Chapter 5, Problem 6E

Davis Snowflake & Co. produces Christmas stockings in its Cutting and Sewing departments. The Maintenance and Security departments support the production of the stockings. Costs from the Maintenance Department are allocated based on machine hours, and costs from the Security Department are allocated based on asset value. Information about each department is provided in the following table:

Determine the total cost of each production department after allocating all support department costs to the production departments using the reciprocal services method.

To determine

Compute the total cost of each production department after allocating all support costs to the production departments.

Explanation of Solution

Cost allocation:

The cost allocation refers to the process of allocating the costs associated with the production of the products mainly indirectly and are generally ignored. The main objective of cost allocation is to ensure proper pricing of the products. This can be done by several methods.

Maintenance Department Cost to be allocated:

The total Maintenance Department costs include 20% of the Security department costs as,

$\frac{2,000}{\left(2,000+2,500+5,500\right)}$.

Therefore, the Security Department cost is,

$\text{Maintenance department = \$36,000 + }\left(\text{0}\text{.2}\times \text{S}\right)$

Security Department Cost to be allocated:

The total Security Department costs include 10% of the Maintenance department costs as,

$\frac{2,000}{\left(2,000+7,200+10,800\right)}$.

Therefore, the Security Department cost is,

$\text{Security department = \$16,000 + }\left(\text{0}\text{.1}\times \text{M}\right)$

Substitute the equation for M into the S equation:

$\begin{array}{c}\text{Security department = \$16,000 + }\left[\text{0}\text{.1}\times \left[\text{\$36,000 + }\left(\text{0}\text{.2}\times \text{S}\right)\right]\right]\\ =\text{\$16,000 +\$3,600 + }\left(\text{0}\text{.02}\times \text{S}\right)\\ 0.98\times \text{S}=\text{\$19,600}\\ \text{= \$20,000}\end{array}$

Substitute the value of S into the M equation:

$\begin{array}{c}\text{Maintenance department = \$36,000 + }\left(\text{0}\text{.2}\times \text{\$20,000}\right)\\ =\text{\$36,000 +\$4,000 }\\ \text{= \$40,000}\end{array}$

Maintenance Department Cost Allocation:

Compute the allocation of costs from Maintenance Department to Security Department:

$\begin{array}{c}\begin{array}{l}\text{Maintenance}\\ \text{Department}\end{array}\}\text{ =}\left(\frac{\text{Security Department}}{\text{Total cost driver}}\times 100\right)\times \left(\begin{array}{l}\text{Total costs of}\\ \text{Maintenance Department}\end{array}\right)\\ \text{=}\left(\frac{2,000}{2,000+7,200+10,800}\times 100\right)\times \$40,000\\ =10\%\times \$40,000\\ =\$4,000\end{array}$

The costs allocated from Maintenance Department to Security Department is $4,000.

Compute the allocation of costs from Maintenance Department to Cutting Department:

$\begin{array}{c}\begin{array}{l}\text{Maintenance}\\ \text{Department}\end{array}\}\text{ =}\left(\frac{\text{Cutting Department}}{\text{Total cost driver}}\times 100\right)\times \left(\begin{array}{l}\text{Total costs of}\\ \text{Maintenance Department}\end{array}\right)\\ \text{=}\left(\frac{7,200}{2,000+7,200+10,800}\times 100\right)\times \$40,000\\ =36\%\times \$40,000\\ =\$14,400\end{array}$

The costs allocated from Maintenance Department to Cutting Department is $14,400.

Compute the allocation of costs from Maintenance Department to Sewing Department:

$\begin{array}{c}\begin{array}{l}\text{Maintenance}\\ \text{Department}\end{array}\}\text{ =}\left(\frac{\text{Sewing Department}}{\text{Total cost driver}}\times 100\right)\times \left(\begin{array}{l}\text{Total costs of}\\ \text{Maintenance Department}\end{array}\right)\\ \text{=}\left(\frac{10,800}{2,000+7,200+10,800}\times 100\right)\times \$40,000\\ =54\%\times \$40,000\\ =\$21,600\end{array}$

The costs allocated from Maintenance Department to Sewing Department is $21,600.

Security Department Cost Allocation:

Compute the allocation of costs from Security Department to Maintenance Department:

$\begin{array}{c}\begin{array}{l}\text{Security}\\ \text{Department}\end{array}\}\text{ =}\left(\frac{\text{Maintenance Department}}{\text{Total cost driver}}\times 100\right)\times \left(\begin{array}{l}\text{Total costs of}\\ \text{Security Department}\end{array}\right)\\ \text{=}\left(\frac{2,000}{2,000+2,500+5,500}\times 100\right)\times \$20,000\\ =20\%\times \$20,000\\ =\$4,000\end{array}$

The costs allocated from Security Department to Maintenance Department is $4,000.

Compute the allocation of costs from Security Department to Cutting Department:

$\begin{array}{c}\begin{array}{l}\text{Security}\\ \text{Department}\end{array}\}\text{ =}\left(\frac{\text{Cutting Department}}{\text{Total cost driver}}\times 100\right)\times \left(\begin{array}{l}\text{Total costs of}\\ \text{Security Department}\end{array}\right)\\ \text{=}\left(\frac{2,500}{2,000+2,500+5,500}\times 100\right)\times \$20,000\\ =25\%\times \$20,000\\ =\$5,000\end{array}$

The costs allocated from Security Department to Cutting Department is $5,000.

Compute the allocation of costs from Security Department to Sewing Department:

$\begin{array}{c}\begin{array}{l}\text{Security}\\ \text{Department}\end{array}\}\text{ =}\left(\frac{\text{Sewing Department}}{\text{Total cost driver}}\times 100\right)\times \left(\begin{array}{l}\text{Total costs of}\\ \text{Security Department}\end{array}\right)\\ \text{=}\left(\frac{5,500}{2,000+2,500+5,500}\times 100\right)\times \$20,000\\ =55\%\times \$20,000\\ =\$11,000\end{array}$

The costs allocated from Security Department to Sewing Department is $11,000.

Total Costs of Production Departments:

Compute the total cost of the Cutting Department:

$\begin{array}{c}\begin{array}{l}\text{Cutting}\\ \text{Department}\end{array}\}\text{ =}\left(\begin{array}{l}\text{Cost from the }\\ \text{Maintenance }\\ \text{Department}\end{array}\right)\text{+}\left(\begin{array}{l}\text{Cost from the }\\ \text{Security}\\ \text{Department}\end{array}\right)\text{+}\left(\begin{array}{l}\text{Total costs of}\\ \text{Cutting}\\ \text{Department}\end{array}\right)\\ \text{= \$14,400 + \$5,000 + \$64,000}\\ \text{= \$83,400}\end{array}$

The total costs of the Cutting department are $83,400.

Compute the total cost of the Sewing Department:

$\begin{array}{c}\begin{array}{l}\text{Sewing}\\ \text{Department}\end{array}\}\text{ =}\left(\begin{array}{l}\text{Cost from the }\\ \text{Maintenance }\\ \text{Department}\end{array}\right)\text{+}\left(\begin{array}{l}\text{Cost from the }\\ \text{Security}\\ \text{Department}\end{array}\right)\text{+}\left(\begin{array}{l}\text{Total costs of}\\ \text{Sewing}\\ \text{Department}\end{array}\right)\\ \text{= \$21,600 + \$11,000 + \$82,000}\\ \text{= \$114,600}\end{array}$

The total costs of the Sewing department are $114,600.