Question

Break-Even Sales Under Present and Proposed Conditions Darby Company, operating at full capacity, sold 165,500 units at a price of $117 per unit during the current year. Its income statement is as follows: Sales $19,363,500 Cost of goods sold 6,864,000 Gross profit $12,499,500 Expenses: Selling expenses $3,432,000 Administrative expenses 2,067,000 Total expenses 5,499,000 Income from operations $7,000,500 The division of costs between variable and fixed is as follows: Variable Fixed Cost of goods sold 60% 40% Selling expenses 50% 50% Administrative expenses 30% 70% Management is considering a plant expansion program for the following year that will permit an increase of $1,521,000 in yearly sales. The expansion will increase fixed costs by $202,800, 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. Total variable costs $ Total fixed costs $ 2. Determine (a) the unit variable cost and (b) the unit contribution margin for the current year. Unit variable cost $ Unit contribution margin $ 3. Compute the break-even sales (units) for the current year. units 4. Compute the break-even sales (units) under the proposed program for the following year. units 5. Determine the amount of sales (units) that would be necessary under the proposed program to realize the $7,000,500 of income from operations that was earned in the current year. units 6. Determine the maximum income from operations possible with the expanded plant. $ 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? $ 8. Based on the data given, would you recommend accepting the proposal? In favor of the proposal because of the reduction in break-even point. In favor of the proposal because of the possibility of increasing income from operations. In favor of the proposal because of the increase in break-even point. Reject the proposal because if future sales remain at the current level, the income from operations will increase. 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)Calculation of total fixed and variable cost for the Year

	Fixed	Variable
Cost of Sales	$ 2,745,600.00	$ 4,118,400.00
Selling Expense	$ 1,716,000.00	$ 1,716,000.00
Administrative Expense	$ 1,446,900.00	$      620,100.00
TOTAL	$ 5,908,500.00	$ 6,454,500.00

2)Unit Variable Cost ratio= 6,454,500/19,363,500=33%

Unit Contribution Margin Ratio=100%-33%= 67%

Unit Variable Cost= 117* 33%= $39

Unit Contribution Margin=117*67%= $ 78

3)Break even sales in unit= 5908500/78= 75,750 Units

4)Break-even sales for proposed program=(5908500+202800)/78= 78,350 Units

5)Necessary Sales (Units) (proposed)= (5908500+202800+7000500 )/78= 168,100 Units

6)Maximum Income= {(19,363,500+1,521,000)*67%} - (5908500+202800)

=7,811,700

7)Income from Operations (Next Year)=(19,363,500*67%} - (5908500+202800)

=6,797,700