Demand is so high for ElectroToy's newest product that either overtime or a second production shift is needed. The labor rate is $13.85/hour for a normal shift. There is a 50% premium for over- time and a 10% shift differential. Productivity is 5% lower for overtime, and there is a 4-hour
minimum for a second shift. Sick leave, retirement, vacation, and insurance bene?ts add 19% to the direct hourly cost.
For this product, 60 units per hour are produced on the ?rst shift. Each unit has $1.25 in material and $4.50 in purchased parts. The indirect cost for each is $2.12 for other assembly line costs. The ?rm's administrative, sales, and managerial costs are charged at 35% of total labor cost.
Mario has been asked to recommend the most cost-effective way to produce an extra 120 units per week beyond the 480 produced on the regular shift. Based on his experience and talking with others, he concludes the following:
1. The cost for the ?rst 480 and the average cost of the 600 per week are irrelevant. What matters is the marginal cost for another unit.
2. The direct labor cost for each unit produced on the second shift will be 30.2¢ (= $13.85 X 1.1 X 1.19/60). This includes the shift differential and the cost for employee bene?ts.
3. The lower productivity of overtime hours decreases output to 57 per hour (= 60 X .95). Thus, producing 60 takes 1.053 hours, which is the inverse of .95. Thus, the direct labor cost for overtime units is 43.4¢ (= $13.85 X 1.5 X 1.19 X 1.053/60).
4. The $5.75 (= $1.25 + $4.50) in material and purchased-parts cost can be ignored, since it is the same for both alternatives.
5. The indirect assembly line costs are determined by how long the assembly line runs. Thus, the unit cost is $2.12 for the second shift and $2.232 (= $2.12/.95) for overtime.
6. The overhead costs of 35% can be ignored. These costs are allocated based on labor costs, but they will not change between alternatives.
Based on this analysis, Mario concludes that the second shift will save a marginal cost of 29.6¢ per unit (= 43.4¢ + $2.232 - 30.2¢ - $2.12). Thus, he recommends using a second shift. Is this conclusion correct?