Break-Even Sales Under Present and Proposed Conditions Portmann Company, operating at full capacity, sold 1,000,000 units at a price of $189 per unit during the current year. Its income statement is as follows:
Sales $189,000,000
Cost of goods sold (101,000,000)
Gross profit $88,000,000
Expenses:
Selling expenses $16,000,000
Administrative expenses 12,600,000
Total expenses (28,600,000)
Operating income $59,400,000
The division of costs between Costs that vary in total dollar amount as the level of activity changes. variable and Costs that tend to remain the same in amount, regardless of variations in the level of activity. fixed 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 for the following year that will permit an increase of $13,230,000 in yearly sales. The expansion will increase fixed costs by $4,500,000 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 The dollars available from each unit of sales to cover fixed costs and provide operating profits. 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 $59,400,000 of operating income that was earned in the current year.
units
6. Determine the maximum operating income possible with the expanded plant.
$
7. If the proposal is accepted and sales remain at the current level, what will the operating income or loss be for the following year?
$ Income
Loss

1. Total variable costs = $89,000,000

Total fixed costs = $40,600,000

2. a Unit variable cost = $89

b. Unit contribution margin = $100

3. Break-even sales (units) = Fixed cost/Contribution margin per unit

= $40,600,000/$100

= 406,000 units

4. Break-even sales (units) = Fixed cost/Contribution margin per unit

= $45,100,000/$100

= 451,000 units

5. Break-even sales (units) to achieve target profit = (Fixed cost + Target Profit)/Contribution margin per unit

= ($45,100,000 + $59,400,000)/$100

= 1,045,000 units

6. Maximum operating income possible with the expanded plant is:

= $61,900,000

7. Operating income if the proposal is accepted and sales remain at the current level is:

= $54,900,000

Explanation:

a) Data and Calculations:

Sales volume during current year = 1,000,000

Sales price per unit during current year = $189

Income statement is as follows:

Sales                                $189,000,000

Cost of goods sold           (101,000,000)

Gross profit                      $88,000,000

Expenses:

Selling expenses             $16,000,000

Administrative expenses  12,600,000

Total expenses                (28,600,000)

Operating income          $59,400,000

                                      Variable    Fixed

Cost of goods sold           70%        30%

Selling expenses              75%        25%

Administrative expenses 50%        50%

Total variable costs for the current year:

                                      Variable  

Cost of goods sold           70% * $101,000,000 = $70,700,000

Selling expenses              75% * $16,000,000 =     12,000,000

Administrative expenses 50% * $12,600,000 =      6,300,000

Total variable costs = $89,000,000

Variable unit cost = $89 ($89,000,000/1,000,000)

Contribution per unit = $100 ($189 - $89)

Total fixed costs for the current year:

                                          Fixed

Cost of goods sold             30% * $101,000,000 = $30,300,000

Selling expenses                25% * $16,000,000  =      4,000,000

Administrative expenses   50% * $12,600,000 =       6,300,000

Total fixed costs =  $40,600,000

Projected sales for the next year = $202,230,000 ($189,000,000 + $13,230,000)

Percentage Increase in sales for the next year = $13,250,000/$189,000,000 * 100 = 7%

Fixed costs caused by expansion = $4,500,000

Total fixed costs = $45,100,000 ($40,600,000 + $4,500,000)

Variable costs = $95,230,000 ($89,000,000 * 1.07)

Contribution margin:

Sales                                $202,230,000

Variable costs                      95,230,000

Contribution margin        $107,000,000

Expenses:

Fixed costs                          45,100,000

Operating income            $61,900,000

Sales volume = 1,070,000 units (1,000,000 * 1.07)

Contribution per unit = $107,000,000/1,070,000 = $100

Sales at current level:

Sales                                $189,000,000

Variable costs                     89,000,000

Contribution                    $100,000,000

Fixed costs                          45,100,000  

Operating income           $54,900,000