Question

HomeLife Life Insurance Company has two service departments (actuarial and premium rating) and two production departments (advertising and sales). The distribution of each service department’s efforts (in percentages) to the other departments is shown in the following table:

	To
From	Actuarial			Premium Rating			Advertising			Sales
Actuarial		—			80	%		10	%		10	%
Premium		20	%		—			20			60

The direct operating costs of the departments (including both variable and fixed costs) are:

Actuarial	$	89,000
Premium rating		24,000
Advertising		69,000
Sales		49,000

Required:

1. Determine the total costs of the advertising and sales departments after using the direct method or allocation.

2. Determine the total costs of the advertising and sales departments after using the step method of allocation.

3. Determine the total costs of the advertising and sales departments after using the reciprocal method of allocation.

Answer 1

1) Direct method:

Department	Sum of the percentages	Weight	Weight
Advertising	Sales
Actuarial	10+10=20	10/20	10/20
Premium	20+60=80	20/80	60/80

Department	Advertising	sales	Actuarial	Premium
Allocated Overheads	69000	49000	89000	24000
Dept. Actuarial reallocation	44500	44500	-89000
Dept. Premium reallocation	6000	18000		-24000
Total	119500	111500

2) Step Method

Department	Advertising	sales	Actuarial	Premium
Allocated Overheads	69000	49000	89000	24000
Dept. Actuarial reallocation	8900	8900	-89000	71200
Dept. Premium reallocation	23800	71400		-95200
Total	101700	129300

Note: First the cost of the Actuarial department has been apportioned in the given percentage in question.

second, the total of the premium department has been apportioned in the ratio of 20: 60 to the production departments.

3) Reciprocal Method:

Equations for the allocation of service department costs

R = 24000 + 0.8A

A = 89000 + 0.2R

Where the variables A and R represent the total costs to allocate from each of these service departments

Solving the two equations we get

R = 24000 + 0.8(89000 + 0.2R)

0.84R = 95200

R = $113333

Therefore,

A = 89000 + 0.2*113333

A = $111667

Department	Advertising	sales	Actuarial	Premium
Allocated Overheads	69000	49000	89000	24000
Dept. Actuarial reallocation	11167	11167	-111667	89333
Dept. Premium reallocation	22667	68000	22667	-113333
Total	102834	128167