Question

Jake's Battery Company has two service departments, Maintenance and Personnel. Maintenance Department costs of $300,000 are allocated on the basis of budgeted machine-hours. Personnel Department costs of $100,000 are allocated based on the number of employees. The costs of operating departments A and B are $160,000 and $240,000, respectively. Data on budgeted maintenance-hours and number of employees are as follows:

	Support Departments		Production Departments
	Maintenance Department	Personnel Department	A	B
Budgeted costs	$300,000	$100,000	$160,000	$240,000
Budgeted maintenance-hours	NA	800	1,200	600
Number of employees	50	NA	200	600

a. Using the direct method, what amount of Maintenance Department costs will be allocated to Departments A and B, respectively? (Round up)

b. Using the step-down method, what amount of Maintenance Department costs will be allocated to Departments A and B, respectively if the service department with the highest percentage of interdepartmental support service is allocated first? (Round up)

c. Using the reciprocal method, what amount of Maintenance Department costs will be allocated to Departments A and B, respectively? (Round up)

*Asker notes* I am mostly confused on how to attain the percentages, especially the percentages for the cost of the personnel department to the maintenance department based on number of employees and the percent off budgeted-maintenance hours to the personnel department, especially because you need the percentages of these items in order to solve the reciprocal method with a linear equation.

Answer 1

a) Allocation of support department cost using the direct method (Amounts in $)

	To
From	Maintenance	Personnel	A	B
Budgeted Costs	300,000	100,000	160,000	240,000
Maintenance Department (in the ratio of 12:6)	(300,000)	-	200,000 (300,000*12/18)	100,000 (300,000*6/18)
Personnel Department (in the ratio of 2:6)	-	(100,000)	25,000 (100,000*2/8)	75,000 (100,000*6/8)
Totals	0	0	385,000	415,000

Therefore $200,000 of maintenance department will be allocated to Department A and $100,000 will be allocated to Department B.

b) As u can see in requirement c, the highest percentage of interdepartmental support service is 30.76923% which is of Maintenance department (i.e. X). Therefore the cost of maintenance department will be allocated first.

Allocation of support department cost using the step down method (Amounts in $)

	To
From	Maintenance	Personnel	A	B
Budgeted Costs	300,000	100,000	160,000	240,000
Maintenance Department (in the ratio of 12:6)	(300,000)	92,308 (300,000*8/26)	138,461 (300,000*12/26)	69,231 (300,000*6/26)
Personnel Department (in the ratio of 2:6)	-	(192,308)	48,077 (192,308*2/8)	144,231 (192,308*6/8)
Totals	0	0	346,538	453,462

Therefore $138,461 of maintenance department will be allocated to Department A and $69,231 will be allocated to Department B.

c) Let total cost of Maintenance department = X and total cost of Personnel department = Y

X = 300,000+(50/850)*Y [850 = 50+200+600]

X = 300,000+Y*5.88235% - Equation 1 (Percentage = 50/850*100 = 5.88235%)

Y = 100,000+X*30.76923% - Equation 2   (Percentage = 8/26*100 = 30.76923%)

Now put the value of Y (i.e. Equation 2) in Equation 1.

X = 300,000+[(100,000+X*30.76923%)*5.88235%]

X = 300,000+[(100,000*5.88235%)+(X*30.76923%*5.88235%)]

X = 300,000+5882.35+X*0.0180995)

X - X*0.0180995 = 300,000+5882.35

0.9819005 X = 305,882.35

X = 305,882.35/0.9819005 = $311,521

Y = 100,000+X*(30.76923%)

Y = 100,000+(311,521*30.76923%) = $195,853

Allocation of support department cost using the step down method (Amounts in $)

	To
From	Maintenance	Personnel	A	B
Budgeted Costs	300,000	100,000	160,000	240,000
Maintenance Department (in the ratio of 12:6)	(311,521)	95,853 (311,521*8/26)	143,779 (311,521*12/26)	71,889 (311,521*6/26)
Personnel Department (in the ratio of 2:6)	11,521 (195,853*50/850)	(195,853)	46,083 (195,853*200/850)	138,249 (195,853*600/850)
Totals	0	0	349,862	450,138