Chapter 5, Problem 9E

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.

Janitorial Department Cost to be allocated:

The total Janitorial Department costs include 20% of the Cafeteria department costs as,

$\frac{10}{\left(10+30+10\right)}$.

Therefore, the Cafeteria Department cost is,

$\text{Janitorial department = \$310,000 + }\left(\text{0}\text{.2}\times \text{C}\right)$

Cafeteria Department Cost to be allocated:

The total Cafeteria Department costs include 50% of the Janitorial department costs as,

$\frac{5,000}{\left(5,000+1,000+4,000\right)}$.

Therefore, the Cafeteria Department cost is,

$\text{Cafeteria department = \$169,000 + }\left(\text{0}\text{.5}\times \text{J}\right)$

Substitute the equation for J into the C equation:

$\begin{array}{c}\text{Cafeteria department = \$169,000 + }\left[\text{0}\text{.5}\times \left[\text{\$310,000 + }\left(\text{0}\text{.2}\times \text{C}\right)\right]\right]\\ =\text{\$169,000 +\$155,000 + }\left(\text{0}\text{.1}\times \text{C}\right)\\ 0.9\times \text{C}=\text{\$324,000}\\ \text{= \$360,000}\end{array}$

Substitute the value of C into the J equation:

$\begin{array}{c}\text{Janitorial department = \$310,000 + }\left(\text{0}\text{.2}\times \text{\$360,000}\right)\\ =\text{\$310,000 +\$72,000 }\\ \text{= \$382,000}\end{array}$

Janitorial Department Cost Allocation:

Compute the allocation of costs from Janitorial Department to Cafeteria Department:

$\begin{array}{c}\begin{array}{l}\text{Janitorial}\\ \text{Department}\end{array}\}\text{ =}\left(\frac{\text{Cafeteria Department}}{\text{Total cost driver}}\times 100\right)\times \left(\begin{array}{l}\text{Total costs of}\\ \text{Janitorial Department}\end{array}\right)\\ \text{=}\left(\frac{5,000}{5,000+1,000+4,000}\times 100\right)\times \$382,000\\ =50\%\times \$382,000\\ =\$191,000\end{array}$

The costs allocated from Janitorial Department to Cafeteria Department is $191,000.

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

$\begin{array}{c}\begin{array}{l}\text{Janitorial}\\ \text{Department}\end{array}\}\text{ =}\left(\frac{\text{Cutting Department}}{\text{Total cost driver}}\times 100\right)\times \left(\begin{array}{l}\text{Total costs of}\\ \text{Janitorial Department}\end{array}\right)\\ \text{=}\left(\frac{1,000}{5,000+1,000+4,000}\times 100\right)\times \$382,000\\ =10\%\times \$382,000\\ =\$38,200\end{array}$

The costs allocated from Janitorial Department to Cutting Department is $38,200.

Compute the allocation of costs from Janitorial Department to Assembly Department:

$\begin{array}{c}\begin{array}{l}\text{Janitorial}\\ \text{Department}\end{array}\}\text{ =}\left(\frac{\text{Assembly Department}}{\text{Total cost driver}}\times 100\right)\times \left(\begin{array}{l}\text{Total costs of}\\ \text{Janitorial Department}\end{array}\right)\\ \text{=}\left(\frac{4,000}{5,000+1,000+4,000}\times 100\right)\times \$382,000\\ =40\%\times \$382,000\\ =\$152,800\end{array}$

The costs allocated from Janitorial Department to Assembly Department is $152,800.

Cafeteria Department Cost Allocation:

Compute the allocation of costs from Cafeteria Department to Janitorial Department:

$\begin{array}{c}\begin{array}{l}\text{Cafeteria}\\ \text{Department}\end{array}\}\text{ =}\left(\frac{\text{Janitorial Department}}{\text{Total cost driver}}\times 100\right)\times \left(\begin{array}{l}\text{Total costs of}\\ \text{Cafeteria Department}\end{array}\right)\\ \text{=}\left(\frac{10}{10+30+10}\times 100\right)\times \$360,000\\ =20\%\times \$360,000\\ =\$72,000\end{array}$

The costs allocated from Cafeteria Department to Janitorial Department is $72,000.

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

$\begin{array}{c}\begin{array}{l}\text{Cafeteria}\\ \text{Department}\end{array}\}\text{ =}\left(\frac{\text{Cutting Department}}{\text{Total cost driver}}\times 100\right)\times \left(\begin{array}{l}\text{Total costs of}\\ \text{Cafeteria Department}\end{array}\right)\\ \text{=}\left(\frac{30}{10+30+10}\times 100\right)\times \$360,000\\ =60\%\times \$360,000\\ =\$216,000\end{array}$

The costs allocated from Cafeteria Department to Cutting Department is $216,000.

Compute the allocation of costs from Cafeteria Department to Assembly Department:

$\begin{array}{c}\begin{array}{l}\text{Cafeteria}\\ \text{Department}\end{array}\}\text{ =}\left(\frac{\text{Assembly Department}}{\text{Total cost driver}}\times 100\right)\times \left(\begin{array}{l}\text{Total costs of}\\ \text{Cafeteria Department}\end{array}\right)\\ \text{=}\left(\frac{10}{10+30+10}\times 100\right)\times \$360,000\\ =20\%\times \$360,000\\ =\$72,000\end{array}$

The costs allocated from Cafeteria Department to Assembly Department is $72,000.