Homework 1
Download the shells from this folder to your machine. Use the shells as the basis for solving the
problems. Submit the workbook via Canvas by the assigned due date.
1. Julie Esrog is opening up a lemonade stand. She believes the fixed cost per week of
running the stand is $50.00. Her best guess is that she can sell 300 cups per week at
$0.50 per cup. The variable cost of producing a cup of lemonade is $0.20.
a. Given her other assumptions, what level of sales will enable Julie to break even?
b. Given her other assumptions, create a one-way data table and discuss how a change
in sales volume affects profits.
c. Given her other assumptions, create a two-way table and discuss how a change in
sales volume and variable cost jointly affect profits.
d. Use Excel’s auditing tool to show which cells in your spreadsheet affect profit. Note
that the auditing results can’t be saved.
2.
We are thinking of opening a small copy shop. It costs us $5000 to rent a copier for a year.
It costs us $0.03 per copy to operate the copier. Other fixed costs of running the store
amount to $400 per month. We charge an average of $0.10 per copy. We are open 365
days per year. Each copier can make up to 100,000 copies per year. Formulate a model for
annual profit.
a. Create a two-way table for 1 to 5 copiers rented and daily demands of 500, 1000,
1500, and 2000 copies per day. That is, compute annual profit for each of these
combinations of copiers rented and daily demand.
b. If we rent three copiers, what daily demand for copies will allow us to break even?
c. Using the data table from part a, chart profit as a function of the number of copiers;
for a daily demand of 500 copies, and for a daily demand of 2000 copies. Show both
lines on the same chart. Interpret your results.
3.
Microsoft is trying to determine whether to give a $10 rebate, a $6 price cut, or have no
price change on a software product. Currently 40,000 units of the product are sold each
week for $45. The variable cost of the product is $5. The most likely case appears to be
that a $10 rebate will increase sales 30% and half of all people will claim the rebate. For
the price cut, the most likely case is that sales will increase 20%. Formulate a model that
shows profit for each of the three options, current situation, rebate or price cut.
a. What percent increase in sales from the rebate would make the profit with
rebates equal to the current profit from a price cut? Use Goal Seek to make the value of
profits with rebate equal to the numerical value of profits with price cut, using the percent
increase in sales with rebates as the changing cell.
b. Microsoft does not really know the increase in sales that will result from a
rebate or price cut. However, it is quite sure that the rebate will increase sales by between
15% and 40% and that the price cut will increase sales by between10% and 30%. Develop
a two-way data table for the best policy as a function of both of these changes. In the table,
the row should be percent increase in sales from a price cut, and column should be percent
increase in sales from a rebate. The output of the table should be the best strategy, “No
Change”, “Price Cut” or “Rebate.” Place a formula for the best policy in cell B27 and
use that as the link.
4.
For the Links example in the text suppose you have an extra six months of data on demand
and prices, in addition to the data in the example. These extra data points are given in the
shell. Find the best fitting exponential, power and quadratic trend lines that fit the data.
Find the fit coefficients to four decimal places. Calculate the MAPE for each of these. Does
the power curve still have the smallest MAPE?
5.
In the Sam’s Bookstore problem, the quantity discount structure is such that all the units
ordered have the same unit cost. Sometimes, the quantity discount structure is such that the
unit cost for the first so many items is one value, the unit cost for the next so many values
is a lower value, and so on. Modify the model so that Sam’s pays $24 for units 1 to 2000,
$23 for units 2001 to 3500, and $22 for units 3501 and above.
Next develop a two-way data table showing profit as a function of order quantity and
demand. Then, using the table showing the probabilities that the demands occur, use the
data table array to calculate expected profit as a function of order quantity. expected profit
for the order quantities shown in cells A42 through A50. Finally, insert a bar chart showing
expected profit as a function of order quantity.
6.
We are entering the widget business. It costs $500,000, payable in year 1, to develop a
prototype. This cost can be depreciated on a straight-line basis during years 1-5. Each
widget sells for $40 and incurs a variable cost of $20. During year 1 the market size is
100,000, and the market size is growing at 10% per year. Profits are taxed at 40%, but
there are no taxes on negative profits.
a) Given our other assumptions, what market share (in %) is needed to ensure the total
free cash flow (FCF) of $0 over the five year period? Note: FCF during a year equals aftertax profits plus depreciation minus fixed costs (if any).
b) Describe how an increase in percent market growth rate changes total FCF over years
1-5.
c) Describe how simultaneous changes in percent market share and changes in percent
market growth rate changes total FCF over years 1-5.