Chapter 17, Problem 7AP

a.

To determine

Calculate the amount of Maintenance Department costs that would be allocated to each robot model (on a per-unit basis) using machine-hours as a single activity base.

Explanation of Solution

Calculate the amount of Maintenance Department costs that would be allocated to each robot model (on a per-unit basis) using machine-hours as a single activity base.

Robot model	Machine hours per unit (A)	Per machine  hours in $ (B)	Amount  in  $ $\left(\text{A}\times \text{B}\right)$
A3B4	3.2(3)	2.50 (2)	8.00
BC11	3.0(3)	2.50(2)	7.50
C3PO	2.0(3)	2.50(2)	5.00

 (Table 1)

Working Notes:

Calculate total machine hours:

$\begin{array}{c}\begin{array}{l}\text{Total machine hours at normal }\\ \text{production levels}\end{array}\}\text{ =}\left[\begin{array}{l}\left(\begin{array}{l}\text{Machine hours of}\\ \text{ Robot A3B4}\end{array}\right)+\left(\begin{array}{l}\text{Machine hours of}\\ \text{ Robot BC11}\end{array}\right)+\\ \left(\begin{array}{l}\text{Machine hours of}\\ \text{ Robot C3PO}\end{array}\right)\end{array}\right]\\ =\left(\begin{array}{l}20,000\text{Machine}\\ \text{ hours}\end{array}\right)\text{ +}\left(\begin{array}{l}\text{15},000\text{Machine }\\ \text{hours}\end{array}\right)+\left(\begin{array}{l}5,000\text{Machine}\\ \text{ hours}\end{array}\right)\\ \text{=40,000 Machine hours }\end{array}$ (1)

Calculate the overhead application rate per machine hours:

$\begin{array}{c}\begin{array}{l}\text{Overhead application rate }\\ \text{per machine hours}\end{array}\}=\frac{\text{Total cost}}{\text{Total machine hours at normal productive levels}}\\ =\frac{\$100,000}{40,000\left(1\right)}\\ =\$2.50\text{ per machine hour}\end{array}$ (2)

Calculate the machine hours on per-unit basis:

Robot model	Machine hours (A)	Units of  production  (B)	Machine hours per  -unit $\left(\frac{\text{A}}{\text{B}}\right)$
A3B4	20,000	6,250	3.2
BC11	15,000	5,000	3.0
C3PO	5,000	2,500	2.0

(Table 2)

(3)

b.

To determine

Calculate the amount of Maintenance Department costs that would be allocated to each robot model (on a per-unit basis) using the proposed ABC method.

Explanation of Solution

Activity-based costing:

It is a method that helps in finding the activities performed by a company and it tracks the indirect costs to the activities of the company that consumes resources.

Calculate the amount of Maintenance Department costs that would be allocated to each robot model (on a per-unit basis) using the proposed ABC method.

Particulars	Robot model
Total costs allocated	A3B4 in $	BC11 in $	C3PO in $	Total in $
Repairs cost pool (9)	2,500	7,500	10,000	20,000
Add: Janitorial cost pool (11)	10,000	20,000	50,000	80,000
Total costs allocated (A)	12,500	27,500	60,000	100,000
Units produced (B)	6,250	5,000	2,500
Maintenance cost per unit (A÷B)	2	6	24

(Table 3)

Working notes:

Calculate the percent of work orders used for repairs activities:

$\begin{array}{c}\begin{array}{l}\text{Percent of work orders }\\ \text{of repairs activity}\end{array}\}\text{ = }\frac{\text{Work orders of repairs activities }}{\text{Total work orders}}\times 100\\ =\frac{400}{2,000}\times 100\\ =20\%\end{array}$ (4)

Calculate the percent of machine hours used for janitorial activities:

$\begin{array}{c}\begin{array}{l}\text{Percent of work orders }\\ \text{of janitorial activity}\end{array}\}\text{ = }\frac{\text{Work orders of janitorial activities }}{\text{Total work orders}}\times 100\\ =\frac{1,600}{2,000}\times 100\\ =80\%\end{array}$ (5)

Calculate percent of work orders used in each activity pools:

Particulars	Work orders	Percent to total
Repairs activities	400	20% (4)
Janitorial activities	1,600	80% (5)
Total  work orders issued	2,000	100%

(Table 4)

(6)

Product lines	Total amount in $ (A)	Percentage of  Allocation (B)	Cost Allocated $\text{(A}\times \text{B)}$
Repairs activities	100,000	20% (6)	20,000
Janitorial activities	100,000	80% (6)	80,000
Total			80,000

(Table 5)

(7)

Calculate the percent of repairs cost pool to the allocated to each product line using the number of production runs as an activity base.

Particulars	Number of production  runs	Percent of total
Production runs for A3B4	50	12.5%
Production runs for BC11	150	37.5%
Production runs for C3PO	200	50.0%
Total production runs	400	100.0%

(Table 6)

(8)

Allocate the repairs cost pool to each of the product line based on the percentage.

Particulars	Amount in $
Costs allocated to A3B4 $\left(\$20,000\times 12.5\%\right)$	2,500
Costs allocated to BC11 $\left(\$20,000\times 37.5\%\right)$	7,500
Costs allocated to C3PO $\left(\$20,000\times 50.0\%\right)$	10,000
Total order costs allocated to products	20,000

(Table 7)

(9)

Calculate the percent of janitorial pool to the allocated to each product line using the number of production runs as an activity base.

Particulars		Percent of total
Production runs for A3B4	5,000	12.5%
Production runs for BC11	10,000	25.0%
Production runs for C3PO	25,000	62.5%
Total square feet occupied	40,000	100.0%

(Table 8)

(10)

Allocate the janitorial cost pool to each of the product line based on the percentage.

Particulars	Amount in $
Costs allocated to A3B4 $\left(\$80,000\times 12.5\%\right)$	10,000
Costs allocated to BC11 $\left(\$80,000\times \text{ 25}.0\%\right)$	20,000
Costs allocated to C3PO $\left(\$80,000\times \text{ 62}\text{.5}\%\right)$	50,000
Total order costs allocated to products	80,000

(Table 9)

(11)

c.

To determine

Explain whether cost allocations distorted using machine-hours as a single activity base

Explanation of Solution

Using machine hours as a single activity base will result in cost distortions for Company D. The largest distortion, related to robot model C3PO are due to two reasons:

• The machine hours taken for producing robot model C3PO is comparatively less and  the company needs more number of production runs to produce robots.
• The robot C3PO denotes a relatively small portion of total production on a per-unit basis and it requires relatively large proportion of square footage to produce.
• The company considers production run and square footage as primary cost drivers. Therefore, the amount allocated for producing robot C3PO is understated on a per-unit basis, and they are shown below:

Particulars	Robot model A3B4	Robot model BC11	Robot model C3PO
Maintenance cost per unit (Using activity based  costing )	$ 2.00	$ 5.50	$ 24.00
Maintenance cost per unit (Using machine  hours)	$ 8.00	$ 7.50	$ 5.00

(Table 10)