Question

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 2,900 new vehicles annually: AVERAGE DEALERSHIP FINANCIAL PROFILE Composite Income Statement Sales $58,000,000 Cost of goods sold 47,850,000 Gross profit $10, 150,000 Operating costs Variable 1,667,500 Mixed 4,466,000 Fixed 3,584,400 Operating income $ 432,100 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% of the mixed costs shown are variable for purposes of this analysis. He also suggests performing regression analyses on the various components of the mixed costs to more definitively determine their variability. Required: 1. Calculate the composite dealership profit if 4,100 units are sold. 3. The regression equation that Jack Snyder developed to project annual sales of a dealership has an R-squared of 60% and a standard error of the estimate of $8,700,000. If the projected annual sales for a dealership total $55,100,000, determine the approximate 95% confidence interval for Jack's prediction of sales. (Hint: The 95% confidence interval uses 2 standard errors in determining the interval.) Complete this question by entering your answers in the tabs below.
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Answer 1

United States Motors Inc. Requirement 1 1. Assuming that all purchases of autos for resale (cost of goods sold) represent variable costs Price = $58,000,000/2,900 = $20,000 Variable cost per unit = ($1,667,500 + (0.9 x $4,466,000) + $47,850,000]/2,900 = $18,461 Fixed cost = $3,584,400 + (0.1 x $4,466,000) = $4,031,000 4,100 x $20,000 4,100 x $18,461 Profit for 4,100 units sold Sales Less Variable costs Contribution Margin Less Fixed costs Profit 82000000 75690100 6309900 4031000 2278900 Requirement 2 2. Using the regression equation that Jack Snyder developed, the approximate range of sales that could occur during the year is calculated below. Range of sales = Sales +/- (Standard error x 2) = $55,100,000 +/-($8,700,000 x 2) = $55,100,000 +/-$17,400,000 = $37,700,000 to $72,500,000 Note that this is a relatively wide range for the confidence interval. Consider that the ratio of the standard error to the predicted amount is $8,700,000/$55,100,000 = 15.79%, an indication of a relatively poor SE and a relatively poor regression. The mediocre R-Squared of 60% is a further indication of the weakness of the model and therefore of the lack of precision of the predictions from the model.