Question

Darby Company, operating at full capacity, sold 98,550 units at a price of $123 per unit during the current year. Its income statement for the current year is as follows:

Sales			$12,121,650
Cost of goods sold			5,986,000
Gross profit			$6,135,650
Expenses:
Selling expenses	$2,993,000
Administrative expenses	2,993,000
Total expenses			5,986,000
Income from operations			$149,650

The division of costs between fixed and variable is as follows:

	Variable		Fixed
Cost of goods sold	70%		30%
Selling expenses	75%		25%
Administrative expenses	50%		50%

Management is considering a plant expansion program that will permit an increase of $1,107,000 in yearly sales. The expansion will increase fixed costs by $110,700, but will not affect the relationship between sales and variable costs.

Determine (a) the unit variable cost and (b) the unit contribution margin for the current year. Enter the final answers rounded to two decimal places.

Unit variable cost	$
Unit contribution margin	$

Determine (a) the unit variable cost and (b) the unit contribution margin for the current year. Enter the final answers rounded to two decimal places.

Unit variable cost	$
Unit contribution margin	$

Answer 1

a. Unit Variable Cost

Unit Variable Cost = Total variable Cost / Units Sold

Total variable Cost = COGS * 70% + Selling Expenses * 75% + Administrative expenses * 50%

Total variable Cost = 5986000 * 70% + 2993000 * 75% + 2993000 * 50%

Total variable Cost = 4190200 + 2244750 + 1496500

Total variable Cost = 7931450

Unit Variable Cost = Total variable Cost / Units Sold

Unit Variable Cost = 7931450 / 98550

Unit Variable Cost = $80.48

b. Unit Contribution margin = Unit selling price - Unit variable cost

Unit Contribution margin = $123 - $80.48

Unit Contribution margin = $42.52