Question

Break-Even Sales Under Present and Proposed Conditions

Darby Company, operating at full capacity, sold 139,000 units at a price of $72 per unit during the current year. Its income statement is as follows:

Sales			$10,008,000
Cost of goods sold			3,552,000
Gross profit			$6,456,000
Expenses:
Selling expenses	$1,776,000
Administrative expenses	1,056,000
Total expenses			2,832,000
Income from operations			$3,624,000

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 $792,000 in yearly sales. The expansion will increase fixed costs by $105,600, 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	$

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

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

5. Determine the amount of sales (units) that would be necessary under the proposed program to realize the $3,624,000 of income from operations that was earned in the current year.
units

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

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?
$ Income

Answer 1

Part 1: Total variable and fixed cost for the current year

Particulars	Total Cost	Variable Cost	Fixed cost
Cost of goods sold	$3552000	$2131200 ($3552000 * 60%)	$1420800 ($3552000 * 40%)
Selling Expenses	$1776000	$888000 ($1776000 * 50%)	$888000 ($1776000 * 50%)
Administrative expenses	$1056000	$316800 ($1056000 * 30%)	$739200 ($1056000 * 70%)
Total	$6384000	$3336000	$3048000

Part 2:

(a): Unit Variable Cost for the current year

Variable cost = $3336000

No. of units = 139000

Unit Variable cost = $3336000 / 139000 units = $24 per unit

(b): Contribution Margin cost for the current year

Selling Price = $72 per unit

Variable cost = $24 per unit

Contribution Margin = $72 per unit - $24 per unit = $48 per unit

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

Break-even sales(units) = Fixed cost / Contribution margin

Fixed cost = $3048000

Contribution Margin = $48 per unit

Break-even sales (units) = $3048000 / $48 per unit = 63500 units

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

Break-even sales(units) = Fixed cost / Contribution margin

Fixed cost = $3048000 + $105600 = $3153600

Contribution Margin = $48 per unit

Break-even sales (units) = $3153600 / $48 per unit = 65700 units

Part 5: Sales (units) under the proposed program to realize $3624000 of income from operations

Desired Profit = $3624000

Fixed cost = $3048000 + $105600 = $3153600

Contribution = $3624000 + $3153600 = $6777600

Contribution Margin per unit = $48 per unit

Units to be sold = $6777600 / $48 per unit = 141200 units

Part 6: Maximum income from operations possible with the expanded plant

Existing Sales = $10008000

Increase in sales = $792000

Expanded sales = $1008000 + $792000 = $10800000

Sales units = $10800000 / $72 per unit = 150000 units

Maximum income from operation = (Sales units * contribution margin per unit) - Fixed cost

Maximum income from operation = (150000 units * $48 per unit) - $3153600 = $4046400

Part 7: Income from operation for the following year when sales remain at the current level

Sales units = 139000 units

Contribution margin per unit = $48 per unit

Income from operation = (Sales units * contribution margin per unit) - Fixed cost

Income from operation = (139000 * $48 per unit) - $3153600 = $3518400

All the best...