Chapter 6 Class Problem and Solution
James R. Martin, Ph.D., CMA
Professor Emeritus, University of South Florida
Chapter 6 | MAAW's Textbook Table of Contents
Assume the Stage Company has two service departments and two producing departments in a small factory. The relevant data are provided below.
| Department | Direct Cost | Cost Allocation Basis |
Kilowatt hours used by each department |
Maintenance
hours used by each Department |
| Power (S1) | $500,000 | Kilowatt hours | 100 | 600 |
| Maintenance (S2) | 100,000 | Maintenance hours | 100 | 200 |
| Cutting (P1) | 400,000 | 800 | 1,000 | |
| Finishing (P2) | 200,000 | 400 | 600 | |
| Totals | $1,200,000 | 1,400 | 2,400 |
Note: Use S1, S2, P1 and P2 to represent the costs in your equations when the amounts would otherwise have to be calculated. If the dollar amounts are available, use the dollar amounts rather than the symbols.
1. Using the direct method, develop the equation for determining the total costs of the Cutting Department after all service department allocations and solve the equation.
2. Using the direct method, develop the equation for determining the total costs of the Finishing Department, after all service department allocations and solve the equation.
3. If the step-down method is used, which service department should be closed first? Explain why.
4. Now disregard your previous answer and assume that the Maintenance department is closed first. Based on this assumption, develop the equation for determining the total cost of the Maintenance department after all service department allocations to maintenance and solve the equation.
5. Again using the step-down method and assuming the Maintenance department is closed first, develop the equation for determining the total costs of the Power Department, after all service department allocations and solve the equation.
6. Using the step-down method and assuming the Maintenance department is closed first, develop the equation for determining the total costs of the Finishing Department, after all service department allocations and solve the equation.
7. Using the reciprocal method, determine the equation needed for calculating the total costs of the Power Department, after all service department allocations to the Power Department.
8. Using the reciprocal method, determine the equation needed to calculate the total costs of the Cutting Department, after all service department allocations.
9. Which stage I method or methods ignore some or all self services?
a. direct
b. step-down c. reciprocal
d. a and b
e. all of these.
10. Which stage I method or methods ignore some or all reciprocal services?
a. direct
b. step-down
c. reciprocal
d. a and b
e. all of these.
____________________________________________
Solution
A useful way to set up the problem is to rearrange the information in the table to reflect a From/To perspective as follows.
| From\To | Power (S1) |
Maintenance (S2) |
Cutting (P1) |
Finishing (P2) |
Total |
| Power (S1) | 100 KWH | 100 KWH | 800 KWH | 400 KWH | 1,400 KWH |
| Maintenance (S2) | 600 hrs | 200 hrs | 1,000 hrs | 600 hrs | 2,400 hrs |
1. Using the direct method, develop the equation for determining the total costs of the Cutting Department after all service department allocations and solve the equation.
Since we ignore the self services and reciprocal services, the relevant information for the direct method changes as indicated below. The denominators for the allocation proportions become 1,200 for Power and 1,600 for maintenance as indicated in the revised From\To table.
| From\To | Power (S1) |
Maintenance
(S2) |
Cutting (P1) |
Finishing (P2) |
Total |
| Power (S1) | Ignore | Ignore | 800 KWH | 400 KWH | 1,200 KWH |
| Maintenance (S2) | Ignore | Ignore | 1,000 hrs | 600 hrs | 1,600 hrs |
P1 = $400,000 + (800/1,200)($500,000) + (1,000/1600)($100,000) = 795,833.33
2. Using the direct method, develop the equation for determining the total costs of the Finishing Department, after all service department allocations and solve the equation.
P2 = $200,000 + (400/1,200)($500,000) + (600/1,600)($100,000) = 404,166.67
3. If the step-down method is used, which service department should be closed first? Explain why.
Maintenance if proportions are used since it provides 25% of its service to power while power provides only 7.1% of its service to maintenance.
Power if the dollar amounts are used since 7.1% of $500,000 is greater than 25% of $100,000.
4. Now disregard your previous answer and assume that the Maintenance department is closed first. Based on this assumption, develop the equation for determining the total cost of the Maintenance department after all service department allocations to maintenance.
The relevant information for the step-down method changes to include the 600 hours provided from maintenance to power. This causes the denominator for the maintenance allocation proportions to change to 2,200.
| From\To | Power (S1) |
Maintenance (S2) |
Cutting (P1) |
Finishing (P2) |
Total |
| Power (S1) | Ignore | Ignore | 800 KWH | 400 KWH | 1,200 KWH |
| Maintenance (S2) | 600 hrs | Ignore | 1,000 hrs | 600 hrs | 2,200 hrs |
Maintenance receives no allocations, therefore S2 = $100,000
5. Again using the step-down method and assuming the Maintenance department is closed first, develop the equation for determining the total costs of the Power Department, after all service department allocations.
S1 = $500,000 + (600/2,200)($100,000) = $527,273.73
6. Using the step-down method and assuming the Maintenance department is closed first, develop the equation for determining the total costs of the Finishing Department, after all service department allocations.
P2 = $200,000 + (400/1200)($527,273.73) + (600/2,200)($100,000)
7. Using the reciprocal method, determine the equation needed for calculating the total costs of the Power Department, after all service department allocations to the Power Department.
In the reciprocal method we consider all the relationships as in the original From\To table. Therefore the denominators for the allocation proportions become 1,400 for Power and 1,600 for Maintenance.
| From \ To | Power (S1) |
Maintenance (S2) |
Cutting (P1) |
Finishing (P2) |
Total |
| Power (S1) | 100 KWH | 100 KWH | 800 KWH | 400 KWH | 1,400 KWH |
| Maintenance (S2) | 600 hrs | 200 hrs | 1,000 hrs | 600 hrs | 2,400 hrs |
S1 = $500,000 + (100/1,400)(S1) + (600/2,400)(S2)
8. Using the reciprocal method, determine the equation needed to calculate the total costs of the Cutting Department, after all service department allocations.
P1 = $400,000 + (800/1,400)(S1) + (1,000/2,400)(S2)
9. Which stage I method or methods ignore some or all self services?
d. a and b
10. Which stage I method or methods ignore some or all reciprocal services?
d. a and b