Question

The Long Term Care Plus Company has two service departments - actuarial and premium rating, and two operations departments - marketing and sales. The distribution of each service department's efforts to the other departments is shown below:

	Actuarial	Rating	Marketing	Sales
Actuarial	0%	10%	10%	80%
Rating	20%	0%	30%	50%

The direct operating costs of the departments (including both variable and fixed costs) were as follows:

Actuarial	$10,000
Premium Rating	$200,000
Marketing	$62,000
Sales	$67,000

The total cost accumulated in the sales department using the reciprocal method is (calculate all ratios and percentages to 4 decimal places, for example 33.3333%, and round all dollar amount to the nearest whole dollar):

a: $128,633

b: $148,813

c: $210,367

d: $168,882

e: $176,461

Answer 1

Correct option is "C"- 210367

Let the total cost of actuarial be "X" and that of Rating be "Y"

Total Cost of Actuarial =Direct cost+ (Total cost of Rating* % allocation)

   X = 10000 + (Y*.20)

X = 10000 +.20Y                   [Equation 1]

Total cost of Rating =Direct cost+ (Total cost of Actuarial* % allocation)

Y = 200000 + (X* .10)

Putting the value of X from equation 1 to this equation

Y = 200000+ [(10000+.20 Y ) *.10 ]

Y = 200000 + [1000 + .02 Y]

Y-.02Y = 200000+1000

.98 Y = 201000

Y = 201000/.98 = 205102

Total cost of Rating = 205102

Total cost of Actuarial = 10000 + (.20 *205102 )

                 = 10000 + 41020

               = 51020

	SALES
Direct cost	67000
Allocation from Actuarial (51020*80%)	40816
Allocation from Rating (205102 *50%)	102551
Total cost accumulated in sales department	210367