Determine the amount of sales (units) that would be necessary under Break-Even S

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 99,900 units at a price of $75 per unit during the current year. Its income statement for the current year is as follows: Sales Cost of goods sold Gross profit $7,492,500 3,700,000 $3,792,500 $1,850,000 Selling expenses Administrative expenses 1,850,000 Total expenses 3,700,000 Income from operations $92,500 The division of costs between fixed and variable is as follows: Variable Fixed 70% 75% 50% 30% 25% 50% Cost of goods sold Selling expenses Administrative expenses Management is considering a plant expansion program that will permit an increase of $600,000 in yearly sales. The expansion will increase fixed costs by $60,000, 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

Explanation / Answer

1.

A. Total Variable Cost = 70% of Cost of goods sold + 75 % Selling Expenses + 50 % of Administrative Expenses

= 70 % of $ 3,700,000 + 75% of $ 1,850,000 + 50% of $ 1,850,000

= $ 2,590,000 + $ 1,387,500 + $ 925,000

= $ 49,02,500

B. Total Fixed Cost = 30% of Cost of goods sold + 25 % Selling Expenses + 50 % of Administrative Expenses

= 30 % of $ 3,700,000 + 25% of $ 1,850,000 + 50% of $ 1,850,000

= $ 1,110,000 + $ 462,500 + $ 925,000

= $ 2,497,500

2.

A. Unit Variable Cost = Total Variable Cost / Sales Units

= $ 4,902,500 / 99,900 units

= $ 49.07 Per Unit

B. Unit Contribution Margin = Sales Per Unit - Unit Variable Cost

= $ 75 - $ 49.07

= $ 25.93

3. Break even sale (Unit) for current year = Total Fixed Cost / Unit Contribution Margin

= $ 2,497,500 / $ 25.93

= 96,333 Units (Rounded nearest to whole unit)

4. Break even sale (Unit) for Proposed Programe = (Total Fixed Cost + New Fixed Cost) / Unit Contribution Margin

= ($ 2,497,500 + $ 60,000) / $ 25.93

= $ 2,557,500 / $ 25.93

= 98,647 Units (Rounded nearest to whole unit)

Incremental Break even Units will be 2,314 units [($ 60,000 / $ 25.93) or (98,647 - 96,333)

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