United States Motors Inc. (USMI) manufactures automobiles andlight trucks and distributes them for sale to consumers throughfranchised retail outlets. As part of the franchise agreement,dealerships must provide monthly financial statements following theUSMI accounting procedures manual. USMI has developed the followingfinancial profile of an average dealership that sells 3,100 newvehicles annually:
| AVERAGE DEALERSHIP FINANCIAL PROFILE |
| Composite Income Statement |
| Sales | $ | 62,000,000 | |
| Cost of goods sold | | 51,150,000 | |
| Gross profit | $ | 10,850,000 | |
| Operating costs | | | |
| Variable | | 1,782,500 | |
| Mixed | | 4,774,000 | |
| Fixed | | 3,831,600 | |
| Operating income | $ | 461,900 | |
|
USMI is considering a major expansion of its dealership network.The vice president of marketing has asked Jack Snyder, corporatecontroller, to develop some measure of the risk associated with theaddition of these franchises. Jack estimates that 90% of the mixedcosts shown are variable for purposes of this analysis. He alsosuggests performing regression analyses on the various componentsof the mixed costs to more definitively determine theirvariability.
Required:
1. Calculate the composite dealership profit if 4,400 units aresold.
3. The regression equation that Jack Snyder developed to projectannual sales of a dealership has an R-squared of 60% and astandard error of the estimate of $9,300,000. If the projectedannual sales for a dealership total $58,900,000, determine theapproximate 95% confidence interval for Jack’s prediction of sales.(Hint: The 95% confidence interval uses 2 standard errorsin determining the interval.)
