Question

Break-Even Sales Under Present and Proposed Conditions

Howard Industries Inc., operating at full capacity, sold 64,000 units at a price of $45 per unit during the current year. Its income statement is as follows:
Sales $2,880,000
Cost of goods sold 1,400,000
Gross profit $1,480,000
Expenses: Selling expenses $400,000 Administrative expenses 387,500 Total expenses 787,500
Income from operations $ 692,500
The division of costs between variable and fixed is as follows:
Variable Fixed
Cost of goods sold 75% 25% Selling expenses 60% 40% Administrative expenses 80% 20% Management is considering a plant expansion program for the following year that will permit an increase of $900,000 in yearly sales. The expansion will increase fixed costs by $212,500 but will not affect the relationship between sales and variable costs.
Required:
1. Determine the total fixed costs and the total variable 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 $692,500 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

To determine total fixed costs and total variable costs, calculate the fixed portion of each expense and subtract it from the total expense. The break-even sales can be calculated by dividing the total fixed costs by the unit contribution margin. Accepting the proposal would result in a reduction in the break-even point and the potential for increased income from operations.

Step-by-step explanation:

• Total Fixed Costs and Total Variable Costs:

The total fixed costs for the current year can be calculated by adding the fixed portion of each expense:

Cost of goods sold = $1,400,000 * 25% = $350,000

Selling expenses = $400,000 * 40% = $160,000

Administrative expenses = $387,500 * 20% = $77,500

Total fixed costs = $350,000 + $160,000 + $77,500 = $587,500

• The total variable costs for the current year can be calculated by subtracting the fixed portion of each expense from the total expense:

Cost of goods sold = $1,400,000 - $350,000 = $1,050,000

Selling expenses = $400,000 - $160,000 = $240,000

Administrative expenses = $387,500 - $77,500 = $310,000

Total variable costs = $1,050,000 + $240,000 + $310,000 = $1,600,000

• Unit Variable Cost and Unit Contribution Margin:

The unit variable cost is calculated by dividing the total variable costs by the number of units sold:

Unit variable cost = $1,600,000 / 64,000 = $25 per unit

The unit contribution margin is calculated by subtracting the unit variable cost from the selling price per unit:

Unit contribution margin = $45 - $25 = $20 per unit

• Break-Even Sales (Units):

The break-even sales is calculated by dividing the total fixed costs by the unit contribution margin:

Break-even sales (units) = $587,500 / $20 = 29,375 units

• Break-Even Sales under Proposed Program (Units):

The break-even sales under the proposed program can be calculated by dividing the total fixed costs for the following year by the unit contribution margin:

Break-even sales (units) under proposed program = ($587,500 + $212,500) / $20 = 40,000 units

Sales for $692,500 Income from Operations:

The sales necessary to realize $692,500 of income from operations can be calculated by adding the income from operations to the total fixed costs and dividing the result by the unit contribution margin:

Sales (units) for $692,500 income from operations = ($692,500 + $587,500) / $20 = 64,000 units

• Maximum Income from Operations with Expanded Plant:

The maximum income from operations possible with the expanded plant can be calculated by multiplying the unit contribution margin by the maximum sales under the proposed program:

Maximum income from operations = $20 * 40,000 units = $800,000

• Income or Loss from Operations for Following Year:

If the proposal is accepted and sales remain at the current level, the income or loss from operations for the following year can be calculated by subtracting the total fixed costs for the following year from the current year's income from operations:

Income or loss from operations = $692,500 - ($587,500 + $212,500) = -$107,500 (loss from operations)

• Recommendation:

I would recommend accepting the proposal because of the reduction in break-even point and the possibility of increasing income from operations.