Question

Break-Even Sales Under Present and Proposed Conditions

Darby Company, operating at full capacity, sold 120,200 units at a price of $132 per unit during the current year. Its income statement is as follows:

Sales			$15,866,400
Cost of goods sold			5,632,000
Gross profit			$10,234,400
Expenses:
Selling expenses	$2,816,000
Administrative expenses	1,672,000
Total expenses			4,488,000
Income from operations			$5,746,400

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 $1,452,000 in yearly sales. The expansion will increase fixed costs by $193,600, 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	$fill in the blank 1
Total fixed costs	$fill in the blank 2

2. Determine (a) the unit variable cost and (b) the unit contribution margin for the current year.

Unit variable cost	$fill in the blank 3
Unit contribution margin	$fill in the blank 4

3. Compute the break-even sales (units) for the current year.
fill in the blank 5 units

4. Compute the break-even sales (units) under the proposed program for the following year.
fill in the blank 6 units

5. Determine the amount of sales (units) that would be necessary under the proposed program to realize the $5,746,400 of income from operations that was earned in the current year.
fill in the blank 7 units

6. Determine the maximum income from operations possible with the expanded plant.
$fill in the blank 8

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?

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

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Darby Company
Answer 1	A	B	C=A*B	D=1-B	E=A*D
Type of cost	Total Amount	Variable cost %	Variable cost	Fixed cost %	Fixed cost
Cost of goods sold	5,632,000.00	60%	3,379,200.00	40%	2,252,800.00
Selling expenses	2,816,000.00	50%	1,408,000.00	50%	1,408,000.00
Administrative expenses	1,672,000.00	30%	501,600.00	70%	1,170,400.00
	10,120,000.00		5,288,800.00		4,831,200.00

Total variable costs	5,288,800.00
Total fixed costs	4,831,200.00
Answer 2	Amount $	Note
Total variable costs	5,288,800.00	A
Units sold	120,200.00	B
Variable cost per unit	44.00	C=A/B
Sell price	132.00	D
Contribution per unit	88.00	E=D-C
Contribution margin ratio	66.67%	F=E/D
Answer 3	Amount $
Total fixed costs	4,831,200.00	G
Contribution per unit	88.00	See E
Breakeven units	54,900.00	H=G/E
Answer 4
Total fixed costs	4,831,200.00	See G
Add: expansion costs	193,600.00
Revised fixed costs	5,024,800.00	H
Contribution per unit	88.00	See E
Breakeven units	57,100.00	I=H/E
Answer 5
Revised fixed costs	5,024,800.00	See H
Add: Target income from operations	5,746,400.00
Target Contribution	10,771,200.00	I
Contribution per unit	88.00	See E
Units to be sold	122,400.00	J=I/E
Sell price	132.00	See D
Sales $	16,156,800.00	K=J*D
Answer 6
Increase in sales	1,452,000.00	L
Contribution margin ratio	66.67%	See F
Contribution margin	968,000.00	M=L*F
Less: expansion costs	193,600.00
Increase in income from operations	774,400.00
Add: current income from operations	5,746,400.00
Maximum income from operations possible	6,520,800.00
Answer 7
Current income from operations	5,746,400.00
Less: expansion costs	193,600.00
Income from operations for the following year	5,552,800.00
Answer 8
Option d. Reject the proposal because if future sales remain at the current level, the income from operations will increase.