Question

Break-Even Sales Under Present and Proposed Conditions
Darby Company, operating at full capacity, sold 97,700 units at a price of $93 per unit during the current year. Its income statement is as follows
Sales  $9,086,100Cost of goods sold  3,224,000Gross profit  $5,862,100Expenses:   Selling expenses$1,612,000  Administrative expenses961,000  Total expenses  2,573,000Income from operations  $3,289,100
The division of costs between variable and fixed is as follows:
 VariableFixedCost of goods sold60% 40% Selling expenses50% 50% Administrative expenses30% 70% 
Management is considering a plant expansion program for the following year that will permit an increase of $744,000 in yearly sales. The expansion will increase fixed costs by $99,200, but will not affect the relationship between sales and variable costs.
Required:
1.  Determine the total variable costs and the total fixed costs for the current year.
Total variable costs$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 $3,289,100 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

Answer 1:

Workings are as below:

Answer 2:

Calculations:

Number of Units sold = 99,700

Answer 3:

Break-even sales (units) = Fixed costs / Contribution margin per unit = $2,768,300 / $62 = 44,650

Answer 4:

Total fixed costs with proposed program = $2,768,300 + $99,200 = $2,867,500

The expansion will not affect the relationship between sales and variable costs:

contribution per unit remain same.

Break-even sales (units) = $2,867,500 / $62 = 46,250 units

Answer 5:

Amount of sales (units) that would be necessary under the proposed program to realize the $3,289,100 = (Fixed cost + Target profit) / Contribution margin per unit

= ($2,867,500+$3,289,100) / $62

= 99,300

Answer 6:

Workings are as below:

Answer 7:

If the proposal is accepted and sales remain at the current level, contribution margin will remain same as current year.

Hence,

Income or loss from operations = $6,057,400 - $2,867,500 = $3,189,900

Answer 8:

Correct answer is:

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

Explanation:

Increase in sales units ($744,000 / $93) = 8,000

Incremental Income:

Option 2 is correct.

Option 1 is incorrect as break-even has increased.

Option 3 is incorrect as mere increase in BEP does not qualify it for acceptance

Based on calculations above, options 4 and 5 are incorrect.