17 Service Department Allocation

The Theory

An important use of cost allocation is to assign shares of service department costs to operating departments. Operating departments are revenue-producing departments, while service departments provide services to support both operating departments and other service departments. Examples of service departments include Accounting, Human Resources, Maintenance, and Technology Support.

The costs of service departments are allocated to operating departments so that the managers of revenue-generating departments are made aware of the costs their departments are responsible for covering. To allocate these costs, a cost allocation base is chosen for each service department. When allocating service department costs, the fact that service departments serve each other can be ignored (direct method), fully recognized (reciprocal method), or partially recognized (step-down method). The direct method is the simplest but least accurate, and the reciprocal method is the most accurate but quite complicated. The step-down method represents a compromise between the direct and reciprocal methods in terms of both accuracy and complexity.

The Method

First, set up a chart to use for performing the allocations similar to the following:

Item	Service 1	Service 2	Operating 1	Operating 2	Total
Initial Cost	X	X	X	X	X
Service 1	X	X	X	X	X
Service 2	X	X	X	X	X
Total	X	X	X	X	X

In the columns, list service departments before operating departments, and if the step-down method is used, list service departments in the order they will be allocated, which will help keep the allocation order clear. Rows should contain the initial cost of each service department, then the service departments in the same order they appeared in the columns. Each service department row will contain an allocation from that service department to the other departments. Determine what fraction of costs allocated out of each service department goes to each department allocated, and place that fraction in (part of) the appropriate cell in the chart. The numerator of each fraction should be the amount of cost allocation base used by each department receiving allocations. The denominator should be the total amount of cost allocation base used by all departments receiving allocations.

• Direct method: Only operating departments receive allocations
• Step-down method: All departments not yet allocated receive allocations
• Reciprocal method: All departments except the one being allocated receive allocations

Next, for the reciprocal method only, determine the amount allocated out of each department. This will need to be done algebraically, by forming equations for each department and solving them as a system of equations. The easiest way to express the equations is to read down each service department column. For example, to find the amount allocated out of Service 1, you’d read down the column to see that it’s the initial cost from that column, plus the fraction allocated from Service 2 from that column multiplied by the amount allocated out of Service 2 (see the Illustrative Example for a more practical walkthrough).

Next, allocate costs from the first service department. Subtract the amount allocated out in that service department’s column. For the reciprocal method, this will be the amount you calculated in the previous step. For the direct and step-down methods, this will be the initial cost of the department before allocations. Multiply the amount allocated out by the fraction in each cell, then place the result on the chart. In the total column, add the amount allocated to each department and subtract the amount allocated out of the service department. The total should equal zero.

Next, allocate costs from subsequent service departments. Follow the same procedure as for the first service department, except that for the step-down method, the amount allocated out should equal the initial cost of the department plus any costs allocated from other service departments.

Finally, after all service department costs have been allocated, find the total amount allocated to each operating department. Also total the other columns, and verify that the service department columns total zero and that the total of the Total row equals the total of the Total column.

Illustrative Example

Mufen, Inc. has three service departments (Accounting, Maintenance, and Tech Support) and two operating departments (Production A and Production B). Mufen allocates Accounting costs based on the number of employees in each department, Maintenance costs based on the square footage in each department, and Tech Support costs on the basis of tech support hours used. Initial costs and cost driver usage are as follows:

Item	Accounting	Maintenance	Tech Support	Prod. A	Prod. B
Initial cost	$ 140,000	$ 180,000	$ 350,000	0	0
Employees	12	6	14	60	80
Square feet	2,000	1,500	5,000	20,000	25,000
Tech Support Hours	100	50	50	2,000	1,500

Allocate the service department costs to the operating departments using first the direct method, then using the step-down method with departments allocated in the order listed, then using the reciprocal method.

Direct Method

First, set up the chart, including initial costs and fractions:

Item	Accounting	Maintenance	Tech Suppt.	Prod. A	Prod. B	Total
Initial Cost	$140,000	$180,000	$350,000			$670,000
Accounting				⁶⁄₁₄	⁸⁄₁₄
Maintenance				20000⁄45000	25000⁄45000
Tech Suppt.				2000⁄3500	1500⁄3500  [
Total

Feel free to simplify fractions.

