You just started a summer intership with the successful management consulting firm of Kirk, Spock, and McCoy. You first day on the job was a busy one, as the following problems were presented to you.

Question

FastQ Company, a specialist in printing, has established 500 convenience-copying centers throughout the country. In order to upgrade its services, the company is considering three new models of laser copying machines for use in producing high-quality copies. These high-quality copies would be added to the growing list of products offered in the FastQshops. The selling price to the customer for each laser copy would be the same, no matter which machine is installed in the shop. The three models of laser copying machines under consideration are 1024S, a small-volume model; 1024M, a medium-volume model; and 1024G, a large-volume mode. The annual rental cost oand the operating cost vary with the size of each machine. The machine capacities and costs are as follows:

Copier Model
1024S 1024M 1024G
Annual capacity (copies) 100,000 350,000 800,000
Costs:
Annual machine rental $ 8,000.00 $11,000.00 $20,000.00
Direct material and direct labor 0.02 0.02 0.02
Variable overhead costs 0.12 0.07 0.03

a. Calculate the volume level in copies where FastQ Company would be indifferent to acquiring either the small-volume model laser copier, 1024S, or the medium-volume model laser copier, 1024M.

b. The management of FastQ Company is able to estimate the number of copies to be sold at each establishment. Present a decision rule that would enable FASTQ Company to select the most profitable machine without having to make a separate cost calculation for each establishment. (Hint: To specify a decision rule, determine the volume at which FastQ would be indifferent between the small and medium copiers. Then determine the volume at which FastQ would be indifferent between the medium and large copiers).

Answer 1

a. To calculate the volume level in copies where FastQ Company would be indifferent to acquiring either the small-volume model laser copier, 1024S, or the medium-volume model laser copier, 1024M, we need to compare the costs of using each machine.

The total cost of using the small-volume model 1024S is the sum of the annual machine rental cost, direct material and direct labor cost, and variable overhead costs.
Total cost of 1024S = Annual machine rental + Direct material and direct labor + Variable overhead costs
= $8,000 + ($0.02 * Volume) + ($0.12 * Volume)
= $8,000 + $0.14 * Volume

Similarly, the total cost of using the medium-volume model 1024M is:
Total cost of 1024M = Annual machine rental + Direct material and direct labor + Variable overhead costs
= $11,000 + ($0.02 * Volume) + ($0.07 * Volume)
= $11,000 + $0.09 * Volume

To find the volume level where FastQ Company would be indifferent to acquiring either 1024S or 1024M, we need to set the total costs of both machines equal and solve for Volume:
$8,000 + $0.14 * Volume = $11,000 + $0.09 * Volume

Simplifying the equation, we get:
$0.14 * Volume - $0.09 * Volume = $11,000 - $8,000
$0.05 * Volume = $3,000
Volume = $3,000 / $0.05
Volume = 60,000 copies

Therefore, FastQ Company would be indifferent to acquiring either the small-volume model laser copier, 1024S, or the medium-volume model laser copier, 1024M, when the volume of copies produced is 60,000.

b. To select the most profitable machine without making a separate cost calculation for each establishment, FastQ Company can use the following decision rule:

1. Determine the volume at which FastQ Company would be indifferent between the small and medium copiers (previously calculated as 60,000 copies).
2. Determine the volume at which FastQ Company would be indifferent between the medium and large copiers.
3. If the estimated number of copies to be sold at an establishment is less than the volume at which FastQ Company is indifferent between the small and medium copiers (60,000), select the small-volume model 1024S.
4. If the estimated number of copies to be sold at an establishment is greater than or equal to the volume at which FastQ Company is indifferent between the small and medium copiers (60,000), but less than the volume at which FastQ Company is indifferent between the medium and large copiers, select the medium-volume model 1024M.
5. If the estimated number of copies to be sold at an establishment is greater than or equal to the volume at which FastQ Company is indifferent between the medium and large copiers, select the large-volume model 1024G.

By following this decision rule, FastQ Company can select the most profitable machine without having to make a separate cost calculation for each establishment.