Question

A company is considering additional final inspection costs of $1 per unit before delivery to customers. The additional inspection should reduce the defective rate from 3 percent to 1 percent. If a defective unit is found, it is scrapped at no additional cost. The manufacturing costs before the final inspection are $200 per unit. The management believes that the external failure costs are $40 per defective unit.

Required:

Should the management incur the additional inspection costs?

Answer 1

If the company produced the 100 units, the total cost per good unit without incurring the additional final inspection costs
Manufacturing costs before the final inspection per unit	$              200
Multiply: Number of unit produced	100
Total Manufacturing Costs	$        20,000
External failure cost per unit	$                40
Multiply: Defective units (100*3%)	3
Total External failure cost	$              120
Number of units produced	100
Less: Defective units	3
Number of good units	97
Total Manufacturing Costs	$        20,000
Add: Total External failure cost	$              120
Total Cost	$        20,120
Divided by: Number of good units	97
Total Cost per good unit	$        207.42

If the company produced the 100 units, the total cost per good unit with incurring the additional final inspection costs
Manufacturing costs before the final inspection per unit	$              200
Multiply: Number of unit produced	100
Total Manufacturing Costs	$        20,000
External failure cost per unit	$                40
Multiply: Defective units (100*1%)	1
Total External failure cost	$                40
Number of units produced	100
Less: Defective units	1
Number of good units	99
Total Manufacturing Costs	$        20,000
Add: Total External failure cost	$                40
Add: Additional final inspection costs per unit (1*100)	$              100
Total Cost	$        20,140
Divided by: Number of good units	99
Total Cost per good unit	$        203.43

Total Cost per good unit
If additional inspection costs not incurred	$        207.42
If additional inspection costs incurred	$        203.43
Should the management incur the additional inspection costs	Yes
Lower cost per unit is $203.43 when additional inspection costs incurred. Therefore, management should incur additional inspection costs.