Next, allocate costs from the first service department:

• $140,000 will be allocated out of Accounting
  • Production A receives $140,000 × 6/14 = $60,000
  • Production B receives $140,000 × 8/14 = $80,000

Item	Accounting	Maintenance	Tech Suppt.	Prod. A	Prod. B	Total
Initial Cost	$140,000	$180,000	$350,000			$670,000
Accounting	(140,000)			⁶⁄₁₄ $60,000	⁸⁄₁₄ $80,000	0
Maintenance				20000⁄45000	25000⁄45000
Tech Suppt.				2000⁄3500	1500⁄3500
Total

Next, allocate costs from subsequent service departments:

• $180,000 will be allocated out of Maintenance
  • Production A receives $180,000 × 20,000/45,000 = $80,000
  • Production B receives $180,000 × 25,000/45,000 = $100,000
• $350,000 will be allocated out of Tech Support
  • Production A receives $350,000 × 2,000/3,500 = $200,000
  • Production B receives $350,000 × 1,500/3,500 = $150,000

Item	Accounting	Maintenance	Tech Suppt.	Prod. A	Prod. B	Total
Initial Cost	$140,000	$180,000	$350,000			$670,000
Accounting	(140,000)			⁶⁄₁₄ $60,000	⁸⁄₁₄ $80,000	0
Maintenance		(180,000)		20000⁄45000 $80,000	25000⁄45000 $100,000	0
Tech Suppt.			(350,000)	2000⁄3500 $200,000	1500⁄3500 $150,000	0
Total

Finally, find the total amount allocated to each operating department, and verify that the service department columns total zero and that the total in the Total row equals the total in the Total column:

Item	Accounting	Maintenance	Tech Suppt.	Prod. A	Prod. B	Total
Initial Cost	$140,000	$180,000	$350,000			$670,000
Accounting	(140,000)			⁶⁄₁₄ $60,000	⁸⁄₁₄ $80,000	0
Maintenance		(180,000)		20000⁄45000 $80,000	25000⁄45000 $100,000	0
Tech Suppt.			(350,000)	2000⁄3500 $200,000	1500⁄3500 $150,000	0
Total	$ 0	$ 0	$ 0	$340,000	$330,000	$670,000

 

Step-Down Method

First, set up the chart, including initial costs and fractions:

• Accounting will be allocated to Maintenance, Tech Support, and operating departments
• Maintenance will be allocated to Tech Support and operating departments
• Tech Support will be allocated only to operating departments

Item	Accounting	Maintenance	Tech Suppt.	Prod. A	Prod. B	Total
Initial Cost	$140,000	$180,000	$350,000			$670,000
Accounting		6⁄160	14⁄160	60⁄160	80⁄160
Maintenance			5000⁄50000	20000⁄50000	25000⁄50000
Tech Suppt.				2000⁄3500	1500⁄3500
Total

Feel free to simplify fractions.

Next, allocate costs from the first service department:

• $140,000 will be allocated out of Accounting
  • Maintenance receives $140,000 × 6 / 160 = $5,250
  • Tech Support receives $140,000 × 14 / 160 = $12,250
  • Production A receives $140,000 × 60 / 160 = $52,500
  • Production B receives $140,000 × 80 / 160 = $70,000

Item	Accounting	Maintenance	Tech Suppt.	Prod. A	Prod. B	Total
Initial Cost	$140,000	$180,000	$350,000			$670,000
Accounting	(140,000)	6⁄160 $5,250	14⁄160 $12,250	60⁄160 $52,500	80⁄160 $70,000	0
Maintenance			5000⁄50000	20000⁄50000	25000⁄50000
Tech Suppt.				2000⁄3500  [	1500⁄3500
Total

Next, allocate costs from subsequent service departments:

• $180,000 + $5,250 = $185,250 will be allocated out of Maintenance
  • Tech Support receives $185,250 × 5,000 / 50,000 = $18,525
  • Production A receives $185,250 × 20,000 / 50,000 = $74,100
  • Production B receives $185,250 × 25,000 / 50,000 = $92,625
• $350,000 + $12,250 + $18,525 = $380,775 will be allocated out of Tech Support
  • Production A receives $380,775 × 2,000 / 3,500 = $217,585.71
  • Production B receives $380,775 × 1,500 / 3,500 = $163,189.29

Item	Accounting	Maintenance	Tech Suppt.	Prod. A	Prod. B	Total
Initial Cost	$140,000	$180,000	$350,000			$670,000
Accounting	(140,000)	6⁄160 $5,250	14⁄160 $12,250	60⁄160 $52,500	80⁄160 $70,000	0
Maintenance		(185,250)	5000⁄50000 18,525	20000⁄50000 74,100	25000⁄50000 92,625	0
Tech Suppt.			(380,775)	2000⁄3500 217,585.71	1500⁄3500 163,189.29	0
Total

Finally, find the total amount allocated to each operating department, and verify that the service department columns total zero and that the total in the Total row equals the total in the Total column:

Item	Accounting	Maintenance	Tech Suppt.	Prod. A	Prod. B	Total
Initial Cost	$140,000	$180,000	$350,000			$670,000
Accounting	(140,000)	6⁄160 $5,250	14⁄160 $12,250	60⁄160 $52,500	80⁄160 $70,000	0
Maintenance		(185,250)	5000⁄50000 18,525	20000⁄50000 74,100	25000⁄50000 92,625	0
Tech Suppt.			(380,775)	2000⁄3500 217,585.71	1500⁄3500 163,189.29	0
Total	0	0	0	$344,185.71	$325,814.29	$670,000

Reciprocal Method

First, set up the chart, including initial costs and fractions. All service department costs will be allocated to all other departments.

