Question

Direct Method, Reciprocal Method, Overhead Rates

Macalister Corporation is developing departmental overhead rates based on direct labor hours for its two production departments—Molding and Assembly. The Molding Department employs 20 people, and the Assembly Department employs 80 people. Each person in these two departments works 2,000 hours per year. The production-related overhead costs for the Molding Department are budgeted at $190,000, and the Assembly Department costs are budgeted at $80,000. Two support departments—Engineering and General Factory—directly support the two production departments and have budgeted costs of $216,000 and $370,000, respectively. The production departments’ overhead rates cannot be determined until the support departments’ costs are properly allocated. The following schedule reflects the use of the Engineering Department’s and General Factory Department’s output by the various departments.

	Engineering	General Factory	Molding	Assembly
Engineering hours	—	2,000	2,000	8,000
Square feet	120,000	—	420,000	60,000

For all requirements, round allocation ratios to four significant digits and round allocated costs to the nearest dollar.

Required:

1. Calculate the overhead rates per direct labor hour for the Molding Department and the Assembly Department using the direct allocation method to charge the production departments for support department costs. Round final answers to the nearest cent.

	Overhead rate per DLH
Molding	$
Assembly	$

2. Calculate the overhead rates per direct labor hour for the Molding Department and the Assembly Department using the reciprocal method to charge support department costs to each other and to the production departments. Round final answers to the nearest cent. Round your intermediate calculations to four decimal places.

	Overhead rate per DLH
Molding	$
Assembly	$

3. Explain the difference between the methods, and indicate the arguments generally presented to support the reciprocal method over the direct allocation method. (CMA adapted)

Answer 1

Solution.

1.                                                                                         General

                                                                 Engineering        Factory         Molding        Assembly

Department costs.........................      $   216,000      $   370,000        $190,000      $    80,000

Allocation of:

  Engineering (0.2, 0.8)................         (216,000)                     0            43,200          172,800

  Gen. Factory (0.875, 0.125)......                      0          (370,000)         323,750            46,250

Total overhead cost.....................      $              0      $              0        $556,950        $299,050

Direct labor hours........................                                                      ÷   40,000       ÷160,000

Overhead rate per DLH..............                                                      $      13.92      $        1.87

2.

                                                   Engineering         General Factory        Molding         Assembly

        Engineering hours..........                —                      0.1667                  0.1667            0.6667

        Square feet.....................          0.2000                             —                  0.7000            0.1000

        Algebraic equations for relationship between service departments

        (E = Engineering Department; GF = General Factory Department):

E = $216,000 + 0.2000GF

GF = $370,000 + 0.1667E

               E =  $216,000 + 0.2000($370,000 + 0.1667E)

               E =  $216,000 + $74,000 + 0.0333E

    0.9667E =  $290,000

               E =  $299,990

GF = $370,000 + 0.1667($299,990)

GF = $420,008

                                                                                    General

                                                               Engineering         Factory         Molding         Assembly

Direct overhead costs.............         $   216,000        $   370,000        $190,000       $    80,000

Allocation of:

   Engineering..........................            (299,990)             50,008            50,008           200,003

   General Factory....................                84,002            (420,008)         294,006            42,001

Total overhead cost.................         $            12        $              0        $534,014         $322,004

Direct labor hours...................                                                          ÷   40,000        ÷160,000

Overhead rate per DLH..........                                                          $      13.35       $       2.01

3.     The direct allocation method ignores any service rendered by one support department to another. Allocation of each support department’s total cost is made directly to the production departments. The reciprocal allocation method recognizes all support department support to one another through the use of simultaneous equations or linear algebra. This allocation procedure is more accurate and should lead to better results, which would be of greater value to management. However, the method is infrequently used in actual practice because of the problems associated with developing a more complex or difficult model to recognize the interrelationships between support departments.