Darby Company, operating at full capacity, sold 500,000 units at a price of $94 per unit during the current year. Its income statement is as follows: Sales $47,000,000
Cost of goods sold 25,000,000
Gross profit $22,000,000
Expenses:
Selling expenses $4,000,000
Administrative expenses 3,000,000
Total expenses 7,000,000
Income from operations $15,000,000
The division of costs between variable and fixed is as follows:
Variable Fixed
Cost of goods sold 70% 30%
Selling expenses 75% 25%
Administrative expenses50% 50%
Management is considering a plant expansion program for the following year that will permit an increase of $3,760,000 in yearly sales. The expansion will increase fixed costs by $1,800,000 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.
4. Compute the break-even sales (units) under the proposed program for the following year.
5. Determine the amount of sales (units) that would be necessary under the proposed program to realize the $15,000,000 of income from operations that were earned in the current year.
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?
a. In favor of the proposal because of the reduction in break-even point.
b. In favor of the proposal because of the possibility of increasing income from operations.
c. In favor of the proposal because of the increase in break-even point.
d. Reject the proposal because if future sales remain at the current level, the income from operations will increase.
e. Reject the proposal because the sales necessary to maintain the current income from operations would be below the current year sales.

Darby Company

1. Determination of the total variable costs and the total fixed costs for the current year.

Total variable costs $22,000,000

Total fixed costs $10,000,000

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

Unit variable cost $44 ($22,000,000/500,000)

Unit contribution margin $50 ($94 - $44)

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

Break-even sales (units) = Fixed Costs/Contribution per unit

= $10,000,000/$50 = 200,000 units

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

Break-even sales (units) = Fixed costs/Contribution per unit

= $11,800,000/$50 = 236,000

5. Determine the amount of sales (units) that would be necessary under the proposed program to realize the $15,000,000 of income from operations that were earned in the current year

Break-even sales (units) to achieve income target = (Fixed costs + Income target)/Contribution per unit

= ($11,800,000 + 15,000,000)/$50

= 536,000

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

Income Statement for the current year  

Next Year's Financials:

                                              Total

Sales                                   $50,760,000 ($94 * 540,000)

Expenses:

Total variable                       23,760,000 ($44 * 540,000)

Fixed costs                            11,800,000 ($10,000,000 + $1,800,000)

Income from operations  $15,200,000

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?

                                              Total

Sales                                   $47,000,000 ($94 * 500,000)

Expenses:

Total variable                       22,000,000 ($44 * 500,000)

Fixed costs                            11,800,000 ($10,000,000 + $1,800,000)

Income from operations  $13,200,000

8. Based on the data given, would you recommend accepting the proposal?

Unless the proposal results to an increase in the units sold, it is not acceptable as can be seen from (7) above. However, it is very acceptable if sales unit will increase by 40,000 units as illustrated in (6) above.

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

Explanation:

a) Data and Calculations:

Income Statement for the current year  

Sales                                  $47,000,000        

Cost of goods sold             25,000,000                

Gross profit                      $22,000,000

Expenses:

Selling expenses               $4,000,000

Administrative expenses    3,000,000

Total expenses                    7,000,000

Income from operations $15,000,000

Sales volume = 500,000 units

Selling price = $94

Division of costs between variable and fixed is as follows:

                             Variable  Fixed    Variable        Fixed      Total

Sales                                                                                            $47,000,000

Cost of goods sold  70%     30%     $17,500,00   7,500,000      25,000,000

Gross profit                                                                                 $22,000,000

Expenses:

Selling expenses     75%     25%      3,000,000    1,000,000       4,000,000

Administrative exp. 50%     50%      1,500,000    1,500,000       3,000,000

Total expenses                                 4,500,000   2,500,000       7,000,000

Total variable and fixed costs       22,000,000  10,000,000    32,000,000

Income from operations                                                            $15,000,000

Next Year's Financials:

                             Variable  Fixed    Variable        Fixed      Total

Sales                                                                                            $50,760,000

Cost of goods sold  70%     30%     $17,500,00   7,500,000      25,000,000

Gross profit                                                                                 $22,000,000

Expenses:

Total variable and fixed costs       22,000,000  11,800,000

Income from operations                                                            $15,000,000