Chapter 17, Problem 7BP

a.

To determine

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

Product line	Machine hours per unit (A)	Per machine  hours in $ (B)	Amount  in  $ $\left(\text{A}\times \text{B}\right)$
Boots	0.10(3)	5(2)	0.50
Poles	0.05(3)	5(2)	0.25
Helmets	1.75(3)	5(2)	8.75

 (Table 1)

Working Notes:

Calculate total machine hours:

$\begin{array}{c}\begin{array}{l}\text{Total machine hours at normal }\\ \text{production levels}\end{array}\}\text{ =}\left[\begin{array}{l}\left(\begin{array}{l}\text{Machine hours of}\\ \text{ base }\end{array}\right)+\left(\begin{array}{l}\text{Machine hours of}\\ \text{ poles}\end{array}\right)+\\ \left(\begin{array}{l}\text{Machine hours of}\\ \text{helmets}\end{array}\right)\end{array}\right]\\ =\left(\begin{array}{l}5,000\text{Machine}\\ \text{ hours}\end{array}\right)\text{ +}\left(\begin{array}{l}10,000\text{Machine }\\ \text{hours}\end{array}\right)+\left(\begin{array}{l}35,000\text{Machine}\\ \text{ hours}\end{array}\right)\\ \text{=50,000 Machine hours }\end{array}$ (1)

Calculate the overhead application rate per machine hours:

$\begin{array}{c}\begin{array}{l}\text{Overhead application rate }\\ \text{per machine hours}\end{array}\}=\frac{\text{Total cost}}{\text{Total machine hours at normal productive levels}}\\ =\frac{\$250,000}{50,000\left(1\right)}\\ =\$5\text{ per machine hour}\end{array}$ (2)

Calculate the machine hours on per-unit basis:

Product line	Machine hours (A)	Units of  production  (B)	Machine hours per  -unit $\left(\frac{\text{A}}{\text{B}}\right)$
Boots	5,000	50,000	0.10
Poles	10,000	200,000	0.05
Helmets	35,000	20,000	1.75

(Table 2)

(3)

b.

To determine

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

Particulars	Product lines
Total costs allocated	Boots in $	Poles in $	Helmets in $	Total in $
Setup activities (9)	31,250	18,750	12,500	62,500
Add: custodial activities (11)	56,250	93,750	37,500	187,500
Total costs allocated (A)	87,500	112,500	50,000	250,000
Units produced (B)	50,000	200,000	20,000
Maintenance cost per unit (A÷B)	1.75	0.5625	2.50

(Table 3)

Working notes:

Calculate the percent of work orders used for setup activities:

$\begin{array}{c}\begin{array}{l}\text{Percent of work orders }\\ \text{of setup activity}\end{array}\}\text{ = }\frac{\text{Work orders of setup activities }}{\text{Total work orders}}\times 100\\ =\frac{600}{2,400}\times 100\\ =25\%\end{array}$ (4)

Calculate the percent of machine hours used for custodial activities:

$\begin{array}{c}\begin{array}{l}\text{Percent of work orders }\\ \text{of custodial activity}\end{array}\}\text{ = }\frac{\text{Work orders of custodial activities }}{\text{Total work orders}}\times 100\\ =\frac{1,800}{2,400}\times 100\\ =75\%\end{array}$ (5)

Calculate percent of work orders used in each activity pools:

Particulars	Work orders	Percent to total
Setup activities	600	25% (4)
Custodial activities	1,800	75% (5)
Total  work orders issued	2,400	100%

(Table 4)

(6)

Product lines	Total amount in $ (A)	Percentage of  Allocation (B)	Cost Allocated $\text{(A}\times \text{B)}$
Setup activities	100,000	25% (6)	52,500
Custodial activities	100,000	75% (6)	187,500
Total			250,000

(Table 5)

(7)

Calculate the percent of setup 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 boots	500	50%
Production runs for poles	300	30%
Production runs for helmets	200	20%
Total production runs	1,000	100%

(Table 6)

(8)

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

Particulars	Amount in $
Costs allocated to base $\left(\$62,500\times 50\%\right)$	31,250
Costs allocated to poles $\left(\$62,500\times 30\%\right)$	18,750
Costs allocated to helmets $\left(\$62,500\times 20\%\right)$	12,500
Total order costs allocated to products	62,500

(Table 7)

(9)

Calculate the percent of custodial 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 boots	9,000	30%
Production runs for poles	15,000	50%
Production runs for helmets	6,000	20%
Total square feet occupied	30,000	100%

(Table 8)

(10)

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

Particulars	Amount in $
Costs allocated to base $\left(\$187,500\times 30\%\right)$	56,250
Costs allocated to poles $\left(\$187,500\times 50\%\right)$	93,750
Costs allocated to helmets $\left(\$187,500\times 20\%\right)$ \	37,500
Total order costs allocated to products	187,500

(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 product line helmet. Machine hours taken by company while producing helmet is comparatively more than boots, poles. When activity based costing is used by the company only 20% of the maintenance cost is been used to produce helmets.
• While using activity based costing for production it reduces the maintenance cost of  helmets and  it reallocates the cost with the  production of  boots and  poles
• The following table provides the reallocation of maintenance cost for each product line under activity based costing:

Particulars	Boots	Poles	Helmets
Maintenance cost per unit (Using machine  hours)	0.50	0.25	8.75
Maintenance cost per unit (Using activity based  costing )	1.75	056	2.50
Percentage increase (decrease) using Activity based costing	250%	124%	(71%)

(Table 10)