Chapter 11, Problem 30E

a.

To determine

Calculate the allocation of cost based on the step method starting from maintenance.

Answer to Problem 30E

The total cost allocation is $40,000 and $32,000 for machining and assembly, and there is no cost allocation in maintenance and cafeteria.

Explanation of Solution

Step method:

Step method allows the allocation of the cost to the production department and service departments. Unlike the direct method, it also allocates the cost of the service to various service departments. Allocation of the cost starts from the department that has provided the highest proposition of service to the department that has provided the least service. Step method allows only one-way allocation of cost among service departments.

Calculate the cost allocation based on the step method:

Particular	Maintenance	Cafeteria	Machining	Assembly
Service department cost	$40,000	$32,000
Maintenance	$ (40,000)	$8,000 (1)	$20,000 (1)	$12,000 (1)
Cafeteria		$(40,000)(4)	$20,000(2)	$20,000(3)
Total cost allocation	$0	$0	$40,000	$32,000

Table: (1)

Thus, the total cost allocation is $40,000 and $32,000 for machining and assembly, and there is no cost allocation in maintenance and cafeteria.

Working note 1:

Calculate the maintenance cost allocation:

Particulars	Proposition (a)	Total costs (b)	Cost allocation $\left(c=\left(a\times b\right)\right)$
Cafeteria	20%	$40,000	$8,000
Machining	50%	$40,000	$20,000
Assembly	30%	$40,000	$12,000

Table: (1)

Working note 2:

Calculate the cafeteria cost for the machining department:

$\begin{array}{c}\text{Maintenance cost = }\frac{\text{Ratio of respective cost}}{\text{Total ratio}}\times \text{ Respective cost}\\ =\frac{0.1}{0.1\text{ + 0}\text{.1}}\times \text{ \$40,000}\\ \text{= \$20,000}\end{array}$

Working note 3:

Calculate the cafeteria cost for the assembly department:

$\begin{array}{c}\text{Maintenance cost = }\frac{\text{Ratio of respective cost}}{\text{Total ratio}}\times \text{ Respective cost}\\ =\frac{0.1}{0.1\text{ + 0}\text{.1}}\times \text{ \$40,000}\\ \text{= \$20,000}\end{array}$

Working note 4:

Calculate the cafeteria cost for the assembly department:

$\begin{array}{c}\text{Cafeteria cost = Direct cost of the department +}\text{}\text{ Allocation of the maintenance}\\ \text{= \$32,000 + \$8,000}\\ \text{= \$40,000}\end{array}$

b.

To determine

Calculate the allocation of cost based on the step method starting from the cafeteria.

Answer to Problem 30E

The total cost allocation is $44,200 and $27,800 for machining and assembly, and there is no cost allocation in maintenance and cafeteria.

Explanation of Solution

Cost allocation:

Cost allocation refers to the process of distributing the common cost of the production and service rendered to the various departments of the business. It is used to calculate the actual cost attributed to a specific department.

Calculate the cost allocation based on the step method:

Particular	Maintenance	Cafeteria	Machining	Assembly
Service department cost	$32,000	$40,000
Maintenance	$ (32,000)	$25,600(4)	$3,200(4)	$3,200(4)
Cafeteria		$(65,600)(7)	$41,000(5)	$24,600(6)
Total cost allocation	$0	$0	$44,200	$27,800

Table: (2)

Thus, the total cost allocation is $44,200 and $27,800 for machining and assembly, and there is no cost allocation in maintenance and cafeteria.

Working note 4:

Calculate the cafeteria cost allocation:

Particulars	Proposition (a)	Total costs (b)	Cost allocation $\left(c=\left(a\times b\right)\right)$
Cafeteria	80%	$32,000	$25,600
Machining	10%	$32,000	$3,200
Assembly	10%	$32,000	$3,200

Table: (3)

Working note 5:

Calculate the maintenance cost for the machining department:

$\begin{array}{c}\text{Maintenance cost = }\frac{\text{Ratio of respective cost}}{\text{Total ratio}}\times \text{ Respective cost}\\ =\frac{0.5}{0.5\text{ + 0}\text{.3}}\times \text{ \$65,600}\\ \text{= \$41,000}\end{array}$

Working note 6:

Calculate the maintenance cost for the assembly department:

$\begin{array}{c}\text{Maintenance cost = }\frac{\text{Ratio of respective cost}}{\text{Total ratio}}\times \text{ Respective cost}\\ =\frac{0.3}{0.5\text{ + 0}\text{.3}}\times \text{ \$65,600}\\ \text{= \$24,600}\end{array}$

Working note 7:

Calculate the maintenance cost for the assembly department:

$\begin{array}{c}\text{Maintenance cost = Direct cost of the department +}\text{}\text{ Allocation of the cafeteria}\\ \text{= \$40,000 + \$25,600}\\ \text{= \$65,600}\end{array}$