Item	Accounting	Maintenance	Tech Suppt.	Prod. A	Prod. B	Total
Initial Cost	$140,000	$180,000	$350,000			$670,000
Accounting		6⁄160	14⁄160	60⁄160	80⁄160
Maintenance	2000⁄52000		5000⁄52000	20000⁄52000	25000⁄52000
Tech Suppt.	100⁄3650	50⁄3650		2000⁄3650	1500⁄3650
Total

Notice that extra zeroes have been dropped from each fraction, as both the numerator and denominator will contain those zeroes.

Next, determine the amount allocated out of each service department. Formulate an equation for each department by reading down its column. The total cost for that column will equal its initial cost plus the fraction of each department from which it receives allocations times that department’s total cost. Representing Accounting costs as A, Maintenance costs as M, and Tech Support costs as T, the equations would be as follows:

• A = $140,000 + 2,000 / 52,000 x M + 100 / 3,650 x T
• M = $180,000 + 6 / 160 x A + 50 / 3,650 x T
• T = $350,000 + 14 / 160 x A + 5,000 / 52,000 x M

Then solve this system of equations, which yields the following results:

• A = $157,823.02
• M = $191,153.84
• T = $382,189.69

Next, allocate costs from the first service department:

• $157,823.02 will be allocated out of Accounting
  • Maintenance receives $157,823.02 × 6 / 160 = $5,918.36
  • Tech Support receives $157,823.02 × 14 / 160 = $13,809.51
  • Production A receives $157,823.02 × 60 / 160 = $59,183.63
  • Production B receives $157,823.02 × 80 / 160 = $78,911.51

Item	Accounting	Maintenance	Tech Suppt.	Prod. A	Prod. B	Total
Initial Cost	$140,000.00	$180,000.00	$350,000.00			$670,000.00
Accounting	(157,823.02)	6⁄160 5,918.36	14⁄160 13,809.51	60⁄160 $ 59,183.63	80⁄160 $ 78,911.51	0
Maintenance	2000⁄52000		5000⁄52000	20000⁄52000	25000⁄52000
Tech Suppt.	100⁄3650	50⁄3650		2000⁄3650	1500⁄3650
Total

Next, allocate costs from subsequent service departments:

• $191,153.84 will be allocated out of Maintenance
  • Accounting receives $191,153.84 × 2,000 / 52,000 = $7,352.07
  • Tech Support receives $191,153.84 × 5,000 / 52,000 = $18,380.18
  • Production A receives $191,153.84 × 20,000 / 52,000 = $73,520.71
  • Production B receives $191,153.84 × 25,000 / 52,000 = $91,900.88
• $382,189.69 will be allocated out of Tech Support
  • Accounting receives $382,189.69 × 100 / 3,650 = $10,470.95
  • Maintenance receives $382,189.69 × 50 / 3,650 = $5,235.48
  • Production A receives $382,189.69 × 2,000 / 3,650 = $209,419.01
  • Production B receives $382,189.69 × 1,500 / 3,650 = $157,064.26

Total
Item	Accounting	Maintenance	Tech Suppt.	Prod. A	Prod. B	Total
Initial Cost	$140,000.00	$180,000.00	$350,000.00			$670,000.00
Accounting	(157,823.02)	6⁄160 5,918.36	14⁄160 13,809.51	60⁄160 $ 59,183.63	80⁄160 $ 78,911.51	0
Maintenance	2000⁄52000 7,352.07	(191,153.84)	5000⁄52000 18,380.18	20000⁄52000 73,520.71	25000⁄52000 91,900.88	0
Tech Suppt.	100⁄3650 10,470.95	50⁄3650 5,235.48	(382,189.69)	2000⁄3650 209,419.01	1500⁄3650 157,064.26	0

Finally, find the total amount allocated to each operating department, and verify that the service department columns total zero and that the total in the Total row equals the total in the Total column:

Total	$ 0	$ 0	$ 0	$342,123.35	$327,876.65	$670,000
Item	Accounting	Maintenance	Tech Suppt.	Prod. A	Prod. B	Total
Initial Cost	$140,000.00	$180,000.00	$350,000.00			$670,000
Accounting	(157,823.02)	6⁄160 5,918.36	14⁄160 13,809.51	60⁄160 $ 59,183.63	80⁄160 $ 78,911.51	0
Maintenance	2000⁄52000 7,352.07	(191,153.84)	5000⁄52000 18,380.18	20000⁄52000 73,520.71	25000⁄52000 91,900.88	0
Tech Suppt.	100⁄3650 10,470.95	50⁄3650 5,235.48	(382,189.69)	2000⁄3650 209,419.01	1500⁄3650 157,064.26	0

Lecture Examples