Question

Break-Even Sales Under Present and Proposed Conditions Portmann Company, operating at full capacity, sold 1,000,000 units at a price of $190 per unit during the current year. Its income statement is as follows: Sales $190,000,000 Cost of goods sold (101,000,000) Gross profit $89,000,000 Expenses: Selling expenses $14,000,000 Administrative expenses 17,600,000 Total expenses (31,600,000) Operating income $57,400,000 The division of costs between variable and 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 $9,500,000 in yearly sales. The expansion will increase fixed costs by $5,000,000 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 $57,400,000 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? $ ?

Answer 1

1. Total variable costs = Variable cost of goods sold + Variable selling expenses + Variable administrative expenses

where, Variable cost of goods sold = 70 % of total cost of goods sold = 70% of $101,000,000 = $70,700,000

Variable selling expenses = 75% of total selling expenses = 75% of $14,000,000 = $10,500,000

Variable administrative expenses = 50% of total administrative expenses = 50% of $17,600,000 = $8,800,000

Total variable costs = $70,700,000 + $10,500,000 + $8,800,000 = $90,000,000.

Total Fixed costs = Fixed cost of goods sold + Fixed selling expenses + Fixed administrative expenses

where, Fixed cost of goods sold = 30 % of total cost of goods sold = 30% of $101,000,000 = $30,300,000

Fixed selling expenses = 25% of total selling expenses = 25% of $14,000,000 = $3,500,000

Fixed administrative expenses = 50% of total administrative expenses = 50% of $17,600,000 = $8,800,000

Total fixed costs = $30,300,000 + $3,500,000 + $8,800,000 = $42,600,000.

2. Unit variable cost = Total Variable costs / 1,000,000 units = $90,000,000 / 1,000,000 units = $90 per unit.

Unit contribution margin for the current year = Selling price per unit - Variable costs per unit = $190 - $90 = $100 per unit.

3. Break-even sales ( units) for the current year = Total Fixed costs for the year / Unit contribution margin = $42,600,000 / $100 per unit = 426,000 units.

4. Break-even sales (units) under the proposed program = New fixed costs / Unit contribution margin

New fixed costs = Fixed costs in the previous year + $5,000,000 = $42,600,000 + $5,000,000 = $47,600,000

Where, unit contribution margin will remain the same to $100 per unit as the relationship between the variable costs and sales remains the same.

Break-even sales (units) under the proposed program = $47,600,000 / $100 per unit = 476,000 units.