Question

Exercise 7-29 Departmental Cost Allocation [LO 7-3]

Robinson Products Company has two service departments (S1 and S2) and two production departments (P1 and P2). The distribution of each service department’s efforts (in percentages) to the other departments is:

From	To
	S1		S2			P1			P2
S1	—			20	%		30	%		?	%
S2	20	%		—			?			40

The direct operating costs of the departments (including both variable and fixed costs) are:

S1	$	170,000
S2		64,000
P1		51,000
P2		125,000

Required:

1. Determine the total cost of P1 and P2 using the direct method.

2. Determine the total cost of P1 and P2 using the step method.

3. Determine the total cost of P1 and P2 using the reciprocal method.

Answer 1

Solution:

Workings:

Let X be the total cost of S1 Department

   & Y be the total cost of S2 Department

Then,

                X = $170,000 + 20% of Y

                Y = $64,000 + 20% of X

Therefore, the equations will be:

                X = $170,000 + 0.2 Y              ......................           (1)

                Y = $64,000 + 0.2 X                ......................           (2)

Solving the Above Two Equation:

On Multiplying both equation by 10, we get

10 X = $1,700,000 + 2 Y                         ......................           (3)

10 Y =    $640,000 + 2 X                         ......................           (4)

Now, multiplying equation (3) by 5, we get

50 X = $8,500,000 + 10 Y                   ......................           (5)

Rearranging & adding equation (4) & (5), we get

                 50 X = $8,500,000 + 10 Y

                - 2 X =     $640,000 – 10 Y

                48 X = $9,140,000

                       X = $190,417

Substituting this value in equation (4), we get

10 Y = $640,000 + 2 X

10 Y = $640,000 + 2 × $190,417

10 Y = $1,020,834

     Y = $102,083

Hence, Total cost of S1 Dept. = $190,416.67 & S2 Dept. = $102,083