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 114,750 units at a price of $135 per unit during the current year. Its income statement for the current year is as follows:

Sales			$15,491,250
Cost of goods sold			7,650,000
Gross profit			$7,841,250
Expenses:
Selling expenses	$3,825,000
Administrative expenses	3,825,000
Total expenses			7,650,000
Income from operations			$191,250

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 $1,215,000 in yearly sales. The expansion will increase fixed costs by $121,500, 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 $191,250 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.
$

7. If the proposal is accepted and sales remain at the current level, what will the income or loss from operations be for the following year? Enter the final answer rounded to the nearest dollar.
$ Income

8. Based on the data given, would you recommend accepting the proposal?

1. In favor of the proposal because of the reduction in break-even point.
2. In favor of the proposal because of the possibility of increasing income from operations.
3. In favor of the proposal because of the increase in break-even point.
4. Reject the proposal because if future sales remain at the current level, the income from operations will increase.
5. Reject the proposal because the sales necessary to maintain the current income from operations would be below the current year sales.

Choose the correct answer.
b

Answer 1

1. Total Variable and Fixed Cost

All figures are in $

Total Variable Cost
Cost of Goods Sold (70%)	5355000
Selling Expenses (75%)	2868750
Administration expenses (50%)	1912500
Total	10136250
Total Fixed Cost
Cost of Goods Sold (30%)	2295000
Selling Expenses (25%)	956250
Administration expenses (50%)	1912500
Total Fixed Cost	5163750

2 Unit Variable cost and Unit Contribution

Sales (114750 * 135)	15491250
Less - Variable COGS	5355000
Gross Profit Margin	10136250
Less - Variable Selling Expense	2868750
Less- Variable Administration Expense	1912500
Contribution	5355000
Contribution per unit - Contribution / Sales Units 5355000 / 114750	46.67
Variable Cost per unit Total Variable cost / Units sold 10136250 / 114750	88.33

3. Break Even Sales

Break Even Sales = Fixed cost / Contribution per unit

5163750 / 46.67 = 110643.9 i.e. 110644 is break even sale units and in value it is 14936940 (110644 * 135)

4. Break even sales in proposed plan

Break Even Sales = Fixed cost / Contribution per unit

Sales (114750 + 9000) * 135	16706250
Less- Total Variable Cost (114750+ 9000)*88.33	10930837
Contribution	5775413
Contribution per unit - Contribution / Sales Units 5775413 / 123750	46.67

Note - Sales Value increased = 1215000, Units increased = 1215000 / 135 i.e. 9000 units

Fixed Cost =    5163750

Add Additional FC = 121500

Total Revised FC = 5285250

Break Even Sales = 5285250 / 46.67

Break Even Sales units = 113247.26 i.e. 113248

Sales in value = 113248 * 135 = 15288480

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