Question

Break-Even Sales Under Present and Proposed Conditions Darby Company, operating at full capacity, sold 105,300 units at a price of $45 per unit during the current year. Its income statement for the current year is as follows: Sales $4,738,500 Cost of goods sold 2,340,000 Gross profit $2,398,500 Expenses: Selling expenses $1,170,000 Administrative expenses 1,170,000 Total expenses 2,340,000 Income from operations $58,500 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 $360,000 in yearly sales. The expansion will increase fixed costs by $36,000, 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 $58,500 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? 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. b Feedback 1. Multiply the percentages for fixed and variable costs by each cost. 2. a. Divide the total variable costs by number of units. 2. b. Sales price per unit minus variable costs per unit equals contribution margin per unit. 3. Fixed costs divided by unit contribution margin equals break-even point. 4. Fixed costs under the proposed program divided by contribution margin equals new break-even point. 5. (Fixed costs + Target profit) divided by unit contribution margin equals sales units. 6. Determine the increase in units by dividing the sales increase by the price per unit. Add the additional revenue and additional fixed costs when calculating: Sales minus fixed and variable costs equals income from operations. 7. Subtract the additional fixed costs from the operating income. 8. Consider the break-even point and the sales needed for the proposed level. Learning Objective 2, Learning Objective 3.

Answer 1

Table:

Particulars	Amount (in $)			Variable (in $)	Fixed (in $)
Sales			4,738,500
Cost of Goods Sold		-2,340,000		-1,638,000	-702,000
Gross Profit			2,398,500
Selling Expenses	-1,170,000			-877,500	-292,500
Administrative Expenses	-1,170,000			-585,000	-585,000
Total Expenses		-2,340,000
Income			58,500
				-3,100,500	-1,579,500

1.

Total Variable Cost = $ 3,100,500.

Total Fixed Cost = $ 1,579,500.

2.

(a) Unit Variable Cost = Total Variable Cost / Number of units sold = 3,100,500 / 105,300 = $ 29.44

(b) Unit contribution margin = Unit Selling price – Unit Variable Cost = 45 – 29.44 = $ 15.56

3.

Breakeven sales for the current year = Total Fixed Cost / Unit contribution margin = 1,579,500 / 15.56 = 101,510 units.

4.

As per the proposed program, increase in annual fixed = $ 36,000.

Breakeven sales for the proposed program = (1,579,500 + 36,000) / 15.56 = 103,824 units.

5.

Let amount of units sold as per the new program = x.

Plant expansion program will result in increase in fixed cost by $ 36,000.

There will be no change in variable cost.

Cost of goods sold due to the proposed program = 1,638,000 + (702,000 + 36,000) = $ 2,376,000.

Income = $ 58,500.

45 x – 2,376,000 – 2,340,000 = 58,500

45 x = 58,500 + 2,376,000 + 2,340,000 = 4,774,500

x = 4,774,500 / 45 = 106,100.

The number of units that would be needed to be sold to achieve an income of $ 58,500 = 106,100.

6.

New sales = 4,738,500 + 360,000 = $ 5,098,500.

Cost of goods sold due to the proposed program = 1,638,000 + (702,000 + 36,000) = $ 2,376,000.

Maximum income possible with the expanded plant = 5,098,500 – 2,376,000 – 2,340,000 = $ 382,500.

7.

Sales remain at the previous level.

Income as per the new proposal = 4,738,500 – 2,376,000 – 2,340,000 = $ 22,500.

8.

We may accept the new proposal as income can increase to a maximum of $ 382, 500 from the existing value of $ 58,500, which is an increase of $ 324,000.