United States Motors Inc. (USMI) manufactures automobiles and light trucks and distributes them for sale to consumers through franchised retail outlets. As part of the franchise agreement, dealerships must provide monthly financial statements following the USMI accounting procedures manual. USMI has developed the following financial profile of an average dealership that sells 1,500 new vehicles annually.

AVERAGE DEALERSHIP FINANCIAL PROFILE

Composite Income Statement

Sales ................$30,000,000

Cost of goods sold ............ 24,750,000

Gross profit .............. $ 5,250,000

Operating costs

Variable expenses ........... 862,500

Mixed expenses ............ 2,300,000

Fixed expenses ............. 1,854,000

Operating income ............ $ 233,500

USMI is considering a major expansion of its dealership network. The vice president of marketing has asked Jack Snyder, corporate controller, to develop some measure of the risk associated with the addition of these franchises. Jack estimates that 90 percent of the mixed expenses shown are variable for purposes of this analysis. He also suggested performing regression analyses on the various components of the mixed expenses to more definitively determine their variability.

Required

1. Calculate the composite dealership profit if 2,000 units are sold.

2. Assume that regression analyses were performed on the separate components of the mixed expenses and that a coefficient of determination value of .60 was determined as applicable to aggregate mixed expenses over the relevant range.

a. Define the term relevant range.

b. Explain the significance of an R - squared value of .60 to USMI’s analysis.

c. Describe the limitations that may exist in applying the composite-based relationships to specific new dealerships that have been proposed.

d. Define the standard error of the estimate.

3. The regression equation that Jack Snyder developed to project annual sales of a dealership has an R - squared of 60 percent and a standard error of the estimate of $4,500,000. If the projected annual sales for a dealership total $28,500,000, determine the approximate 95 percent confidence range for Jack’s prediction of sales.

4. What is the strategic role of regression analysis for USMI?