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 97,200 units at a price of $120 per unit during the current year. Its income statement for the current year is as follows:

Sales			$11,664,000
Cost of goods sold			5,760,000
Gross profit			$5,904,000
Expenses:
Selling expenses	$2,880,000
Administrative expenses	2,880,000
Total expenses			5,760,000
Income from operations			$144,000

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 $1,080,000 in yearly sales. The expansion will increase fixed costs by $108,000, 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 $144,000 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.
$  

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.

Answer 1

1.

Total variable costs = 5,760,000*70% + 2,880,000*75% + 2,880,000*50%

= $7,632,000

Total Fixed Costs = 5,760,000*30% + 2,880,000*25% + 2,880,000*50%

= $3,888,000

2.Unit variable cost = total variable cost/number of units ‘

= 7,632,000/97,200

= $78.52 per unit

Unit contribution margin = unit selling price – unit variable cost

= $120-$78.52

= $41.48 per unit

3.Break even units = Total Fixed costs/unit contribution margin

= 3,888,000/41.48

= 93,732 units

4.Proposed program = (3,888,000+108,000)/41.48

= 96,336 units

5.Desired Income = $144,000

+Fixed Costs 3,996,000

Desired Contribution Margin = $4,140,000

Unit contribution Margin = $41.48

Number of units =99,807 units

6.Maximum Income:

Maximum Sales = 11,664,000+1,080,000 = $12,744,000

Contribution Margin = 12,744,000*41.48/120 = $4,405,176

Less: Fixed Costs = $3,996,000

Maximum Income = $409,176

7.Contribution Margin = 11,664,000*41.48/120 = $4,031,856

Less: Fixed Costs = $3,996,000

Income = $35,856

8. b In favor of the proposal because of the possibility of increasing income from operations.