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 125,550 units at a price of $135 per unit during the current year. Its income statement for the current year is as follows:

Sales			$16,949,250
Cost of goods sold			8,370,000
Gross profit			$8,579,250
Expenses:
Selling expenses	$4,185,000
Administrative expenses	4,185,000
Total expenses			8,370,000
Income from operations			$209,250

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 $1,350,000 in yearly sales. The expansion will increase fixed costs by $135,000, 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 $209,250 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.
$

Answer 1

1.

Total variable cost = COGS * 70% + Selling Exps * 75% + Admin Exps * 50%

= 8,370,000 * 70% + 4,185,000 * 75% + 4,185,000 * 50%

= $11,090,250

Total Fixed cost = COGS * 30% + Selling Exps * 25% + Admin Exps * 50%

= 8,370,000 * 30% + 4,185,000 * 25% + 4,185,000 * 50%

= $5,649,750

2.

Unit Variable Cost = $11,090,250/125,550

= $88.33

Unit Contribution Margin = $135 - $88.33

= $46.67

3.

Break even units = Fixed Costs/Contribution per unit

= $5,649,750/$46.67

= 121,057.42 units

4.

Break even units (proposed program) = Fixed Costs/Contribution per unit

= $5,649,750 + $135,000/$46.67

= 123,950.07 units

5.

Units to be sold to get profit of $209,250

= (Profit + Fixed costs)/Contribution per unit

= (209,250+5,784,750)/46.67

= 128,433.68 units

6.

Maximum income from operations

= (Total sales * Contribution per unit) - Total fixed costs

= ($18,299,250/135*46.67) - 5,784,750

= $541,368.5

7.

Income/loss from operations

= (Total sales * Contribution per unit) - Total fixed costs

= (125,550 * 46.67) - 5,784,750

= $74,668.5