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 16 people, and the Assembly Department employs 77 people. Each person in these two departments works 2,020 hours per year. The production-related overhead costs for the Molding Department are budgeted at $198,000, and the Assembly Department costs are budgeted at $83,000. Two support departments—Engineering and General Factory—directly support the two production departments and have budgeted costs of $208,000 and $393,000, 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	2,300	7,700
Square feet	98,240	—	417,520	98,240

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)

The reciprocal allocation method is preferred because it recognizes that all support departments serve one another.

Feedback

1. Overhead rate is computed by adding the allocated service costs to the overhead costs that are directly traceable to the producing department and dividing this total by some measure of activity, such as direct labor hours or machine hours.

2. The reciprocal method, as well as direct and sequential methods, allocates all support department costs to the producing departments.

3. Consider the various methods and why you might prefer one versus another.

Answer 1

Solution 1

Statement showing Secondary Distribution
Particulars			Production Department
Service Department	Basis of Allocation	Total	Molding Department	Assembly Department
Engineering Dept	Engineering hours: 2300:7700	$208,000	47840	160160
General Factory Dept	Square feet: 417520:98240	$393,000	318142.86	74857.14
Total Allocated Overheads			365982.86	235017.14
			Production Department
			Molding Department	Assembly Department
Budgeted Production Overheads			198000	83000
Allocated Service Dept Overheads			365982.86	235017.14
Total Overheads			563982.86	318017.14
Direct Labour Hours			16*2020	77*2020
			32320	155540
Overhead Rate per direct labour hour in $			563982.86/32320	318017.14/155540
			17.45	2.04

Solution 2:

		Production Dept		Service Dept
		Molding Department	Assembly Department	Engineering Dept	General Factory Dept
Service Dept
Engineering Dept		(2300/12000)*100	(7700/12000)*100		(2000/12000)*100
		19.17%	64.17%		16.66%
General Factory Dept		(417520/614000)*100	(98240/614000)*100	(98240/614000)*100
		68.00%	16.00%	16.00%

Let A = Total Overhead of Engineering Dept.

Let B = Total Overhead of General factory Dept.

A = 208000 + 16% of B

= 208000 + 0.16B

B = 393000 + 16.66% of A

B = 393000 + 16.66/100 * (208000+.16B)

B = 393000 + 34652.80 + .026656 B

B - 0.026656 B = 427652.80

.973344 B = 427652.80

B = 427652.80/0.973344

B = 439364.50

Now, A = 208000 + 16% of B

= 208000 + (0.16 * 439364.50)

= 208000 + 70298.32

= 278298.32

Statement showing Secondary Distribution
Particulars			Production Department
Service Department	Basis of Allocation	Total	Molding Department	Assembly Department
As per Primary Distribution		$281,000	198000	83000
Engineering Dept (83.34% of $ 278298.32)	2300:7700	$231,928.82	$53,343.63	$178,585.19
General Factory Dept (84% of $ 439364.50)	Square feet: 417520:98240	$369,066.18	298767.86	70298.32
Total Allocated Overheads			352111.49	248883.51
Direct Labour Hours			16*2020	77*2020
			32320	155540
Overhead Rate per direct labour hour in $			352111.49/32320	248883.51/155540
			$10.89	$1.60

Solution 3

	Production Department
	Molding Department	Assembly Department
Total Overheads under Direct Method	$                  563,982.86	$                     318,017.14
Total Overheads under Reciprocal Method	$                  352,111.49	$                     248,883.51
Difference	$                  211,871.37	$                        69,133.63

	Production Department
	Molding Department	Assembly Department
Overhead rate under Direct Method	$                             17.45	$                                  2.04
Overhead rate under Reciprocal Method	$                             10.89	$                                  1.60
Difference	$                               6.56	$                                  0.44

The reciprocal method is the most accurate for allocating service dept costs, because it recognizes reciprocal services among service depts.