Chapter 5, Problem 10E

Support department cost allocation —comparison

Refer to your answers to Exercises 7-9. Compare the total support department costs allocated to each production department under each cost allocation method. Which production department is allocated the most support department costs (a) under the direct method, (b) under the sequential method, and (c) under the reciprocal services method?

EX 19-7 Support department cost allocation—direct method

Becker Tabletops has two support departments (Janitorial and Cafeteria) and two production departments (Cutting and Assembly). Relevant details for these departments are as follows:

Allocate the support department costs to the production departments using the direct method.

EX 19-8 Support department cost allocation—sequential method

Refer to the information provided for Becker Tabletops in Exercise 7. Allocate the support department costs to the production departments using the sequential method. Allocate the support department with the highest department cost first.

EX 19-9 Support department cost allocation —reciprocal services method

Refer to the information provided for Becker Tabletops in Exercise 7. Allocate the support department costs to the production departments using the reciprocal services method.

To determine

Identify the production department with greater department cost allocation under each method.

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.

(a) The direct method:

Compute the costs allocated from the support departments.

Cutting Department Total Cost:

$\begin{array}{c}\begin{array}{l}\text{Cutting}\\ \text{Department}\end{array}\}\text{ =}\left(\begin{array}{l}\text{Cost from the }\\ \text{Janitorial }\\ \text{Department}\end{array}\right)\text{+}\left(\begin{array}{l}\text{Cost from the}\\ \text{Cafeteria }\\ \text{Department}\end{array}\right)\\ \text{= \$62,000 + \$126,750}\\ \text{= \$188,750}\end{array}$

Assembly Department Total Cost:

$\begin{array}{c}\begin{array}{l}\text{Assembly}\\ \text{Department}\end{array}\}\text{ =}\left(\begin{array}{l}\text{Cost from the }\\ \text{Janitorial }\\ \text{Department}\end{array}\right)\text{+}\left(\begin{array}{l}\text{Cost from the}\\ \text{Cafeteria }\\ \text{Department}\end{array}\right)\\ \text{= \$248,000 + \$42,250}\\ \text{= \$290,250}\end{array}$

Under the direct method the Assembly department has been allocated the greater costs from the support departments.

Working Notes:

Janitorial Department Cost Allocation:

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

$\begin{array}{c}\begin{array}{l}\text{Janitorial }\\ \text{Department}\end{array}\}\text{ =}\left(\frac{\text{Cutting Department}}{\text{Total cost driver}}\times 100\right)\times \left(\begin{array}{l}\text{Total costs of}\\ \text{Janitorial Department}\end{array}\right)\\ \text{=}\left(\frac{1,000}{1,000+4,000}\times 100\right)\times \$310,000\\ =20\%\times \$310,000\\ =\$62,000\end{array}$

The costs from Janitorial Department that should be allocated to Cutting department is $62,000.

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

$\begin{array}{c}\begin{array}{l}\text{Janitorial }\\ \text{Department}\end{array}\}\text{ =}\left(\frac{\text{Assembly Department}}{\text{Total cost driver}}\times 100\right)\times \left(\begin{array}{l}\text{Total costs of}\\ \text{Janitorial Department}\end{array}\right)\\ \text{=}\left(\frac{4,000}{1,000+4,000}\times 100\right)\times \$310,000\\ =80\%\times \$310,000\\ =\$248,000\end{array}$

The cost allocated from Janitorial Department to Assembly department is $248,000.

Cafeteria Department Cost Allocation:

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

$\begin{array}{c}\begin{array}{l}\text{Cafeteria}\\ \text{Department}\end{array}\}\text{ =}\left(\frac{\text{Cutting Department}}{\text{Total cost driver}}\times 100\right)\times \left(\begin{array}{l}\text{Total costs of}\\ \text{Cafeteria Department}\end{array}\right)\\ \text{=}\left(\frac{30}{30+10}\times 100\right)\times \$169,000\\ =75\%\times \$169,000\\ =\$126,750\end{array}$

The costs allocated from Cafeteria Department to Cutting department is $126,750.

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

$\begin{array}{c}\begin{array}{l}\text{Cafeteria}\\ \text{Department}\end{array}\}\text{ =}\left(\frac{\text{Assembly Department}}{\text{Total cost driver}}\times 100\right)\times \left(\begin{array}{l}\text{Total costs of}\\ \text{Cafeteria Department}\end{array}\right)\\ \text{=}\left(\frac{10}{30+10}\times 100\right)\times \$169,000\\ =25\%\times \$169,000\\ =\$42,250\end{array}$

The cost allocated from Cafeteria Department to Assembly department is $42,250.

(b) The sequential method:

Compute the costs allocated from the support departments.

Cutting Department Total Cost:

$\begin{array}{c}\begin{array}{l}\text{Cutting}\\ \text{Department}\end{array}\}\text{ =}\left(\begin{array}{l}\text{Cost from the }\\ \text{Janitorial }\\ \text{Department}\end{array}\right)\text{+}\left(\begin{array}{l}\text{Cost from the}\\ \text{Cafeteria }\\ \text{Department}\end{array}\right)\\ \text{= \$31,000 + \$243,000}\\ \text{= \$274,000}\end{array}$

Assembly Department Total Cost:

$\begin{array}{c}\begin{array}{l}\text{Assembly}\\ \text{Department}\end{array}\}\text{ =}\left(\begin{array}{l}\text{Cost from the }\\ \text{Janitorial }\\ \text{Department}\end{array}\right)\text{+}\left(\begin{array}{l}\text{Cost from the}\\ \text{Cafeteria }\\ \text{Department}\end{array}\right)\\ \text{= \$124,000 + \$81,000}\\ \text{= \$205,000}\end{array}$

Under the sequential method the Cutting department has been allocated the greater costs from the support departments.

