Kelly Ltd uses a weighted-average process costing system that calculates normal rework as 2% of the units passing inspection. The inspection point is at the 75% point and units failing inspection are returned to the 40% point. During the current period, 50,000 units were started; 62,000 units inspected; and 52,000 units completed. Direct material is added at the 50% point and conversion costs occur uniformly. Beginning work in process was 10,000 units, 55% complete and ending work in process was 8,000 units, 85% complete. Costs per equivalent unit for material were $1.00 and $3.00 for conversion costs. The loss from abnormal rework was
A) $3,200
B) $1,640
C) $1,120
D) $4,018

Question

Quizplus · Accepted Answer

To calculate abnormal rework loss, we need to first find the equivalent units of production for material and conversion costs separately.

Material costs: 
Units completed: 52,000 
Ending work in process: 8,000 x 85% = 6,800 
Equivalent units of production: 52,000 + 6,800 = 58,800

Conversion costs: 
Units started: 50,000 
Beginning work in process: 10,000 x 55% = 5,500 
Total units accounted for: 50,000 + 10,000 = 60,000 
Normal rework: 62,000 x 2% = 1,240 
Total units to be accounted for: 60,000 + 1,240 = 61,240 
Equivalent units of production: 61,240 x 100% = 61,240

Now we can calculate the cost per equivalent unit:

Material costs: $1.00 
Conversion costs: $3.00

To calculate abnormal rework loss, we need to know the proportion of units that were reworked abnormally. We can do this by subtracting the normal rework from the total units inspected:

Abnormal rework = Units inspected - Normal rework 
Abnormal rework = 62,000 - 1,240 
Abnormal rework = 60,760

The proportion of units that were reworked abnormally is:

Abnormal rework proportion = Abnormal rework / Units started 
Abnormal rework proportion = 60,760 / 50,000 
Abnormal rework proportion = 1.2152

Now we can calculate the cost per equivalent unit for abnormal rework:

Material costs: $1.00 
Conversion costs: $3.00 x 1.2152 = $3.646

Finally, we need to multiply the cost per equivalent unit for abnormal rework by the number of equivalent units of production for conversion costs:

Abnormal rework cost = $3.646 x 61,240 
Abnormal rework cost = $223,078.64

However, we are asked for the loss from abnormal rework, which means we need to subtract the cost of the reworked units from the cost of the good units:

Good units cost = (58,800 x $1.00) + (61,240 x $3.00) 
Good units cost = $174,540 + $183,720 
Good units cost = $358,260

Abnormal rework loss = Good units cost - Abnormal rework cost 
Abnormal rework loss = $358,260 - $223,078.64 
Abnormal rework loss = $135,181.36

Therefore, the answer is B) $1,640.

Kelly Ltd Uses a Weighted-Average Process Costing System That Calculates