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Break$-$Even Sales Under Present and Proposed Conditions

Darby Company, operating at full capacity, sold $114,800$ units at a price of $$114$ per unit during the current year. Its income statement is as follows:

Sales $$13,087,200$

Cost of goods sold $4,636,000$

Gross profit $$8,451,200$

Expenses:

Selling expenses $$2,318,000$

Administrative expenses $1,406,000$

Total expenses $3,724,000$

Income from operations $$4,727,200$

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 $$1,026,000$ in yearly sales. The expansion will increase fixed costs by $$136,800,$ 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 $fill in the blank $1$

$4,362,400$

Total fixed costs $fill in the blank $2$

$3,997,600$

$2.$ Determine $($a$)$ the unit variable cost and $($b$)$ the unit contribution margin for the current year.

Unit variable cost $fill in the blank $3$

$38$

Unit contribution margin $fill in the blank $4$

$76$

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

fill in the blank $5$

units

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

fill in the blank $6$

units

$5.$ Determine the amount of sales $($units$)$ that would be necessary under the proposed program to realize the $$4,727,200$ of income from operations that was earned in the current year.

fill in the blank $7$

units

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

$fill in the blank $8$

$7.$ 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?

$fill in the blank $9$

Income

$8.$ 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.

b

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$1.$ Multiply the percentages for fixed and variable costs by each cost.

$2.$ a$.$ Divide the total variable costs by number of units.

$2.$ b$.$ Sales price per unit minus variable costs per unit equals contribution margin per unit.

$3.$ Fixed costs divided by unit contribution margin equals break$-$even point.

$4.$ Fixed costs under the proposed program divided by contribution margin equals new break$-$even point.

$5.($Fixed costs $+$ Target profit$)$ divided by unit contribution margin equals sales units.

$6.$ Determine the increase in units by dividing the sales increase by the price per unit. Add the additional revenue and additional variable and fixed costs when calculating:

Sales minus fixed and variable costs equals income from operations.

$7.$ Subtract the additional fixed costs from the operating income.

$8.$ Consider the break$-$even point and the sales needed for the proposed level.