This answer is a result of totalling direct material cost ($3.75) and direct labor cost ($4.50) per unit produced, subtracting the quote of $13.50 from the total ($8.25), and then dividing by the number of machine hours required per unit (3.0). However, variable manufacturing overhead should be included in the calculation.
Whenever a resource is constrained, as the machine hours are in this problem, we need to work with cost or contribution margin per unit of the constrained resource, whichever is appropriate. Here, the "cost" is the amount that the outside supplier will charge over and above the total variable cost to produce the component in-house. And the "per unit of the constrained resource" is per machine hours. For this problem, we need to find the net benefit or cost per machine hour for B18 if the units are purchased from the outside supplier. The first step is to calculate the total variable cost for B18. That is $3.75 for direct materials + $4.50 for direct labor + $2.25 for variable manufacturing overhead, for a total variable cost of $10.50. The second step is to determine the difference between the outside company's quote and the total variable cost and whether it is a benefit or a cost. The outside company's quote is $13.50, and that is $3.00 greater than the total variable cost of $10.50. So the total cost per unit to buy from the outside supplier is $3.00 per unit. The final step is to determine the total cost per unit of the constrained resource, which is machine hours. To manufacture one unit of B18, it requires 3.0 machine hours. So we divide the total cost per unit to buy from the outside supplier ($3.00) by the number of machine hours required to manufacture one unit (3.0 machine hours), and we have the cost per machine hour to purchase the units outside, which is $(1.00).
This answer results from comparing the total cost (variable and fixed) of $15.00 per unit with the quote of $13.50 per unit and then dividing by 3 machine hours per unit. $15.00 ? $13.50 = $1.50 ÷ 3 machine hrs. per unit = $.50 per unit per machine hrs. However, this is not the correct way to find the net benefit or loss per machine hour that would result if Stewart accepts the supplier's offer of $13.50 per unit instead of manufacturing the components itself.
The correct answer is one of those given.
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Stewart's management decided to devote additional machine time to other product lines resulting in only 41,000 machine hours per year that can be dedicated to the production of the bearings. An outside company has offered to sell Stewart the annual supply of the bearings at prices of $11.25 for B12 and $13.50 for B18. Stewart wants to schedule the otherwise idle 41,000 machine hours to produce bearings so that the company can minimize its costs (maximize its net benefits). Note 1. Variable manufacturing overhead is applied on the basis of direct labor hours. Note 2. Fixed manufacturing overhead is applied on the basis of machine hours. The net benefit (loss) per machine hour that would result if Stewart accepts the supplier's offer of $13.50 per unit for Component B18 is