Question

I have the first two parts to this question but I cannot seem to get the reciprocal method amounts to come out right. The question says to round to the nearest 4 decimals.

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 Actuarial Premium Rating Advertising 80 $ 10% 25 % Sales 108 60 15 The direct operating costs of the departments (including both variable and fixed costs) are: Actuarial Premium rating Advertising Sales $90,000 25,000 70,000 50,000 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

Suppose total expense of Actuarial (including share of premium) is X and total expense of premium (including Actuarial) is Y

Then,

X = 90,000 + 0.25Y........(1)

Y = 25,000 + 0.80X........(2)

Put the value of X in equation 2

Y= 25,000 + 0.80(90,000 + 0.25Y)

Y = 25,000 + 72,000 + 0.2Y

Y - 0.2Y = 97,000

0.8Y = 97,000

Y = 121,250, premium expense (including Actuarial) = 121,250

X = 90,000 + 0.25Y

X = 90,000 + 0.25(121,250)

X = 90,000 + 30,312

X = 120,312 , Actuarial expense (including premium) = 120,312

	Advertising	Sale
Direct cost	70,000	50,000
Actuarial	120,312 x 10% = 12,031	120,312 x 10% = 12,031
Premium	121,250 × 15% = 18,187	121,250 × 60% = 72,750
Total cost	100,218	134,781