Data Tables
Exercises
1. You’ve been assigned to analyze the profitability of Bill Clinton’s
new autobiography. The following assumptions have been made:
❑ Bill is receiving a $12-million royalty.
❑. The fixed cost of producing the hardcover version of the book is $1 million.
❑ The variable cost of producing each hardcover book is $4.
❑ The publisher’s net from book sales per hardcover unit sold is $15.
❑ The publisher expects to sell 1 million hardcover copies.
❑ Paperback sales will be double hardcover sales.
❑ The fixed cost of producing the paperback is $100,000.
❑ The variable cost of producing each paperback book is $1.
❑ Publisher’s net from book sales per paperback unit sold is $4.
Use this information to answer the following questions.
❑. Determine how the publisher’s before-tax profit will vary as hardcover sales vary between
100,000 and 1,000,000 copies.
❑. Determine how the publisher’s before-tax profit varies as hardcover sales vary between
100,000 and 1,000,000 copies and the ratio of paperback to hardcover sales varies between 1 and
2.4.
2. The annual demand for a product equals where p = price of product in dollars and a =
hundreds of dollars spent on advertising the product. The annual fixed cost of selling
the product is $10,000 and the unit variable cost of producing the product is $12. Determine a
price (within $10) and amount of advertising (within $100) that maximizes profit.
3. Microsoft is thinking of translating a software product into Swahili. Currently, 200,000 units
per year of the product are sold at a price of $100. Unit variable cost is $20.00. The cost of
translation is $5 million. Translating the product into Swahili will increase sales during each of
the next three years by some unknown percentage over the current level of 200,000 units. Show
how the change in profit resulting from the translation depends on the percentage increase in
product sales. You can ignore the time value of money and taxes in your calculations.
4. This exercise deals with mortgages, but the same mathematical model we used for car loans
can be used here. Suppose you know the annual interest rate will be 5.5 percent. Create a table
that shows for amounts borrowed between $300,000 and $600,000 (in $50,000 increments) the
difference in payments between a 15-year, 20-year, and 30-year mortgage.
5. Currently we sell 40,000 units of a product for $45. The unit variable cost of producing the
product is $5. We are thinking of cutting the product price by 30 percent. We are sure this will
increase sales by an amount between 10 percent and 50 percent. Perform sensitivity
analysis to show how profit will change as a function of the percentage increase in sales. Ignore
fixed costs.
6. Let’s assume that at the end of each of the next 40 years, we will put the same amount in our
retirement fund and earn the same interest rate each year. Show how the amount of money we
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will have at retirement changes as we vary our annual contribution between $5,000 and $25,000
and the rate of interest varies between 3 percent and 15 percent.
7. (Set this problem this problem up as if you were going to do sensitivity analysis. The
narrative that follows explains how to set up the mathematical model portion of the sensitivity
analysis.) Many companies use e-mail to advertise their products. Your company is trying to
sell a new product and is advised to use e-mail. The profit on each unit sold is $200. Developing
the attractive e-mail message, use of 2,750,000 e-mail addresses, and sending the message would
cost $25,000. Experience shows that 5 percent of the initial recipients forward such messages to
friends and family. Experience also shows that 2 percent of all recipients actually click the Web
address included in the message and the commercial site. Of these visitors 0.5 percent end up
purchasing the advertised item. Using Excel, answer the following questions: (1) Would you
generate a profit if you used this advertising opportunity? (2) Would you profit if you could email only 1,000,000 people? (3) What kinds of sensitivity analysis could you set up for this
situation? (p. 99, Oz 5th ed)
8. (This type of problem has been used on past tests.) The total cost of producing an item is as
follows:
Cost=40 + 4x +6y + (x2y)/100
The variable x is the cost per pound of raw materials and the variable y is the cost per hour for
labor. You are interested in seeing how cost is impacted by variations in x and y. You decide to
build a two variable data table where you vary raw material cost (x) from $5/pound to $12/pound
in increments of a dollar, and vary labor cost per hour (y) from $10 to $14 in increments of
$0.50. A partially developed spreadsheet is show below.
Answer the following questions relative to the partially developed spreadsheet above.
a. What is the formula that you would use for cell C11?
b. What are the cell references for the input variables?
c. What is the cell reference for the output variable?
d. The upper left hand corner of the data table is going to be at E4. What would you put in
E4?
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e. If raw material cost is your row variable, enter the first five values on the spreadsheet
above.
f. If labor cost is your column variable, enter the first five values on the spreadsheet.
g. When you are prompted to complete the Window below, how will you respond?
9. Suppose you are enrolled in a course where the instructor determines your grade through
the following measures:
Exam #1 – 20%
Exam #2 – 20%
Exam #3 – 20%
Final
- 10%
Projects - 20%
Homework – 10%
There are three projects in the course. Projects 1, 2, and 3 are weighted at 10, 5, and 5
percent, respectively. There are 11 homework exercises and the instructor drops the lowest
one.
9. When you take the final you don’t know the score on project 3 or the score on the final.
You would like to use a data table to see how different scores on these measures impact your
course grade. Set up a two-variable data table to do this where course average is the output
variable. Vary the scores on the final exam starting at 75 and going to 85 by increments of
one for the vertical input variable. For the horizontal input variable, vary scores on the last
project from 80 to 100 by increments of five.
Based on your table, explain what you need to do in order to get in the B range (>80).
Accompany your analysis with a printout of the spreadsheet and a printout of the formulas.
Before you start, you need to build a mathematical model for calculating the course average.
This means you will need formulas for the Exam Average, Project Average, Homework
Average, and Course Average. Exam Average is obvious. The project average can be
calculated as (2*Project 1 + Project 2 + Project 3)/4. The Homework Average is calculated
as Sum (the homework scores)-Min(homework scores). The Course Average is calculated as
.6*ExamAverage + .2*ProjectAverage + .1*HomeworkAverage + .1*FinalExam
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Exam #1
Exam #2
Exam #3
Exam Average
75
78
78
77
Project 1
Project 2
Project 3
Project Average
HomeWork Scores
Homework 1
Homework 2
Homework 3
Homework 4
Homework 5
Homework 6
Homework 7
Homework 8
Homework 9
Homework 10
Homework 11
Homework Average
Final exam
Course average
85
85
95
87.5
10
10
8
6
7
0
9
8
10
8
8
84
78
79.9
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