Chapter 19, Problem 2BP

a.

To determine

Calculate the target cost for Product B and Product M.

Explanation of Solution

Target costing:

Target costing is a business procedure that targets at the earliest stages of new product and service development, before creating and designing of production techniques.

Calculate the target cost for Product B.

$\begin{array}{c}\text{Target}\text{cost}\text{=}\text{Target}\text{price}-\text{Target}\text{profit}\\ \text{=\$120}-\text{\$14}\text{.40}\text{(1)}\\ \text{=\$105}\text{.60}\end{array}$

Working note:

$\begin{array}{c}\text{Target}\text{profit}\text{=}\text{Percentage}\text{of}\text{return}\text{on}\text{sales}\text{×}\text{Target}\text{price}\\ \text{=12\%}\text{×}\text{\$120}\\ \text{=\$14}\text{.40}\end{array}$

(1)

Calculate the target price of the Product M.

$\begin{array}{c}\text{Target}\text{cost=}\text{Target}\text{price}-\text{Target}\text{profit}\\ \text{=\$180}-\text{\$21}\text{.60}\text{(2)}\\ \text{=\$158}\text{.40}\end{array}$

Working note:

$\begin{array}{c}\text{Target}\text{profit}\text{=}\text{Percentage}\text{of}\text{return}\text{on}\text{sales}\text{×}\text{Target}\text{price}\\ \text{=12\%}\text{×}\text{\$180}\\ \text{=\$21}\text{.60}\end{array}$

(2)

Therefore, the target cost of Product B is $105.60 and Product M is $158.40.

b.

To determine

Estimate the total manufacturing cost per unit of each product if fixed overhead costs are assigned to products on the basis of estimated production in units and state the product that is earning the desired income.

Explanation of Solution

Manufacturing overhead costs:

Manufacturing overhead costs are costs that are not directly related with the manufacturing of the products and it is also known as indirect costs. For example, indirect materials, indirect labour, indirect supplies.

Calculate the total manufacturing cost per unit:

Particulars	Product B	Product M
Direct materials cost per unit	$25	$40
Direct labor cost per unit	$20	$50
Variable overhead cost	$5	$12.50
Fixed overhead cost  (3)	$62.50	$62.50
Total manufacturing cost per unit	$112.50	$165

Table (1)

• The cost per unit of Product B is above its target cost of $105.60 thus, it is not earnings the desired 12% return.
• The cost per unit of Product M is below its target cost of $158.40 thus, it is not earning a greater return than the desired rate.

Working note:

Calculate the fixed overhead cost per unit:

$\begin{array}{c}\text{Allocation}\text{rate}\text{per}\text{unit}\text{=}\frac{\text{Fixed}\text{overhead}}{\text{Total}\text{units}\text{of}\text{production}}\\ \text{=}\frac{\text{\$2,500,000}}{\text{30,000}\text{(Product}\text{k)+10,000}\text{(Product}\text{Q)}}\\ \text{=}\text{\$62}\text{.50}\text{per}\text{unit}\end{array}$

(3)

Conclusion

• The manufacturing cost per unit of Product B is $112.50 and for Product M is $165.
• Both of the products are not earning a return greater than the desired rate since the cost per unit is above the target cost.

c.

To determine

Recalculate the total manufacturing cost per unit if fixed overhead costs are assigned to products on the basis of direct labor hours and state the product that is earning the desired income.

Explanation of Solution

Manufacturing overhead costs:

Manufacturing overhead costs are costs that are not directly related with the manufacturing of the products and it is also known as indirect costs. For example, indirect materials, indirect labour, indirect supplies.

Recalculate the total manufacturing cost per unit of the products:

Particulars	Product B	Product M
Direct materials cost per unit	$25	$40
Direct labor cost per unit	$20	$50
Variable overhead cost	$5	$12.50
Fixed overhead cost	$45.46	$113.65
Total manufacturing cost per unit	$95.46	$216.15

Table (2)

• The cost per unit of Product B is below its target cost of $105.60 thus, it is earning a greater return than the desired rate.
• The cost per unit of Product M is above its target cost of $158.40 thus, it is not earnings the desired return.

