Chapter 19, Problem 2AP

a.

To determine

Calculate the target cost for Product K and Product Q.

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 K.

$\begin{array}{c}\text{Target}\text{cost}\text{=}\text{Target}\text{price}-\text{Target}\text{profit}\\ \text{=\$120}-\text{\$18}\text{(1)}\\ \text{=\$102}\end{array}$

Working note:

$\begin{array}{c}\text{Target}\text{profit}\text{=}\text{Percentage}\text{of}\text{return}\text{on}\text{sales}\text{×}\text{Target}\text{price}\\ \text{=15\%}\text{×}\text{\$120}\\ \text{=\$18}\end{array}$

(1)

Calculate the target cost of the product Q.

$\begin{array}{c}\text{Target}\text{cost}\text{=}\text{Target}\text{price}-\text{Target}\text{profit}\\ \text{=\$220}-\text{\$33}\text{(2)}\\ \text{=\$187}\end{array}$

Working note:

$\begin{array}{c}\text{Target}\text{profit}\text{=}\text{Percentage}\text{of}\text{return}\text{on}\text{sales}\text{×}\text{Target}\text{price}\\ \text{=15\%}\text{×}\text{\$220}\\ \text{=\$33}\end{array}$

(2)

Therefore, the target cost of product K is $102 and product Q is $187.

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 which 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 K	Product Q
Direct materials cost per unit	$30	$45
Direct labor cost per unit	$24	$60
Variable overhead cost	$6	$15
Fixed overhead cost  (3)	$50	$50
Total manufacturing cost per unit	$110	$170

Table (1)

• The cost per unit of Product K is above its target cost of $102, thus it is not earnings the desired 15% return.
• The cost per unit of Product Q is below its target cost of $187, thus it is earnings a greater return than the desired rate.

Working note:

Calculate the fixed overhead cost per unit:

$\begin{array}{c}\text{Allocation}\text{rate}\text{per}\text{unit}\text{=}\frac{\text{Fixed}\text{overhead}}{\text{Total}\text{units}\text{of}\text{production}}\\ \text{=}\frac{\text{\$2,000,000}}{\text{25,000}\text{(Product}\text{k)+15,000}\text{(Product}\text{Q)}}\\ \text{=}\text{\$50}\text{per}\text{unit}\end{array}$

(3)

Conclusion

• The manufacturing cost per unit of product K is $110 and for product Q is $170.
• Product Q is earning the desired income from the above estimation.

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 identify 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 K	Product Q
Direct materials cost per unit	$30	$45
Direct labor cost per unit	$24	$60
Variable overhead cost	$6	$15
Fixed overhead cost	$32	$80
Total manufacturing cost per unit	$92	$200

Table (2)

• The cost per unit of Product K is below its target cost of $102 thus, it is earning a greater return than the desired rate.
• The cost per unit of Product Q is above its target cost of $187 thus, it is not earnings the desired return.

Working notes:

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

$\begin{array}{c}\begin{array}{l}\text{Time}\text{taken}\text{to}\text{produce}\\ \text{each}\text{unit}\text{of}\text{product}\text{K}\end{array})\text{=}\frac{\text{Total}\text{labor}\text{cost}\text{per}\text{unit}}{\text{Per}\text{hour}\text{wage}\text{rate}}\\ \text{=}\frac{\text{\$24}}{\text{\$12}}\\ \text{=2}\text{hours}\end{array}$

(4)

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

$\begin{array}{c}\begin{array}{l}\text{Time}\text{taken}\text{to}\text{produce}\\ \text{each}\text{unit}\text{of}\text{product}\text{Q}\end{array})\text{=}\frac{\text{Total}\text{labor}\text{cost}\text{per}\text{unit}}{\text{Per}\text{hour}\text{wage}\text{rate}}\\ \text{=}\frac{\text{\$60}}{\text{\$12}}\\ \text{=5 hours}\end{array}$

(5)

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

$\begin{array}{c}\text{Total}\text{time}\text{taken}\text{=}\left(\begin{array}{l}\text{Estimated}\text{prodction}\text{×}\text{Time}\text{taken}\text{to}\\ \text{produce}\text{each}\text{unit}\text{of}\text{product}\text{K}\end{array}\right)\\ \text{=}\text{25,000}\text{units}\text{×}\text{2}(4)\text{hours}\text{per}\text{unit}\\ \text{=}\text{50,000}\text{hours}\end{array}$

