Question

Break-Even Sales Under Present and Proposed Conditions Darby Company, operating at full capacity, sold 167,200 units at a price of $111 per unit during the current year. Its income statement is as follows: Sales $18,559,200 Cost of goods sold 6,586,000 Gross profit $11,973,200 Expenses: Selling expenses $3,293,000 Administrative expenses 1,961,000 Total expenses 5,254,000 Income from operations $6,719,200 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 $1,665,000 in yearly sales. The expansion will increase fixed costs by $222,000, 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.

Total variable costs $ NEED THIS - please show work

I have the total fixed cost so I do not need that.

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

Unit variable cost $ NEED THIS - please show work

Unit contribution margin $ NEED THIS - please show work

3. Compute the break-even sales (units) for the current year.

NEED THIS - please show work

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

NEED THIS - please show work

5. Determine the amount of sales (units) that would be necessary under the proposed program to realize the $6,719,200 of income from operations that was earned in the current year. units

NEED THIS - please show work

6. Determine the maximum income from operations possible with the expanded plant.

NEED THIS - please show work

Answer 1

Answer-  the total variable costs and the total fixed costs for the current year:-

	Variable Costs	Fixed Costs
Cost of goods sold	$3,951,600 ($6,586,000*60%)	$2,634,400 ($6,586,000*40%)
Selling expenses	$1,646,500 ($3,293,000*50%)	$1,646,500 ($3,293,000*50%)
Administrative expenses	$588,300 ($1,961,000*30%)	$1,372,700 ($1,961,000*70%)
Total Cost	$6,186,400	$5,653,600

2-(a)-(a) the unit variable cost:-

Unit Variable Cost= Total variable costs/ Total units sold

=$6,186,400/ 167,200 units

=$37

(b)-Unit contribution margin= Sales Price per unit- Unit variable cost

= $111-$37

=$74

3- the break-even sales (units) for the current year:-

Break even sales in units= Total fixed costs/ unit contribution margin

=$5,653,600/ $74

=76,400 units

4- the break-even sales (units) under the proposed program for the following year:-

Break-even sales= (Total fixed costs+ Increased in fixed costs )'/ Units contribution margin per unit

=($5,653,600+$222,000)/ $74

=79,400 units

5-the amount of sales (units) that would be necessary under the proposed program to realize the $6,719,200 of income from operations that was earned in the current year:-

Amount of sales in units= (Desired income+ Total fixed cost+ Increased fixed cost)/ Unit contribution margin per unit

=($6,719,200+$5,653,600+$222,000)/ $74

=$12,594,800/ $74

=170,200 units

6- the maximum income from operations possible with the expanded plant:-

Increase in sales units= (Increase in sales / selling price per unit)+ Current year sales unit

= ($1,665,000/ $111)+167,200 units

=15,000+167,200 units

=182,200 units

Increase in sales units	182,200
Sales (182,200 units *$111)	$20,224,200
Less: Variable cost (182,200 *$37)	$6,741,400
Contribution	$13,482,800
Less: Fixed costs ($5,653,600+$222,000)	$5,875,600
Net Income	$7,607,200

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