Chapter 6, Problem 25P

To determine

To compute: The unit production cost in each year under absorption costing method. And segregate the variable and fixed cost.

Answer to Problem 25P

Solution: The cost per unit is $11.60 in year 1, $10 in year 2 and $14 in year 3.

Explanation of Solution

Statement that shows the calculation of unit cost of product,

Particulars	Year 1($)	Year 2($)	Year 3($)
Production (A)	50,000	60,000	40,000
Variable manufacturing cost $\left(\text{A}\times \$2\right)$	100,000	120,000	80,000
Add: Fixed manufacturing expense (given)	480,000	480,000	480,000
Total manufacturing cost (B)	580,000	600,000	560,000
Cost per unit $\left(\frac{\text{A}}{\text{B}}\right)$	11.6	10	14

Table (2)

Thus, the cost per unit is $11.60 in year 1, $10 in year 2 and $14 in year 3.

b.

To determine

Reconcile the variable costing and absorption costing net operating income for each year.

Answer to Problem 25P

Solution: The net income under absorption costing for year 1 is $30,000, for year 2 is $60,000 and net loss for year 3 is $-$ $10,000.

Explanation of Solution

Reconcile the variable costing and absorption costing net operating income for each year.

Particulars	Year 1($)	Year 2($)	Year 3($)
Net income (loss) under variable costing (A)	30,000	(100,000)	30,000
Add/ (deduct) fixed manufacturing overhead cost (working notes) (B)		160,000	(160,000)
Realized in year 2 and in year 3
Add/ (deduct) fixed manufacturing overhead cost (working notes) (C)			120,000
Realized in year 3
Net income (loss) under absorption costing $\left(\text{B}-\text{A}-\text{C}\right)$	30,000	60,000	(10,000)

Table (3)

Working Notes:

Particulars	Year 1	Year 2	Year 3
Ending inventory units (A)	0	20,000 units	10,000 units
Ending inventory value under absorption costing (B)	-	200,000	140,000
Variable manufacturing cost per unit (C)	2	2	2
Ending inventory value under variable costing $\left(\text{A}\times \text{C}\right)$ (D)	0	40,000	20,000
Cost of production carried over to next month under absorption costing is $\left(\text{B}-\text{D}\right)$	0	160,000	120,000

Table (4)

Thus, the net income under absorption costing for year 1 is $30,000, for year 2 is $60,000 and net loss for year 3 is $-$ $10,000.

3.

To determine

To explain: With the help of absorption costing statement given in question the operating income of year 2 is higher than the operating income of year 1 as the sold units are less than the year 1.

Answer to Problem 25P

Solution: The operating income of year 2 is more than year 1 although the unit sold of year 2 is less than the year 1; the reason of more operating income is gross margin ratio. As the gross margin ratio of year 2 is more than year 1.

Explanation of Solution

Statement that shows the calculation of gross margin ratio.

Particulars	Year 1($)	Year 2($)
Gross margin (given) (A)	220,000	240,000
Sales revenue (given) (B)	800,000	640,000
Gross margin ratio$\left[\frac{\text{A}}{\text{B}}\times 100\right]$	27.5%	37.5%

Table (5)

Thus, the operating income of year 2 is more than year 1.

4.

To determine

To explain: The reason why company suffered a loss in year 3 as it has profit in year 1 and the number of unit sold is same in year 1 and in year 3.

Answer to Problem 25P

Solution: The reason of loss in year 3 is that the gross margin is less than the selling and administrative expense. As the company planning related to selling and administrative expense is not correct and the reason is gross margin ratio. The gross margin ratio of year 3 is less than year 1.

Explanation of Solution

Statement that shows the calculation of gross margin ratio.

Particulars	Year 1($)	Year 3($)
Gross margin (given) (A)	220,000	180,000
Sales revenue (given) (B)	800,000	800,000
Gross margin ratio$\left[\frac{\text{A}}{\text{B}}\times 100\right]$	27.5%	22.5%

Table (6)

Thus, the reason of loss is that in year 3 the gross margin ratio is less as compare to year 1.

5.

a.

To determine

To explain: If company uses lean production, how operation is differed in year 2 and in year 3 and the ending inventory is zero.

Answer to Problem 25P

Solution: If company uses the technique of lean production with zero inventories then in that case the company uses the full resources optimally. In this case the level of production will increase, sales quantity will increase and ultimately the operating profit will increase.

Explanation of Solution

Lean production is a managerial approach that manager uses to reduce the amount of wastage. The aim of lean production is to minimize the wastage and maximize the profit.

Thus, the use of lean accounting increases the efficiency of work and reduces the wastage.

b.

To determine

To compute: The operating income of the company under absorption costing with the help of lean accounting.

Answer to Problem 25P

Solution: The net operating income of year 1 is $30,000, year 3 is 50,000 and loss for year 2 is $ $-$ 4,000.

Explanation of Solution

Statement that shows the calculation of operating income is,

Particulars	Year 1($)	Year 2($)	Year 3($)
Production unit (A)	50,000 units	50,000 units	40,000 units
Sales units (given) (B)	50,000 Units	40,000 Units	50,000 Units
Sales (given)	800,000	640,000	800,000
Cost of goods sold
Variable manufacturing cost $\left(\text{A}\times \$2\right)$	100,000	100,000	80,000
Fixed manufacturing cost	480,000	480,000	480,000
Total manufacturing cost	580,000	580,000	560,000
Less: Ending inventory $\left(10,000\text{ units}\times \$11.60\right)$	0	116,000	0
Cost of goods sold	580,000	464,000	560,000
Gross margin (1) $\left(\text{Sales}-\text{Cost of goods sold}\right)$	220,000	176,000	240,000
Sales and administrative expense
Add: Variable selling and administrative $\left(\text{B}\times \$1\right)$	50,000	40,000	50,000
Fixed selling and administrative expense	140,000	140,000	140,000
Total selling and administrative expense (2)	190,000	180,000	190,000
Net operating income $\left(1-2\right)$	30,000	$-4,000$	50,000

Table (7)

Thus, the net operating income of year 1 is $30,000, year 3 is 50,000 and loss for year 2 is $ $-$ 4,000.