(6)

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

$\begin{array}{c}\text{Total}\text{time}\text{taken}\text{=}\left(\begin{array}{l}\text{Estimated}\text{prodction}\text{×}\text{Time}\text{taken}\text{to}\\ \text{produce}\text{each}\text{unit}\text{of}\text{product}\text{K}\end{array}\right)\\ \text{=}15\text{,000}\text{units}\text{×}5(5)\text{hours}\text{per}\text{unit}\\ \text{=}75\text{,000}\text{hours}\end{array}$

(7)

Calculate the allocation rate per hour:

$\begin{array}{c}\text{Allocation}\text{rate}\text{per}\text{unit}\text{=}\frac{\text{Fixed}\text{Overhead}}{\text{Total}\text{direct}\text{labor}\text{hours}}\\ \text{=}\frac{\text{\$2,000,000}}{\text{125,000}\text{hours}}\\ \text{=\$16}\text{per}\text{hour}\end{array}$

Note:$\text{125,000}\text{hours}\text{=}\text{50,000}\text{hours}\text{+}\text{75,000}\text{hours}$

(8)

Calculate the fixed overhead cost of product K:

$\begin{array}{c}\text{Fixed}\text{overhead}\text{cost}\text{of}\text{Product}\text{k}\text{=}\left(\begin{array}{l}\text{Time}\text{taken}\text{to}\text{produce}\text{each}\text{unit}\text{of}\\ \text{product}\text{×}\text{Allocation}\text{rate}\text{per}\text{unit}\end{array}\right)\\ \text{=2}\text{hours}(\text{4)×}\text{\$16/}\text{hours (8)}\\ \text{=}\text{\$32}\end{array}$

(9)

Calculate the fixed overhead cost of product Q:

$\begin{array}{c}\text{Fixed}\text{overhead}\text{cost}\text{of}\text{Product}\text{Q}\text{=}\left(\begin{array}{l}\text{Time}\text{taken}\text{to}\text{produce}\text{each}\text{unit}\text{of}\\ \text{product}\text{×}\text{Allocation}\text{rate}\text{per}\text{unit}\end{array}\right)\\ \text{=5}\text{hours}(5)\text{×}\text{\$16/}\text{hours}\text{(8)}\\ \text{=}\text{\$80}\end{array}$

(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 K	Product Q
Direct materials cost per unit	$30	$45
Direct labor cost per unit	$24	$60
Variable overhead cost	$6	$15
Fixed overhead cost (11)	$36.40	$72.67
Total manufacturing cost per unit	$96.40	$192.67

Table (3)

Therefore, the total manufacturing cost per unit of product K and Product Q is $96.40 and $192.67.

Working note:

Calculate the fixed overhead allocation per unit:

Particulars	Product K (In numbers)	Product Q (In numbers)	Allocation rate per unit	Total fixed overhead cost
Activity cost pools	(a)	(b)	(c)	Product K (d) = (a) × (c)	Product Q (d) = (b) × (c)
Setup costs	100	400	$800	$80,000	$320,000
Purchase orders	200	100	$2,000	$400,000	$200,000
Machining	2,000	6,000	$63	$125,000	$375,000
Inspection	50	30	$2,500	$125,000	$75,000
Shipping	300	200	$600	$180,000	$120,000
Total fixed overhead allocated units produced				$910,000	$1,090,000
÷Units produced				÷25000	÷15000
Fixed overhead cost per unit				$36.40	$72.67

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 k) (b)	Rate per set up ( Product Q) (c)	Total rate per set up (d)=(b)+(c)	Allocation rate per unit activity (e) = (a) ÷ (d)
Machine setups $400,000	$100	$400	$500	$800
Purchase orders $600,000	$200	$100	$300	$2,000
Machining rate $500,000	$2,000	$6,000	$8,000	$62.50 (or) $63
Inspection  $200,000	$50	$30	$80	$2,500
Shipping $300,000	$300	$200	$500	$600

 Table (5)

(12)

Conclusion

• The cost per unit of Product K is below the target cost of $102, thus it is earning a return greater than the desired rate.
• The cost per unit of Product Q is above the target cost of $187, 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:

