were asked to tackle
At the end of March this year a major retailer advertised the deal in the attached advertisement.
This firm sells a range of electronic equipment (TVs, videos, stereos etc), computers and
peripherals etc and household items.
Your objective is to explain how the deal works from the point of view of (a) the customer, (b) the
retailer and (c) the finance company.
The following statements have been provided to help you construct your answer.
(a) Imagine you are a customer of this firm. Select an item and a retail price you think would
be appropriate. (Look at advertisements. Be sure not to discuss your selection with anyone
else in the class.)
(b) You may assume the customer takes exactly 30 months to pay the item off.
(c) To explain how the deal works you need to make up an appropriate interest rate. Explain
why you chose that interest rate and describe the effect of that interest rate on the customer,
the retailer and the finance company.
(d) Using your retail price and your interest rate calculate the dollar amounts involved.
(e) Make sure you include all features of the deal in your answer.
The question did prompt the student to realise there were three parties involved so it was expected
the solution would cover the effect of a specific transaction on each party.
The students who were involved in this study were taking a level 5 paper called The Mathematics of
Finance. This is a paper in which the concepts of simple interest, compound interest and annuities
are explored from a mathematical point of view and using practical examples. Students had never
been exposed to an example like the retailing question that is the subject of this paper, however by
the time they met this question they had discussed many different examples of annuities. Students
should therefore have realised that the question would more than likely involve an annuity. They
had also handled annuity questions where the interest rate had to be calculated so they knew that it
is considerably easier to calculate a discounted value when the interest rate is specified than it is to
calculate the yield given the discounted value.
When the marked exercises were returned to the students they were furnished with the following
model solution. This was followed by a class discussion during which the model solution was
scrutinised.
Model solution to the question
From the customer’s point of view
Assume the customer sees the $35 establishment fee as being a legitimate cost of setting up the deal
(Paperwork etc.) They could see it as an interest charge, but this would introduce unnecessary
difficulty that was not intended when the question was devised. You might find it difficult to
imagine who receives the $35. It actually goes to the finance company.
For this model solution I chose a DVD/CD player at $1499
The customer is required to pay $1499 + 35 = $1534 over 24 months starting in month 7
Every month the customer pays $63.92 (say)
23 $63.92 
24th @ $63.84
$1470.16
63.84
1534.00
For the purposes of this question take the value to be $63.92.
Interest rate for this customer is 0%.
From the retailer’s point of view
The retailer sells the debt of $(1499 + 35) = $1534 to the finance company. It is certain the finance
company will want a return on the debt (called a yield). What the finance company will buy is a
stream of payments of (say) $63.92 (24 payments) from months 7 to 30.
Say the finance company wants a return on the debt of 12% p.a.
PV  $63.92  a24 0.01  1.016  $1279.18
The finance company will therefore give the retailer $1279.18 and receive in return the right to
collect the 24 payments of $63.92. The $35 establishment fee is spread over the 24 payments too.
The retailer gets $1279.18 for the item with a ticket price of $1499 i.e. losing $219.82.
From the finance company’s point of view
The finance company specifies that they require a return of 12%. By giving the retailer $1279.18
and receiving in return the 24 payments of $63.92 this will be achieved. The $35 is absorbed into
the transaction. It could, for instance, be spread evenly over the 24 payments. (The PV of $35
spread evenly over 24 payments at 12% is $29.21.)
Therefore the interest rate to be discussed is the yield received by the finance company. The greater
the yield the less the finance company will give the retailer for the payment stream. A smaller yield
will allow the finance company to give a greater sum to the retailer.
0.07
and the PV  $1378.70
12
0.24
 0.02 and the PV  $1073.54
If 24 % return is demanded i 
12
This is excessive and would more likely be the penalty interest charged by the finance company to
the customer if they go beyond the 30 months or if they fall behind with a monthly payment. It is
important that you do not confuse these two situations. Remember the retailer is missing out on the
difference between this amount and the ticket price. If it were too high the retailer would not
participate in the scheme.
E.g.
If 7% return is acceptable i 
The study
The results of this study are from the responses of 23 students. While this sample is quite small it,
in my opinion, represents a typical cross-section of students at our university. In posing a question
of this type you run the risk of selecting an example that is new to the students and therefore places
them at an immediate disadvantage. In discussion, however, no student admitted they had no prior
knowledge of the type of deal. Two students had actually taken advantage of the deal. All students
knew the name of the firm and some had seen the advertisement or a similar one on TV. It seems
appropriate therefore to suggest that the element of unfamiliarity is not a factor. Unlike members of
the public these students had the opportunity to weigh up the meaning of each word and statement
in the advertisement. They probably also had the opportunity to consult with others who might help
them to better understand the detail. This therefore is not a controlled study in the sense that the
written answers furnished by the students may have been the result of collaboration with any
number of others.
At the time this was not an issue, because with the emphasis of the paper being the Mathematics of
Finance any help received in the area of context was not discouraged. In fact the point of the
question was to provide students with the chance to see a mathematical model in a business context
and to make the necessary assumptions and approximations so that the model could be applied.
It is inevitable that when an open-ended question is provided a wide variety of answers is to be
expected. Much can be learnt, however, from some of the misconceptions expressed by the
students in their answers. The discussion that follows focuses on these misconceptions without
trying to explain or justify them.
