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 3,100 new vehicles 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, 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 4,400 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 $9,300,000. If the projected annual sales for a dealership total $58,900,000, 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.)

Answer 1

SOLUTION:

1. The composite dealership profit if 4,400 units are sold:

Selling price per Unit = Sales / Units = 62,000,000 / 3100 = 20,000 units

	Total (100%)	Variable (90%)	Fixed(10%)
Mixed Costs	4,774,000	4296600 (4774000*90%)	477400 (4774000*10%)

Total Variable Cost = 1782500(VC) + 4296600(Of mixed) + 51,150,000(COGS) = 57,229,100

Variable cost per unit = 57,229,100 / 3100 = 18,461

Total Fixed Cost = 3831600 + 477400 = 4,309,000

If 4400 units are sold ,

Particulars	Calculations	Amount
Sales	(4400 * 20000)	88,000,000
Less: Variable Cost	(4400 * 18461)	81,228,400
Contribution		6,771,600
Less: Fixed Cost		4,309,000
Profit		2,462,600

Hence if 4400 units are sold, dealership profit will be $ 2,462,600

3. Range of Sales:

Range of Sales = (Estimated sales + Standard x 2) or (Estimated sales - Standard x 2)

= [58,900,000 + (9,300,000 x 2) ] or [58,900,000 - (9,300,000 x 2) ]

= (58,900,000 + 18,600,000) or (58,900,000 - 18,600,000)

= 77,500,000 or 40,300,000

Range of Sales = 40,300,000 to 77,500,000