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 82,350 units at a price of $72 per unit during the current year. Its income statement for the current year is as follows:

Sales			$5,929,200
Cost of goods sold			2,928,000
Gross profit			$3,001,200
Expenses:
Selling expenses	$1,464,000
Administrative expenses	1,464,000
Total expenses			2,928,000
Income from operations			$73,200

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 $504,000 in yearly sales. The expansion will increase fixed costs by $50,400, but will not affect the relationship between sales and variable costs.

Required: Please Provide Answers Only

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 $73,200 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

SOLUTION

1. Total variable cost = Cost of goods sold + Selling expenses + Administrative expenses

= (2,928,000*70%) + (1,464,000*75%) + (1,464,000*50%)

= 2,049,600 + 1,098,000 + 732,000

= $3,879,600

Total fixed costs = Cost of goods sold + Selling expenses + Administrative expenses

= (2,928,000*30%) + (1,464,000*25%) + (1,464,000*50%)

= 878,400 + 366,000 + 732,000

= $1,976,400

2. Unit variable cost = Total variable costs / Number of units

= $3,879,600 / 82,350 = $47.11

Unit contribution margin = Selling price - Unit variable cost

= $72 - $47.11 = $24.89

3. Break-even Sales Units = Total Fixed Costs / Unit Contribution margin

= $1,976,400 / 24.89 = 79,405 units

4. Break-even sales = Increased Fixed Cost / Unit Contribution margin

= $50,400 / 24.89

= 2,025 units

5. Amount of sales (units) = (Desired Income + Total Fixed Cost + Increased Fixed Cost) / Unit Contribution margin

= (73,200 + 1,976,400 + 50,400) / $24.89

= 2,100,000 / 24.89 = 84,371 units

6. No. of Sales (in units) increased due to expansion = 504,000 / 72 = 7,000 units

Maximum income from operations possible with expanded plan

= [(7,000+82,350)*$24.89] - (1,976,400 + 50,400)

= 2,223,922 - 2,026,800

= 197,122