The results of the study
The $35 establishment fee
Much is made of the issue of “the fine print” in contracts and for the purposes of this deal the $35
establishment fee was mentioned in the fine print at the bottom of the advertisement. Of the 23
students six failed to mention the fee at all in their answer and of those that did mention it six failed
to include it in the calculations they made. Two students thought the fee was paid when the goods
were purchased and one stated that the establishment fee went to the retailer. One student stated
that the establishment fee was the total received by the finance company and one student regarded
the $35 fee as insignificant even though it amounted to 2.3% of the purchase price in that student’s
case.
The period of deferment
The advertisement clearly provided enough information to allow students to understand the
meaning of the six months deferred payments, however two students thought the six months
extended the 30-month period to 36 months. Another two students recognised the period of
deferment in the words they wrote then calculated the monthly payments by dividing by 30.
The 30-month period
The 30 months interest free undoubtedly provided the most opportunity for misconceptions to be
revealed. Only three people stated clearly that the finance company would not charge interest for
the first 30 months to the customer then start charging interest after 30 months. Two people stated
the finance company would charge penalty interest if the customer fell behind with their monthly
payments within the 30-month period, however, both those students said this was how the finance
company made its profits.
Three students thought the finance company benefited by wanting the customers to take longer than
30 months so they could charge penalty interest and most importantly three other students thought
the finance company made no profit unless the customer took over 30 months.
A typical comment: “If the customer can pay off the item before 30 months the finance company
will make no profit.”
The interest rate to consider
The advertisement mentioned the finance company’s prevailing interest rate and this possibly led
students to the conclusion that this was the interest rate to discuss in the question. Only three
students took this view. Most students calculated the present value of a deferred annuity but no
student truly identified why they were using their chosen value and no one correctly identified the
present value as the value to the finance company of the deferred annuity.
Even though the advertisement stated that the deal was 30 months interest free, four students
misinterpreted the difference between the present value and the purchase price as the interest paid
by the customer. Five other students performed similar but less complex calculations to arrive at
the conclusion that the customers paid interest. One of those even went so far as to state that the
finance company and retailer would split the interest received from the customer 50:50. One stated
the interest rate would not affect the retailer at all.
From the customer’s point of view
Most student identified benefits of the deal and some creative thought was evident. One student
discussed the issue of buying a more expensive item so that the $35 would be a smaller proportion.
Another discussed the chance to buy an expensive item this way rather than raising a loan at the
bank to pay for it. Two discussed the possibility of being able to pay cash but instead leaving the
money in the bank and getting interest on it while taking advantage of the deal. One of those,
however, went further and reminded us that the interest earned would not amount to much.
From the retailer’s point of view
Six students stated that the deal would result in increased sales. One has to wonder why everyone
didn’t say this. Maybe it is self-evident. Maybe students were focussed on a single transaction so
didn’t think it necessary to look beyond that.
Of concern is that five students thought the finance company would pay the retailer in full and take
over the debt. Three stated there would be no cost to the retailer at all. A further student stated that
a benefit to the retailer was that it would not have to collect the debt.
From the finance company’s point of view
One student selected a penalty interest of 22% as this encourages customers to pay on time. Student
assumed there would be monthly payments and that these would go to the finance company. It is
clear, however, that students would need to participate in a deal of this nature to observe that a
minimum monthly payment is required regardless of any form of accelerated early payment. No
student discussed the concept of minimum monthly payments even though two actually stated they
were currently buying something with this deal.
Although no student suggested it would be a clever plan to pay nothing for 30 months then
everything on the last day no student suggested you should pay the minimum monthly payment
from months seven to twenty-nine then on month 30 (the last day) pay all of the outstanding
balance. Other comments about the finance company have been previously mentioned.
Conclusions
The example discussed in this paper was not chosen because it was expected to provide the rich
source of information about student misconceptions that transpired. This only emerged when the
students’ answers were marked. At the time the opportunity to dispel those misconceptions by
discussion and further teaching provided the group of students with a worthwhile learning
experience made all the richer because they had already spent time trying to articulate the intent of
the deal for themselves. However, it quickly became clear that the students’ understanding of the
way the deal was likely to affect the parties was clouded by so many misconceptions. This led to the
possibility that the nature of these transactions might be a mystery to members of the general public
as well. It was a worry that students, required to look at the small print to try and establish exactly
what was meant, could get it wrong. This might mean that a member of the public who would have
far less time to check what was intended would potentially have no better understanding. With 26%
of the sample either not bothering or not knowing how to include the establishment fee into the
calculations of the payment required and a further 26% not acknowledging the existence of the
establishment fee the public might be similarly unaware of how to deal with it or might not think it
matters very much. Also the fact that even thought the deal said no interest for 30 months 39% of
the sample of students somehow thought the customer would be paying interest. Another
interesting result was the number who thought the finance company would not be making very
much profit unless the customer took longer than 30 months.
While these are only a few of the questions that this study brings to mind it would be inappropriate
at this early stage to suggest any patterns are emerging. To try to answer questions of this nature
further research needs to be conducted. These misconceptions will be further explored amongst
students enrolled in this course in future semesters to see if it is possible to establish a pattern of
misunderstanding. Further potential research should be undertaken to explore the understanding
that members of the public might have about the nature of these deals. It is obvious that the more
we understand about the nature of the transactions we enter into the more likely we are to make
informed decisions. Education in this area might be necessary and appears to be lacking.
References
Zima, P., Brown, R.L. (1996). Mathematics of Finance. New York: McGraw-Hill