Working notes:

Calculate the time taken to produce each unit of Product B:

$\begin{array}{c}\begin{array}{l}\text{Time}\text{taken}\text{to}\text{produce}\\ \text{each}\text{unit}\text{of}\text{product}\text{B}\end{array})\text{=}\frac{\text{Total}\text{labor}\text{cost}\text{per}\text{unit}}{\text{Per}\text{hour}\text{wage}\text{rate}}\\ \text{=}\frac{\text{\$20}}{\text{\$10}}\\ \text{=2}\text{hours}\end{array}$

(4)

Calculate the time taken to produce each unit of Product M:

$\begin{array}{c}\begin{array}{l}\text{Time}\text{taken}\text{to}\text{produce}\\ \text{each}\text{unit}\text{of}\text{product}\text{M}\end{array})\text{=}\frac{\text{Total}\text{labor}\text{cost}\text{per}\text{unit}}{\text{Per}\text{hour}\text{wage}\text{rate}}\\ \text{=}\frac{\text{\$50}}{\text{\$10}}\\ \text{=5 hours}\end{array}$

(5)

Calculate the total time taken to produce the estimated production of Product B:

$\begin{array}{c}\text{Total}\text{time}\text{taken}\text{=}\left(\begin{array}{l}\text{Estimated}\text{prodction}\text{×}\text{Time}\text{taken}\text{to}\\ \text{produce}\text{each}\text{unit}\text{of}\text{product}\text{B}\end{array}\right)\\ \text{=}\text{30,000}\text{units}\text{×}\text{2}\text{(4)hours}\text{per}\text{unit}\\ \text{=}\text{60,000}\text{hours}\end{array}$

(6)

Calculate the total time taken to produce the estimated production of Product M:

$\begin{array}{c}\text{Total}\text{time}\text{taken}\text{=}\left(\begin{array}{l}\text{Estimated}\text{prodction}\text{×}\text{Time}\text{taken}\text{to}\\ \text{produce}\text{each}\text{unit}\text{of}\text{product}M\end{array}\right)\\ \text{=}10\text{,000}\text{units}\text{×}5(5)\text{hours}\text{per}\text{unit}\\ \text{=}50\text{,000}\text{hours}\end{array}$

(7)

Calculate the allocation rate per hour:

$\begin{array}{c}\text{Allocation}\text{rate}\text{per}\text{unit}\text{=}\frac{\text{Fixed}\text{Overhead}}{\text{Total}\text{direct}\text{labor}\text{hours}}\\ \text{=}\frac{\text{\$2,500,000}}{\text{110,000}\text{hours}}\\ \text{=\$22}\text{.73per}\text{hour}\end{array}$

Note:$\text{110,000}\text{hours}\text{=}6\text{0,000}\text{hours}\text{+}50\text{,000}\text{hours}$

(8)

Calculate the fixed overhead cost of Product B:

$\begin{array}{c}\text{Fixed}\text{overhead}\text{cost}\text{of}\text{Product}\text{B}\text{=}\left(\begin{array}{l}\text{Time}\text{taken}\text{to}\text{produce}\text{each}\text{unit}\text{of}\\ \text{product}\text{×}\text{Allocation}\text{rate}\text{per}\text{unit}\end{array}\right)\\ \text{=2}\text{hours}\text{(4)×}\text{\$22}\text{.73/}\text{hours (8)}\\ \text{=}\text{\$45}\text{.46}\end{array}$

(9)

Calculate the fixed overhead cost of Product M:

$\begin{array}{c}\text{Fixed}\text{overhead}\text{cost}\text{of}\text{Product}\text{M}\text{=}\left(\begin{array}{l}\text{Time}\text{taken}\text{to}\text{produce}\text{each}\text{unit}\text{of}\\ \text{product}\text{×}\text{Allocation}\text{rate}\text{per}\text{unit}\end{array}\right)\\ \text{=5}\text{hours}\text{(5)×}\text{\$22}\text{.73/}\text{hours}\text{(8)}\\ \text{=}\text{\$113}\text{.65}\end{array}$

(10)

d.

To determine

Estimate the total manufacturing cost per unit of each product if activity-based costing is used for assigning fixed overhead costs and state the product that is earning the desired income under this method.

