HomeLife Life Insurance Company has two service departments (actuarial and premi
ID: 366897 • Letter: H
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
1. Determine the total cost allocated to the advertising and sales departments using the direct method.
2. Determine the total cost allocated to advertising and sales using the step method.
3. Determine the total cost allocated to advertising and sales using the reciprocal method. (Round your intermediate calculations to the nearest whole dollar and final answers to 2 decimal places.)
To
From Actuarial Premium Rating Advertising Sales Actuarial — 80 % 10 % 10 % Premium 25 % — 15 60Explanation / Answer
Total cost allocated to Advertising and Sales department using:
1. Direct method:
Actuarial % to advertising = 10% and sales = 10%, total = 20%
Actuarial % to advertising = 10/20*100 = 50% and sales = 10/20*100 = 50%, total = 100% (ignoring 80% to Premium Rating)
Actuarial cost to advertising = 50%*82,000 = 41,000
Actuarial cost to sales = 50%*82,000 = 41,000
Premium % to advertising = 15% and sales = 60%, total = 75%
Premium % to advertising = 15/75*100 = 20% and sales = 60/75*100 = 80%, total = 100% (ignoring 25% to Actuarial)
Premium cost to advertising = 20%*17,000 = 3,400
Premium cost to sales = 80%*17,000 = 13,600
Total cost allocated to Advertising = 41,000 + 3,400 = 44,400
Total cost allocated to Sales = 41,000 + 13,600 = 54,600
2. Step method:
Actuarial % to advertising = 10% and sales = 10%, total = 20%
Actuarial cost to advertising = 10%*82,000 = 8,200
Actuarial cost to sales = 10%*82,000 = 8,200
Premium % to advertising = 15% and sales = 60%, total = 75%
Premium cost to advertising = 15%*17,000 = 2,550
Premium cost to sales = 60%*17,000 = 10,200
Total cost allocated to Advertising = 8,200 + 2,550 = 10,750
Total cost allocated to Sales = 8,200 + 10,200 = 18,400
3. Reciprocal method:
Let total Actuarial cost = A and total Premium Rating cost = PR
As per question, Direct actuarial cost = 82,000 and direct premium cost = 17,000
Premuim Rating cost allocated to Actuarial = 80% and Actuarial cost allocated to Premium = 25%
A = 82,000 + 80%*PR
PR = 17,000 + 25%*A
Substitute PR into A, we get
A = 82,000 + 80%*(17,000+25%A)
A - 80%*25%*A = 82,000+80%*17,000
0.8A = 95,600
A = 95,600 / 0.8 = 119,500
PR = 17,000 + 25%*A = 17,000 + 0.25 * 119,500 = 17,000 + 29,875 = 46,875
So, total Actuarial cost = 119,500 and total Premium cost = 46,875
(Same as Step method using new costs calculated)
Actuarial % to advertising = 10% and sales = 10%, total = 20%
Actuarial cost to advertising = 10%*119,500 = 11,950
Actuarial cost to sales = 10%*119,500 = 11,950
Premium % to advertising = 15% and sales = 60%, total = 75%
Premium cost to advertising = 15%*46,875 = 7,031.25
Premium cost to sales = 60%*46,875 = 28,125
Total cost allocated to Advertising = 11,950 + 7,031.25 = 18,981.25
Total cost allocated to Sales = 11,950 + 28,125 = 40,075
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