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 87,750 units at a price of $57 per unit during the current year. Its income statement for the current year is as follows: Sales $5,001,750 Cost of goods sold 2,470,000 Gross profit $2,531,750 Expenses: Selling expenses $1,235,000 Administrative expenses 1,235,000 Total expenses 2,470,000 Income from operations $61,750 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 $399,000 in yearly sales. The expansion will increase fixed costs by $39,900, 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 $ 3,272,750 Total fixed costs $ 1,667,250 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 $ 37.30 Unit contribution margin $ 19.70 3. Compute the break-even sales (units) for the current year. Enter the final answers rounded to the nearest whole number. 84,632 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. 86,657 units 5. Determine the amount of sales (units) that would be necessary under the proposed program to realize the $61,750 of income from operations that was earned in the current year. Enter the final answers rounded to the nearest whole number. 89,792 units 6. Determine the maximum income from operations possible with the expanded plant. Enter the final answer rounded to the nearest dollar. $ 494,000 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? 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.

Answer 1

Solution 1			Calculation of Fixed and variable cost
	Particulars	Total	Variable	Fixed
	Cost of goods sold (70/30)	2470000	1729000	741000
	selling (75/25)	1235000	926250	308750
	admin (50/50)	1235000	617500	617500
	Total		3272750	1667250
Solution 2	Unit variable cost and margin
	Sales per unit	57
	Variable cost per unit (3272750/87750)3	37.30	(Total variable cost/ no of units sold)
	Margin	19.70
Solution 3	Break even sales units	= Fixed cost / contribution margin per unit
		= 1667250/19.70
		84631.98
		or 84632
Solution 4	Break even sales unit	= Fixed cost + additional fixed cost/ margin per unit
		= (1667250+39900)/19.70
		86657.36
		or 86657
Solution 5	Break even sales units	= proposed Fixed cost+ profit/ margin per unit
		= (1667250+39900+61750)/19.70
		89791.88
		or 89792
Solution 6	Maximum income	Amount	Units
	Sales (existing + increased)	5400750	94750
	Less: variable	3534175	(94750*37.3)
	Gp	1866575
	Less fixed	1707150	(1667250+39900)
	Profit	159425
Solution 7	If sales remains at same level then new profit will be as follows:
	Existing profit	61750
	Less : new fixed cost	39900
	New profit	21850
Solution 8	Answer is dReject the proposal because the sales necessary to maintain the current income from operations would be below the current year sales as there is possibility of increase in income .