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	$	80,000
Premium rating		15,000
Advertising		60,000
Sales		40,000

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

Answer:

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

	Total Cost Allocated
Advertising department	$103,750
Sales department	$91,250

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

	Total Cost Allocated
Advertising department	$87,750
Sales department	$107,250

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

	Total Cost Allocated
Advertising department	88,690
Sales department	106,310

Calculation:

1.

Here we need to determine the total costs of the advertising and sales departments after using the direct method or allocation.

First we need to find the net service provided to both production departments that is Advertising and Sales for the actuarial service dept.

So,

100% − 80% = 20%

Advertising department share: 10%/20% = 50%

Sales department share: 10%/20% = 50%

Then we need to find the net service provided to both production departments for premium department:

100% − 20% = 80%

Advertising department share: 20%/80% = 25%

Sales department share: 60%/80% = 75%

So the cost allocation will be :

Actuarial department cost allocation:

Advertising Department = 80,000 x 50% = 40,000

Sales Department = 80,000 x 50% = 40,000

Premium department cost allocation:

Advertising Department = 15,000 x 25% = 3,750

Sales Department = 15,000 x 75% = 11,250

Then we need to add the Initial production dept. costs to each department to get the Total cost for each production dept.

	Advertising Department	Sales Department
Actuarial department cost allocation	40,000	40,000
Premium department cost allocation	3,750	11,250
Add: Initial production dept. costs	60,000	40,000
Total cost for each production dept.	103,750	91,250

2.

Here we need to determine the total costs of the advertising and sales departments after using the step method of allocation

In this method, the actuarial department will go first, as it provides the highes t service to other service departments.

Allocation of actuarial dept:

Premium Department = $80,000 × 0.80 = $64,000

Advertising department = $80,000 × 0.10 = $8,000

Sales Dept = $80,000 × 0.10 = $8,000

Allocation of premium dept:

Advertising department = ($64,000 + 15000) × 0.25 = $19,750

Sales Dept = ($64,000 + 15000) × 0.75 = $59,250

Then we need to add the Initial production dept. costs to each department to get the Total cost for each production dept.

	Premium Dept.	Advertising Dept	Sales Dept.
Allocation of actuarial dept.	64000	8000	8000
Allocation of premium dept.		19750	59250
Add: Initial production dept. costs		$60,000	$40,000
Total cost for each production department		$87,750	$107,250

3.

Here we need to determine the total costs of the advertising and sales departments after using the reciprocal method of allocation.

In the reciprocal method, we need to solve the Simultaneous Equations:

So let S1 = Actuarial and S2 = Premium

S1 = 80,000 + (0.20 x S2)

S2 = 15,000 + (0.80 x S1)

S1 = (80,000 + (0.20 x (15,000 + 0.80 x S1))

0.16 S1 = 83,000

S1 = 98,810

S2 = 15,000 + (0.80 x 98,810)

S2 = 94,048

Allocation of actuarial dept:

Premium Department = $98,810 × 0.10 = $9,880.95

Advertising department = $98,810 × 0.10 = $9,880.95

Allocation of premium dept:

Advertising department = 94,048 × 0.20 = $19,750

Sales Dept = 94,048 × 0.60 = $56,428.57

Then we need to add the Initial production dept. costs to each department to get the Total cost for each production dept.

	Adv. Department	Sales Department
Actuarial department cost allocation	9,880.95	9,880.95
Premium department cost allocation	18,809.52	56,428.57
Add: Initial production dept. costs	$60,000	$40,000
Total cost for each production dept.	88,690.48	106,309.52