Working Notes:

Janitorial Department Cost Allocation:

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

$\begin{array}{c}\begin{array}{l}\text{Janitorial }\\ \text{Department}\end{array}\}\text{ =}\left(\frac{\text{Cafeteria Department}}{\text{Total cost driver}}\times 100\right)\times \left(\begin{array}{l}\text{Total costs of}\\ \text{Janitorial Department}\end{array}\right)\\ \text{=}\left(\frac{5,000}{5,000+1,000+4,000}\times 100\right)\times \$310,000\\ =50\%\times \$310,000\\ =\$155,000\end{array}$

The cost allocated from Janitorial Department to Cafeteria department is $155,000.

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

$\begin{array}{c}\begin{array}{l}\text{Janitorial }\\ \text{Department}\end{array}\}\text{ =}\left(\frac{\text{Cutting Department}}{\text{Total cost driver}}\times 100\right)\times \left(\begin{array}{l}\text{Total costs of}\\ \text{Janitorial Department}\end{array}\right)\\ \text{=}\left(\frac{1,000}{5,000+1,000+4,000}\times 100\right)\times \$310,000\\ =10\%\times \$310,000\\ =\$31,000\end{array}$

The costs allocated from Janitorial Department to Cutting department is $31,000.

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

$\begin{array}{c}\begin{array}{l}\text{Janitorial }\\ \text{Department}\end{array}\}\text{ =}\left(\frac{\text{Assembly Department}}{\text{Total cost driver}}\times 100\right)\times \left(\begin{array}{l}\text{Total costs of}\\ \text{Janitorial Department}\end{array}\right)\\ \text{=}\left(\frac{4,000}{5,000+1,000+4,000}\times 100\right)\times \$310,000\\ =40\%\times \$310,000\\ =\$124,000\end{array}$

The cost allocated from Janitorial Department to Assembly department is $124,000.

Cafeteria Department Total Cost:

$\begin{array}{c}\begin{array}{l}\text{Cafeteria }\\ \text{Department}\end{array}\}\text{ =}\left(\begin{array}{l}\text{Cost from the }\\ \text{Janitorial }\\ \text{Department}\end{array}\right)\text{+}\left(\begin{array}{l}\text{Total costs of}\\ \text{Cafeteria }\\ \text{Department}\end{array}\right)\\ \text{= \$155,000 + \$169,000}\\ \text{= \$324,000}\end{array}$

The total costs of Cafeteria Department are $324,000.

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

$\begin{array}{c}\begin{array}{l}\text{Cafeteria}\\ \text{Department}\end{array}\}\text{ =}\left(\frac{\text{Cutting Department}}{\text{Total cost driver}}\times 100\right)\times \left(\begin{array}{l}\text{Total costs of}\\ \text{Cafeteria Department}\end{array}\right)\\ \text{=}\left(\frac{30}{30+10}\times 100\right)\times \$324,000\\ =75\%\times \$324,000\\ =\$243,000\end{array}$

The costs allocated from Cafeteria Department to Cutting department is $243,000.

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

$\begin{array}{c}\begin{array}{l}\text{Cafeteria}\\ \text{Department}\end{array}\}\text{ =}\left(\frac{\text{Assembly Department}}{\text{Total cost driver}}\times 100\right)\times \left(\begin{array}{l}\text{Total costs of}\\ \text{Cafeteria Department}\end{array}\right)\\ \text{=}\left(\frac{10}{30+10}\times 100\right)\times \$324,000\\ =25\%\times \$324,000\\ =\$81,000\end{array}$

The cost allocated from Cafeteria Department to Assembly department is $81,000.

(c) The reciprocal services method:

Compute the costs allocated from the support departments.

Cutting Department Total Cost:

$\begin{array}{c}\begin{array}{l}\text{Cutting}\\ \text{Department}\end{array}\}\text{ =}\left(\begin{array}{l}\text{Cost from the }\\ \text{Janitorial }\\ \text{Department}\end{array}\right)\text{+}\left(\begin{array}{l}\text{Cost from the}\\ \text{Cafeteria }\\ \text{Department}\end{array}\right)\\ \text{= \$38,200 + \$216,000}\\ \text{= \$254,200}\end{array}$

Assembly Department Total Cost:

$\begin{array}{c}\begin{array}{l}\text{Assembly}\\ \text{Department}\end{array}\}\text{ =}\left(\begin{array}{l}\text{Cost from the }\\ \text{Janitorial }\\ \text{Department}\end{array}\right)\text{+}\left(\begin{array}{l}\text{Cost from the}\\ \text{Cafeteria }\\ \text{Department}\end{array}\right)\\ \text{= \$152,800 + \$72,000}\\ \text{= \$224,800}\end{array}$

Under the reciprocal services method the Cutting department has been allocated the greater costs from the support departments.

Working Notes:

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