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 2,500 new vehicles annually:

AVERAGE DEALERSHIP FINANCIAL PROFILE
Composite Income Statement
Sales	$	50,000,000
Cost of goods sold		41,250,000
Gross profit	$	8,750,000
Operating costs
Variable		1,437,500
Mixed		3,850,000
Fixed		3,090,000
Operating income	$	372,500

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% 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 3,500 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 $7,500,000. If the projected annual sales for a dealership total $47,500,000, 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.)

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Answer 1

Page.No O Asoer O Coropasite dealership 3500 unib ane sold Pzekt financial profile f an arerng. dealeyhjp The gien neus rehicles annually · that sells 2500 Por unit price unita Amounts Pasiticular త Coof of goods sold ($ 41,25000) aso0 $ 50,000,000 కీ వం,000 2500 $ 16500 Vaniable 4 1437500) 2500 $ 515 Miaed 1386 2500 (4 3465000) $ 184 61 Tobal vaniable cots ($4615a50) fined corts 2500 ($3475000 Cperating profit $ 312500 (3850,000 x i0y.) (ico :-90y.-10% Mixed 3850,000 385000 3850,000 $ 3465000 fized contr 3090,000 ť 385000 $ 3445000

Paga. NO (2. sold, it 3500 nits are Sales 40, 000,000 20,000 X 35CO Variable corts 64,613, 500 18461 X 3500 fixed corti $ 3445000 Profit 3445000 64,613, 500 70,000,000 $ 1911500 rofit $1911500 O Range f aler Range of cales Cestimated zales + Costandard evror x ) $44,500,000 + ( 4500,000 x 2) 47500,000 ± (15,00,000) 44500,000 + |5000,C00, 475OG000-1SCO0C0 62500,000 325C0,000 " Range of aales 32500,000 to 6a500,000

NO Ratio g fandard to the amcunt to be , Predicted 4500,00 0 X100 47500,000 15.8 % of sE and relatvely Endication ponog mesion . it is an Holire indiati on model The R- square g 60 %. in and a lock of procendem of predichion from the model.