Question

Midland Resources has two production departments (Fabrication and Assembly) and three service departments (Engineering, Administration, and Maintenance). During July, the following costs and service department usage ratios were recorded: Supplying Department Using Department Engineering Administration Maintenance Fabrication Assembly Engineering 0 60 % 0 20 % 20 % Administration 15 % 0 10 % 50 % 25 % Maintenance 0 20 % 0 30 % 50 % Direct cost $ 50,000 $ 290,300 $ 45,000 $ 250,000 $ 90,000

Supplying Department	Using Department
	Engineering			Administration			Maintenance			Fabrication			Assembly
Engineering		0			60	%		0			20	%		20	%
Administration		15	%		0			10	%		50	%		25	%
Maintenance		0			20	%		0			30	%		50	%
Direct cost	$	50,000		$	290,300		$	45,000		$	250,000		$	90,000

Required: Allocate the service department costs to the two operating departments using the reciprocal method. (Do not round intermediate calculations.)

Allocated to: Costs Fabrication Assembly Engineering Administration Maintenance Total $0 $0

Answer 1

Answer -

		Allocated to:
	Costs	Fabrication	Assembly
Engineering	$105500	$21100 (20%)	$21100 (20%)
Administration	$370000	$185000 (50%)	$92500 (25%)
Maintenance	$82000	$24600 (30%)	$41000 (50%)
Total		$230700	$154600

Calculation:

Here,

The equations expressing the usage:

1. Engineering = Direct cost + 15% of Administration

Engineering = $50000 + (15% * Administration)

2. Administration = Direct cost + 60% of Engineering + 20% of Maintenance

Administration = $290300 + (60% * Engineering) + (20% * Maintenance)

3. Maintenance = Direct cost + 10% of Administration

Maintenance = $45000 + (10% * Administration)

So,

Substituting the equations for Engineering and Maintenance into the equation for Administration

Administration = $290300 + [60% * ($50000 + 15% * Administration)] + [20% * ($45000 + 10% * Administration)]

Administration = $290300 + [$30000 + 9% * Administration] + [$9000 + 2% * Administration]

Administration = $370000

Now,

Substituting the Administration amount into the equation for Engineering and Maintenance

Engineering = $50000 + (15% * Administration)

Engineering = $50000 + (15% * $370000)

Engineering = $105500

And

Maintenance = $45000 + (10% * Administration)

Maintenance = $45000 + (10% * $370000)

Maintenance = $82000

So,

Fabrication = ($20% * Engineering) + (50% * Administration) + (30% * Maintenance)

Fabrication = ($20% * $105500) + (50% * $370000) + (30% * $82000)

Fabrication = $21100 + $185000 + $24600

Fabrication = $230700

Assembly = ($20% * Engineering) + (25% * Administration) + (50% * Maintenance)

Assembly = ($20% * $105500) + (25% * $370000) + (50% * $82000)

Assembly = $21100 + $92500 + $41000

Assembly = $154600