BreakEven Sales Under Present and Proposed Conditions Darby

Break-Even Sales Under Present and Proposed Conditions Darby Company, operating at full capacity, sold 150,400 units at a price of $69 per unit during the current year. Its income sta follows Sales Cost of goods sold Gross profit Expenses: $10,377,600 3,680,000 $6,697,600 Selling expenses $1,840,000 Administrative expenses 1,104,000 Total expenses 2,944,000 Income from operations $3,753,600 The division of costs between variable and fixed is as follows: Variable Fixed 6096 50% 30% 40% Cost of goods sold Selling expenses Administrative expenses Management is considering a plant expansion program for the following year that will permit an increase of $966,000 in yearly sale expansion will increase fixed costs by $128,800, 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 50% 70%

Solution

Answer to Part 1:

Cost of Goods Sold:
Variable Proportion of Cost of Goods Sold = $3,680,000 * 60%
Variable Proportion of Cost of Goods Sold = $2,208,000

Fixed Proportion of Cost of Goods Sold = $3,680,000 * 40%
Fixed Proportion of Cost of Goods Sold = $1,472,000

Selling Expense:
Variable Proportion of Selling Expense = $1,840,000 * 50%
Variable Proportion of Selling Expense = $920,000

Fixed Proportion of Selling Expense = $1,840,000 * 50%
Fixed Proportion of Selling Expense = $920,000

Administrative Expenses:
Variable Proportion of Administrative Expenses = $1,104,000 * 30%
Variable Proportion of Administrative Expenses = $331,200

Fixed Proportion of Administrative Expenses = $1,104,000 * 70%
Fixed Proportion of Administrative Expenses = $772,800

Total Variable Cost = $2,208,000 + $920,000 + $331,200
Total Variable Cost = $3,459,200

Total Fixed Cost = $1,472,000 + $920,000 + $772,800
Total Fixed Cost = $3,164,800

Answer to Part 2:

Unit Variable Cost = Total Variable Cost / Units Sold
Unit Variable Cost = 3,459,200 / 150,400
Unit Variable Cost = $23

Unit Contribution Margin = Unit Selling Price - Unit Variable Cost
Unit Contribution Margin = $69 - $23
Unit Contribution Margin = $46

Answer to Part 3:

Break Even Sales (Units) = Fixed Cost / Contribution Margin Ratio
Contribution Margin Ratio = 46 / 69 * 100
Contribution Margin Ratio = 66.67%

Break Even Sales (Units) = 3,164,800 / 0.6667
Break Even Sales (Units) =4,746,962.65
or Break Even Sales (Units) = 4,746,963 Units

Answer to Part 4:

Break Even Sales (Units) = Fixed Cost / Contribution Margin Ratio
Expected Sales = $10,377,600 + $966,000
Expected Sales = $11,343,600

As, the relationship between Sales and Variable Cost will not change. Therefore, Contribution Margin ratio will remain same at 66.67%.

Expected Fixed Cost = $3,164,800 + $128,800
Expected Fixed Cost = $3,293,600

Break Even Sales (Units) = 3,293,600 / 0.6667
Break Even Sales (Units) = 4,940,152.99
or Break Even Sales (Units) = 4,940,153 units