            $\begin{array}{c}\begin{array}{l}\text{Proportion}\text{of}\text{overhead}\\ \text{costs}\text{to}\text{total}\text{fixed}\text{costs}\end{array})\text{=}\frac{\text{Machining}\text{+}\text{Shipping}}{\text{Total}\text{fixed}\text{costs}}\text{×}\text{100}\\ \text{=}\frac{\text{\$500,000+\$300,000}}{\text{\$2,000,000}}\text{×100}\\ \text{=40\%}\end{array}$

• Therefore, the proportion of machining and shipping overheads to total fixed costs is 40%.
• The number of steps taken to produce product Q can be reduced and this 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 K and Product Q:

Particulars	Product K	Product Q
Direct materials cost per unit	$30	$45
Direct labor cost per unit	$24	$60
Variable overhead cost	$6	$15
Fixed overhead cost  (13)	$46	$57
Total manufacturing cost per unit	$106	$177

Table (6)

Working note:

Calculate the fixed overhead cost of product K and product Q:

Particulars	Product K (In numbers)	Product Q (In numbers)	Allocation rate per unit	Total fixed overhead cost
Activity cost pools	(a)	(b)	(c)	Product K (d) = (a) × (c)	Product Q (d) = (b) × (c)
Setup costs	$100	$25	(14)$3,200	$320,000	$80,000
Purchase orders	$200	$100	$2,000	$400,000	$200,000
Machining	$2,000	$6,00	$62.50	$125,000	$375,000
Inspection	$50	$30	$2,500	$125,000	$75,000
Shipping	$300	$200	$600	$180,000	$120,000
Total fixed overhead allocated units produced				$1,150,000	$850,000
÷Units produced				÷25,000	÷15,000
Fixed overhead cost per unit				$46	$56.67

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:

$\begin{array}{c}\text{Allocation}\text{rate}\text{per}\text{unit}\text{(machine}\text{setup)}\text{=}\frac{\text{Fixed}\text{overhead}}{\text{Total}\text{units}\text{of}\text{production}}\\ \text{=}\frac{\text{\$400,000}}{\text{100}\text{(Product}\text{k)+25}\text{(Product}\text{Q)}}\\ \text{=}\text{\$3,200}\text{per}\text{unit}\end{array}$

(14)

Note: Units of production for product Q is reduced to 25 units.

Conclusion

• The cost per unit of Product K is above the target cost of $102 thus, it will not earn the desired 15% return.
• The cost per unit of Product Q is below the target cost of $187 thus, it will earn a return greater 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 Q 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 K	Product Q
Direct materials cost per unit	$30	$45
Direct labor cost per unit	$24	$60
Variable overhead cost	$6	$15
Fixed overhead cost (15)	$34.80	$62
Total manufacturing cost per unit	$94.80	$182

Table (8)

Working note:

Calculate the total fixed overhead allocated per unit:

Particulars	Product K	Product Q	Allocation rate per unit	Total fixed overhead cost
Activity cost pools	(a)	(b)	(c)	Product K (d) = (a) × (c)	Product Q (d) = (b) × (c)
Setup costs	$20	$80	(16)$2,000	$40,000	$160,000
Purchase orders	$200	$100	$2,000	$400,000	$200,000
Machining	$2,000	$6,00	$62.50	$125,000	$375,000
Inspection	$50	$30	$2,500	$125,000	$75,000
Shipping	$300	$200	$600	$180,000	$120,000
Total fixed overhead allocated units produced				$870,000	$930,000
÷Units produced				÷25,000	÷15,000
Fixed overhead cost per unit				$34.80	$62

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:

$\begin{array}{c}\text{Allocation}\text{rate}\text{per}\text{unit}\text{(machine}\text{setup)}\text{=}\frac{\text{Fixed}\text{overhead}}{\text{Total}\text{units}\text{of}\text{production}}\\ \text{=}\frac{\text{\$200,000}}{20\text{(Product}\text{k)+80}\text{(Product}\text{Q)}}\\ \text{=}\text{\$2,000}\text{per}\text{unit}\end{array}$

(16)

Note: Units of production for product K is reduced to 20 units and for product Q is 80 units.

Conclusion

• The machine is purchased because the total manufacturing costs is reduced by $200,000 that will increase profits by $200,000.
• If Product Q is redesigned, there is no increase in profits, just a reallocation of fixed costs between the two products occurs.