Explanation of Solution

Manufacturing overhead costs:

Manufacturing overhead costs are costs that are not directly related with the manufacturing of the products and it is also known as indirect costs. For example, indirect materials, indirect labour, indirect supplies.

Calculate the total manufacturing cost per unit of the products:

Particulars	Product B	Product M
Direct materials cost per unit	$25	$40
Direct labor cost per unit	$20	$50
Variable overhead cost	$5	$12.50
Fixed overhead cost (11)	$38.31	$85.07
Total manufacturing cost per unit	$88.31	$187.57

Table (3)

Therefore, the total manufacturing cost per unit of Product B and Product M is $88.31 and $187.57.

Working note:

Calculate the fixed overhead allocation per unit:

Particulars	Product B	Product M	Allocation rate per unit	Total fixed overhead cost
Activity cost pools	(a)	(b)	(c)	Product B (d) = (a) × (c)	Product M (d) = (b) × (c)
Setup costs	100	$00	$875	$87,500	$262,500
Purchase orders	300	100	$1,625	$487,500	$162,500
Machining	3,000	4,000	$71.43	$214,290	$285,70
Inspection	40	20	$5,000	$200,000	$100,000
Shipping	400	100	$400	$160,000	$40,000
Total fixed overhead allocated units produced				$1,149,290	$850,720
÷Units produced				÷30,000	÷10,000
Fixed overhead cost per unit				$38.31	$85.07

Table (4)

Note: For the calculation of allocation rate per unit refer Table (5)

(11)

Calculate the allocation rate of each overhead:

Overhead costs (a)	Rate per set up ( Product B) (b)	Rate per set up ( Product M) (c)	Total rate per set up (d)=(b)+(c)	Allocation rate per unit activity (e) = (a) ÷ (d)
Machine setups $350,000	100	300	$400	$ 875
Purchase orders $650,000	300	100	$400	$1,625
Machining rate $500,000	3,000	4,000	$7,000	$71.43
Inspection  $200,000	40	20	$60	$5,000
Shipping $300,000	400	100	$500	$400

 Table (5)

(12)

Conclusion

• The cost per unit of Product B is below the target cost of 105.60 thus, it is earning a return greater than the desired rate.
• The cost per unit of Product M is above the target cost of $180 thus, it is not earnings the desired return.

e.

To determine

State the proportion of fixed overhead that is value added and mention the activity which can be improved first.

Explanation of Solution

• Machining and shipping are the two fixed overhead activities that are value added and the proportion of these costs to total fixed overhead is calculated below:

            $\begin{array}{c}\begin{array}{l}\text{Proportion}\text{of}\text{overhead}\\ \text{costs}\text{to}\text{total}\text{fixed}\text{costs}\end{array})\text{=}\frac{\text{Machining}\text{+}\text{Shipping}}{\text{Total}\text{fixed}\text{costs}}\text{×}\text{100}\\ \text{=}\frac{\text{\$500,000+\$200,000}}{\text{\$2,000,000}}\text{×100}\\ \text{=35\%}\end{array}$

• Therefore, the proportion of machining and shipping overheads to total fixed costs is 35 %.
• The number of steps taken to produce Product M can be reduced and it appears to be a logical activity.

f.

To determine

Ascertain the impact of the design changes on the manufacturing costs of both products and mention the products that will earn the desired return.

Explanation of Solution

Manufacturing overhead costs:

Manufacturing overhead costs are costs that are not directly related with the manufacturing of the products and it is also known as indirect costs. For example, indirect materials, indirect labour, indirect supplies.

