Question

LV2-a Company has used a two-stage, reciprocal method
cost allocation system for many years. In the first
stage, overhead costs from its two service departments
(repair and administration) are allocated to its two
production departments (molding and assembly) based
on the following activity levels:

   repair - repair hours

   administration - # of employees

In the second stage, LV2-a calculates pre-determined
overhead rates in the production departments using
the following activity levels:

   molding - machine hours

   assembly - direct labor hours

The following information is available for the four
departments:

                              Repair          Admin
Directly traced overhead      $70,000       $107,000 
Repair hours                   20,000         14,000
Number of employees              30             15

                              Molding        Assembly
Directly traced overhead     $234,000       $178,000  
Repair hours                    4,000          2,000
Number of employees              24              6 
Direct labor hours             12,000         20,000
Machine hours                  40,000          5,000

Calculate the pre-determined overhead rate used in the
assembly department.

Answer 1

Step 1

Tabulate the data given

                                                SERVICE DEPARTMENT                           PRODUCTION DEPARTMENT

	repair	administration	molding	Assembly
Cost	70000	107000	234000	178000
Repair hours used	20000	14000	4000	2000
Number of employees	30	15	24	6

STEP 2:

Determine the allocation bases

Note: exclude cost of the department you are trying to allocate

                                         REPAIR DEPARTMENT                                    ADMINISTRATION DEPARTMENT

	Repair hours	% of total	employees	% of total
Repair	-	-	30	50%
Administration	14000	70%	-	-
Molding	4000	20%	24	40%
Assembly	2000	10%	6	10%
total	20000	100%	60	100%

STEP 3:

Set up the formulas

(a) Total repair cost = repair department cost + cost allocated to repair from administration.

(b) Total Administration cost = Administration department cost + cost allocated to administration from repair.

We will work with the administration cost formula in (b) first:

Total Administration cost = Administration department cost + cost allocated to administration from repair.

we know the cost allocation to administration from repair is (70% x total repair cost). We still do not know what total repair cost but we can plug in this new formula.

Total admin. Cost = 107000 + 0.7 x total repair cost

Insert formula a to b: Total admin. Cost = 107000 + 0.7 x (repair department cost + cost allocated to repair from administration.)

Total administration cost(A) = 107000 + 0.7x(70000) + (0.5xtotal administration cost(A))

A= 107000+49000+ 0.5A

A= 156000+0.5A

A-0.5A= 156000

0.5A=156000

A= 156000/0.5

A( total administration cost) = 312000

Total repair cost = repair department cost + cost allocated to repair from administration.

70000 + 0.5x312000

=226000

step 4:

Show cost allocations

	repair	admin	molding	Assembly
Cost	70000	107000	234000	178000
Repair cost -allocated	-226000	158200	45200	22600
		226000x70%	226000x20%	226000x10%
Admin cost allocated	156000	-312000	124800	31200
	3210000x50%		312000x40%	312000x10%
Total cost				231800

therefoe total predetermined OH cost to assembly using 1stage= 231800

using second stage allocation:

pre determined OH rate to assembly = 178000/20000 =8.9 per direct labor hour