Question

Determine the amount of sales (units) that would be necessary under

Break-Even Sales Under Present and Proposed Conditions

Darby Company, operating at full capacity, sold 99,900 units at a price of $108 per unit during the current year. Its income statement for the current year is as follows:

Sales			$10,789,200
Cost of goods sold			5,328,000
Gross profit			$5,461,200
Expenses:
Selling expenses	$2,664,000
Administrative expenses	2,664,000
Total expenses			5,328,000
Income from operations			$133,200

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 $972,000 in yearly sales. The expansion will increase fixed costs by $97,200, but will not affect the relationship between sales and variable costs.

Required:

1. Determine the total variable costs and the total fixed costs for the current year. Enter the final answers rounded to the nearest dollar.

Total variable costs	$
Total fixed costs	$

2. 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	$

3. Compute the break-even sales (units) for the current year. Enter the final answers rounded to the nearest whole number.
units

4. Compute the break-even sales (units) under the proposed program for the following year. Enter the final answers rounded to the nearest whole number.
units

5. Determine the amount of sales (units) that would be necessary under the proposed program to realize the $133,200 of income from operations that was earned in the current year. Enter the final answers rounded to the nearest whole number.
units

6. Determine the maximum income from operations possible with the expanded plant. Enter the final answer rounded to the nearest dollar.
$

Answer 1

Answer to Requirement 1.

Variable Proportion of Cost of Goods sold = $5,328,000 * 70% = $3,729,600

Variable Proportion of Selling Expense = $2,664,000 * 75% = $1,998,000

Variable Proportion of Administrative Expense = $2,664,000 * 50% = $1,332,000

Total Variable Expense = $3,729,600 + $1,998,000 +$1,332,000

Total Variable Expense = $7,059,600

Fixed Expenses = Total Expenses - Total Variable Expense

Fixed Expense = $10,656,000 - $7,059,600

Total Fixed Expense = $3,596,400

Answer to Requirement 2.

Unit Variable cost = Total Variable Expense/ Unit Sold

Unit Variable cost = 7,059,600/ 99,900

Unit Variable cost = $70.67

Unit Contribution Margin = Unit Selling Price - Unit Variable cost

Unit Contribution Margin = $108 - $70.67

Unit Contribution Margin = $37.33

Answer to Requirement 3.

Break Even Point (Units) = Fixed Cost /Unit Contribution Margin

Break Even Point (Units) = 3,596,400/ 37.33

Break Even Point (Units) = 96,341 Units

Answer to Requirement 4.

Expected Increase in Sales = $972,000

Expected Increase in Units sold = 972,000/108 = 9,000 Units

As the relationship between Sales and Variable cost will not change, Contribution Margin per unit will also remain same at $37.33.

Proposed Fixed Cost = $3,596,400 + $97,200 = $3,693,600

Break Even Point (Units) = Fixed Cost/Unit Contribution Margin

Break Even Point (Units) = 3,693,600/ 37.33

Break Even Point in Proposed Program = 98,945