Calculate the manufacturing costs of Product B and Product M:

Particulars	Product B	Product M
Direct materials cost per unit	$25	$40
Direct labor cost per unit	$20	$50
Variable overhead cost	$5	$12.50
Fixed overhead cost  (13)	$42.06	$73.82
Total manufacturing cost per unit	$92.06	$176.32

Table (6)

Working note:

Calculate the fixed overhead cost of Product B and Product M:

Particulars	Product B	Product M	Allocation rate per unit	Total fixed overhead cost
Activity cost pools	(a)	(b)	(c)	Product B (d) = (a) × (c)	Product M (d) = (b) × (c)
Setup costs	100	75	$2,000	$200,000	$200,000
Purchase orders	300	100	$1,625	$487,500	$162,500
Machining	3,000	4,000	$71.43	$214,290	$285,70
Inspection	40	20	$5,000	$200,000	$100,000
Shipping	400	100	$400	$160,000	$40,000
Total fixed overhead allocated units produced				$1,261,790	$738,220
÷Units produced				÷30,000	÷10,000
Fixed overhead cost per unit				$42.06	$73.82

Table (7)

Note: For the calculation of allocation rate per unit except for setup costs refer Table (5)

(13)

Calculate the new allocation rate per machine setup:

$\begin{array}{c}\text{Allocation}\text{rate}\text{per}\text{unit}\text{(machine}\text{setup)}\text{=}\frac{\text{Fixed}\text{overhead}}{\text{Total}\text{units}\text{of}\text{production}}\\ \text{=}\frac{\text{\$350,000}}{\text{100}\text{(Product}\text{k)+75}\text{(Product}\text{Q)}}\\ \text{=}\text{\$2,000}\text{per}\text{unit}\end{array}$

(14)

Note: Units of production for Product M is reduced to 75 units.

Conclusion

• The cost per unit of Product B is below the target cost of $105.60 thus, it will earn more than the desired return.
• The cost per unit of Product M is above the target cost of $158.40 thus, it is earning lower than the desired rate.

g.

To determine

Calculate the manufacturing costs for each product if the machine is purchased and find out whether the Product M should be redesigned or should the machine be purchased.

Explanation of Solution

Manufacturing overhead costs:

Manufacturing overhead costs are costs that are not directly related with the manufacturing of the products and it is also known as indirect costs. For example, indirect materials, indirect labour, indirect supplies.

Calculate the manufacturing costs for each product if a new machine is purchased:

Particulars	Product B	Product M
Direct materials cost per unit	$25	$40
Direct labor cost per unit	$20	$50
Variable overhead cost	$5	$12.50
Fixed overhead cost (15)	$37.81	$79.12
Total manufacturing cost per unit	$87.81	$181.62

Table (8)

Working note:

Calculate the total fixed overhead allocated per unit:

Particulars	Product B	Product M	Allocation rate per unit	Total fixed overhead cost
Activity cost pools	(a)	(b)	(c)	Product B (d) = (a) × (c)	Product M (d) = (b) × (c)
Setup costs	50	140	$1,450	$72,500	$203,000
Purchase orders	300	100	$1,625	$487,500	$162,500
Machining	3,000	4,000	$71.43	$214,290	$285,70
Inspection	40	20	$5,000	$200,000	$100,000
Shipping	400	100	$400	$160,000	$40,000
Total fixed overhead allocated units produced				$1,134,290	$791,220
÷Units produced				÷30,000	÷10,000
Fixed overhead cost per unit				$37.81	$79.12

Table (9)

Note: For the calculation of allocation rate per unit except for setup costs refer Table (5)

(15)

Calculate the new allocation rate per machine setup:

$\begin{array}{c}\text{Allocation}\text{rate}\text{per}\text{unit}\text{(machine}\text{setup)}\text{=}\frac{\text{Fixed}\text{overhead}}{\text{Total}\text{units}\text{of}\text{production}}\\ \text{=}\frac{\text{\$275,000}}{\text{50}\text{(Product}\text{B)+80}\text{(Product}\text{M)}}\\ \text{=}\text{\$1,450}\text{per}\text{unit}\end{array}$

(16)

Note: Units of production for Product B is reduced to 50 units and for Product M it is reduced to 140 units.

Conclusion

• The cost per unit of product B is below the target cost of $105.6 thus, it is earning a return greater than the desired 12% rate.
• The cost per unit of Product M is above the target cost of $158.60 thus, it will not earn the desired return.
• Purchasing new machine or redesigning of product M makes the cost of both the products below the target cost since, the new machine reduces the fixed set-up costs it might be a cots reducing decision.
• Information relating to purchase of new equipment and purchase price are missing for making decision related to the purchase of new equipment.