Performance Motors sells and services BMWs. The service department has recently leased a computerized diagnostic system for $1,600 per month which is used on both warranty and non-warranty work. The mechanic who runs the diagnostic system is paid a salary of $4,370 per month and has no other responsibilities. No other employees are trained to run the diagnostic system. Demand for time on the diagnostic system is high, and the machine is essentially always fully booked, often for at least one week in advance, and customers that call for an appointment are often told they will not be able to get in right away. Consequently, some customers (about 10% of those who call for an appointment) decide to go elsewhere for service.

Consumables are supplies used in the process of performing an engine diagnosis. (As shown in the table below, non-warranty work tends to require more consumables and more time on the diagnostic machine than does warranty work.)

Non-warranty work is charged to customers at an average rate of $90 per car, which is competitive with other service shops in the area. Warranty work done on the machine is charged directly to BMW of North America at a rate of $76 per car.

Monthly amounts shown in the table below are average results from the last year, and are believed to be representative of future monthly revenues and costs.

Warranty WorkNon-warranty workTotal

Cars processed85242327

Time on machine34 hrs121 hrs155 hrs

Cost of consumables$2,082.50$7,177.72$9,260.22

Revenue$6,460$21,780$28,240

Revenue per car$76.00$90.00

Performance Motors calculates cost per car for warranty work and for non-warranty by pro-rating the lease cost and mechanic's wages based on the number of cars processed, i.e., 26% to warranty work and 74% to non-warranty work.

Warranty WorkNon-warranty workTotal

Cars processed85242327

% of cars processed26%74%

Pro-rata share of lease cost$415.90$1,184.10$1,600.00

Pro-rata share of mechanic's wages$1,135.93$3,234.07$4,370.00

Cost of consumables$2,082.50$7,177.72$9,260.22

Total cost$3,634.33$11,595.89$15,230.22

Cost per car$42.757$47.917

Guy Smart, the owner of Performance Motors, is evaluating a recent offer: "BMW has asked us to take over all the warranty service on cars sold by BMW dealers outside our local area. Because we would be taking on about 40 additional cars of warranty work per month, we would not be able to finish much non-warranty work. I am worried about the effect of this change on profitability of our service operation. I know that we make more profit per car on non-warranty work, so I am concerned that we will see a decline in profit."

Cecil Hooper, the service manager, spoke up: "I am also concerned about the effect of this change on profitability of our service operation, though I look at the numbers slightly differently. To see the effect on profitability, we have to take into account the fact that the total amount of service we can do is constrained by the time available on our diagnostic machine. Therefore, we need to look at profit per hour of available machine time by dividing the profit per car by the number of hours per car required on the machine. However, I still arrive at the same conclusion: Because profit per hour of machine time is higher on non-warranty work, we are going to be less profitable if we do more warranty (and less non-warranty) work."

For the first four questions below, assume that it is not possible to increase the number of hours available on the diagnostic machine beyond 155 hours per month. In question 5, you will consider the possibility of increasing available time on the diagnostic machine.

1. The constraint in this case is time on the diagnostic machine, limited to 155 hours per month. If Performance Motors takes on 40 additional cars of warranty work each month, they will have to reduce the number of non-warranty cars serviced. What will be the required reduction in non-warranty cars?
2. Using the information in the tables above, explain how the profit-per-car and profit-per-hour measures discussed by Guy and Cecil are calculated.
3. Calculate the change in total profit that will result if Performance Motors takes on warranty work for an additional 40 cars per month and makes a corresponding reduction in the number of non-warranty cars serviced, by the amount you calculated in question 1.

Suggestion: There are various ways to finish calculation. One way which is slightly longer than necessary but is also likely to help you see what is wrong with Guy and Cecil's conclusions is to write out the equation that defines profit and use it to compare profit for the original mix of warranty and non-warranty cars and profit for the revised mix of warranty and non-warranty cars. The profit equation is

Profit = Revenue - Cost of Consumables - Cost of Wages and Lease for Diagnostic Machine

The first two terms depend on the mix of warranty versus non-warranty cars (because the revenue per car and consumables cost per car for warranty cars is different from the revenue per car and consumables cost per car for non-warranty cars) while the last term does not depend on the mix - the cost of wages and lease for the diagnostic machine is always $4,370 + $1,600 regardless of the mix.

1. Guy and Cecil both believe their measures can be used to evaluate the effect on profit if Performance Motors adjusts their product mix. However, the profit-per-car and profit-per-hour on the diagnostic machine measures are both misleading. The increase in the number of warranty cars multiplied by the profit per warranty car less the decrease in the number of non-warranty cars multiplied by the profit per non-warranty cars does not equal the change in profit you calculated in question 3. Similarly, theincreasein the number of diagnostic machine hours worked on warranty cars multiplied by the profit per hour on warranty cars less thedecreasein the number of diagnostic machine hours worked on non-warranty cars multiplied by the profit per hour worked on non-warranty cars does not equal the change in profit you calculated in question 3.
2. Explain to Guy and Cecil why the calculation using either of their measures is incorrect. That is, why is the simple intuition of shifting production toward the product with the highest profit per unit or the highest profit per hour on the diagnostic machine misleading?
3. Explain to Guy and Cecil how they could instead use contribution margin per car (or contribution margin per hour on the diagnostic machine) to find the effect of this change in product mix on profit.
4. Guy Smart is considering various ways to increase the total time available on the diagnostic machine each month.
5. First, Guy is considering ways to make a few additional hours on the machine, such as cross-training another employee to operate the machine when the primary mechanic is not available. What is the value to Performance Motors of each additional hour of diagnostic machine time, i.e., what is the maximum amount they could pay for each additional hour of time on the diagnostic machine without incurring a loss on the additional hour?
6. Second, Guy is considering a way to substantially increase diagnostic machine time by leasing a second machine at $1,600 per month and hiring a second mechanic to run the machine at $4,370 per month. Assume there is demand for 90 additional hours of work on non-warranty cars (180 non-warranty cars x .5 hours per car) each month on the second machine and no demand for additional warranty cars. Thus, total demand for time on the first and second machines combined will be 155 + 90 = 245 hours per month.) What will be the incremental effect on profit of leasing the second diagnostic machine?