Question

Break-Even Sales Under Present and Proposed Conditions

Darby Company, operating at full capacity, sold 163,500 units at a price of $66 per unit during the current year. Its income statement is as follows

Sales			$10,791,000
Cost of goods sold			3,828,000
Gross profit			$6,963,000
Expenses:
Selling expenses	$1,914,000
Administrative expenses	1,144,000
Total expenses			3,058,000
Income from operations			$3,905,000

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 $990,000 in yearly sales. The expansion will increase fixed costs by $132,000, 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	$
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 $3,905,000 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?
$

8. Based on the data given, would you recommend accepting the proposal?

In favor of the proposal because of the reduction in break-even point.

In favor of the proposal because of the possibility of increasing income from operations.

In favor of the proposal because of the increase in break-even point.

Reject the proposal because if future sales remain at the current level, the income from operations will increase.

Reject the proposal because the sales necessary to maintain the current income from operations would be below the current year sales.

Choose the correct answer.

Answer 1

1)

Particulars	Variable expenses	Fixed expenses
Cost of goods sold	$3,828,000 * 60% = $2,296,800	$3,828,000 * 40% = $1,531,200
Selling expenses	$1,914,000 *50% = 957,000	$1,914,000 *50% = 957,000
Administrative expenses	$1,144,000*30% = 343,200	$1,144,000*70% = 800,800
Total	$ 3,597,000	$ 3,289,000

2) Unit variable cost = Variable expenses / units sold

                                    = $3,597,000 / 163,500 = $22

Unit contribution margin = Contribution / Units sold = ($10,791,000 – 3,597,000) /163,500 = $44

3) Break even sales for the year = Fixed cost / Contribution per unit = $ 3,289,000 / 44 = 74,750 units

4) Break even sales under proposed program

   Existing Variable expenses relation with sales = $3,597,000 / 10,791,000 *100 = 33.33 %

Existing relationship will continue for proposed method also.

So proposed case sales = $10,791,000 + 990,000 = $11,781,000

So variable expenses = $11,781,000*33.33% = $3,926,607

            Contribution = sales – variable expenses = $11,781,000 - $3,926,607 = $7,854,393

Selling price per unit = $66 so number of units = $11,781,000 / 66 = 178,500 units       

Contribution per unit = $7,854,393 / 178,500 = $44

Breakeven sales = ($3,289,000 +132,000)/44 = 77,750 units

5) To achieve desired income = Fixed cost + desired income / contribution per unit

     Amount of sales in units     = [($3,289,000+132,000) + $3,905,000] / 44 = 166,500 units

6) Maximum income from operations with expanded plant = Sales – variable expenses – fixed expense

   = $ 11,781,000 – 3,926,607 – (3,289,000+132,000) = $4,433,393

7) If sales are at current level

= $10,791,000 – 3,597,000 – (3,289,000+132,000) = $3,773,000

8) In favor of the proposal because of the possibility of increasing income from operation

Since income from operations in the proposed plan is higher as $4,433,393 whereas, as per current state it is $3,905,000