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HomeLife Life Insurance Company has two service departments (actuarial and premium rating) and two production departments (ad

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HomeLife Insurance
Answer 1- Direct Method Actuarial Premium Advertising Sales Total
Actuarial 80.00% 10.00% 10.00% 100.00%
Actuarial % 50.0% 50.0% Service % to Premium will not be considered here.
Premium 25.00% 15.00% 60.00% 100.00%
Premium % 20.0% 80.0% Service % to Actuarial will not be considered here.
Department cost      87,000.00       22,000.00     67,000.00     47,000.00 223,000.00
Allocation
Actuarial     (87,000.00)      43,500.00      43,500.00                    -  
Premium      (22,000.00)        4,400.00      17,600.00                    -  
Total cost after allocation                     -                        -   114,900.00 108,100.00 223,000.00
Answer 2- Step Method Actuarial Premium Advertising Sales Total Actuarial department provides more service so it should be allocated first.
Actuarial 80.00% 10.00% 10.00% 100.00%
Actuarial % 80.0% 10.0% 10.0% Service % to Premium will be considered here.
Premium 25.00% 15.00% 60.00% 100.00%
Premium % 20.0% 80.0% Service % to Actuarial will not be considered here.
Department cost      87,000.00       22,000.00     67,000.00     47,000.00 223,000.00
Allocation
Actuarial     (87,000.00)       69,600.00        8,700.00        8,700.00                    -  
Total                     -         91,600.00      75,700.00      55,700.00 223,000.00
Premium      (91,600.00)      18,320.00      73,280.00                    -  
Total cost after allocation                     -                        -       94,020.00 128,980.00 223,000.00
Answer 3- Reciprocal Method Actuarial Premium Advertising Sales Total
Actuarial 80.00% 10.00% 10.00% 100.00%
Premium 25.00% 15.00% 60.00% 100.00%
Department cost      87,000.00       22,000.00     67,000.00     47,000.00 223,000.00
Let Overhead cost of Actuarial department is $ X and Overhead cost of Premium Department is $ Y
So, X= 87000+ 25% of Y Equation 1
Y= 22000+ 80% of X Equation 2
Or, X= 87000+ 0.25Y
Y= 22000+ 0.80X
Substituting the value of X in equation 2:
Y = 22000 + 0.80(87,000 + 0.25Y)
Y = 22000 + 69,600+.020Y
Y – 0.20Y = 91,600
0.80Y = 91,600
Y = 91600/.80
Y = $ 114,500
Substituting the value of Y in equation 1:
So, X= 87000+ 25% of Y
So, X= 87000+ 25% of 114,500
So, X= 87000+ 28,625
X= $ 115,625
Allocation Summary Actuarial Premium Advertising Sales Total
Actuarial 80.0% 10.0% 10.0%
Premium 25.00% 15.00% 60.00% 100.00%
Department cost      87,000.00       22,000.00     67,000.00     47,000.00 223,000.00
Allocation
Actuarial (115,625.00)       92,500.00      11,562.50      11,562.50                    -  
Premium      28,625.00 (114,500.00)      17,175.00      68,700.00                    -  
Total cost after allocation                     -                        -       95,737.50 127,262.50 223,000.00
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