Determine the amount of sales (units) that would be necessary under Break-Even S

Question

Determine the amount of sales (units) that would be necessary under

Break-Even Sales Under Present and Proposed Conditions

Darby Company, operating at full capacity, sold 125,550 units at a price of $126 per unit during the current year. Its income statement for the current year is as follows:

The division of costs between fixed and variable is as follows:

Management is considering a plant expansion program that will permit an increase of $1,386,000 in yearly sales. The expansion will increase fixed costs by $138,600, 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. Enter the final answers rounded to the nearest dollar.

2. Determine (a) the unit variable cost and (b) the unit contribution margin for the current year. Enter the final answers rounded to two decimal places.

3. Compute the break-even sales (units) for the current year. Enter the final answers rounded to the nearest whole number.
units

4. Compute the break-even sales (units) under the proposed program for the following year. Enter the final answers rounded to the nearest whole number.
units

5. Determine the amount of sales (units) that would be necessary under the proposed program to realize the $195,300 of income from operations that was earned in the current year. Enter the final answers rounded to the nearest whole number.
units

6. Determine the maximum income from operations possible with the expanded plant. Enter the final answer rounded to the nearest dollar.
$

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? Enter the final answer rounded to the nearest dollar.
$ 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

Sales $15,819,300 Cost of goods sold 7,812,000 Gross profit $8,007,300 Expenses: Selling expenses $3,906,000 Administrative expenses 3,906,000 Total expenses 7,812,000 Income from operations $195,300

Explanation / Answer

Ans. 1 Calculation of Total variable cost and fixed cot

                                                 Variable cost                fixed cost

COGS (70:30)           5468400    2343600                                

Admn Exp. (75:25)                 2929500                      976500

Selling cost (50:50)               1953000                      1953000

Total cost                                 10350900                    5273100

Current Year total variable cost = $10350900

Current year total fixed cost       = $5273100

2. Current year variable cost per unit = $10350900/125550 = 82.44

contribution per unit (126-82.44)= $43.56

PV ratio = 43.56/126X100 = 34.57%

3. Computation of break sales in unit for the current year

Break even sales = Total fixed cost/contribution per unit

                                = 5273100/43.56 = 121054 units

4. Calculation of Break even point after under the propsed program

Existing Fixed cost               = 5273100

Add: Increase fixed cost      = 138600

Total fixed cost                      = 5411700

PV ratio is remain same so Variable cost per unit is also same as previous 82.44 per unit and Contribution margin per unit is $43.56

Break Even point = 5411700/43.56 = 124236 units

5. Computation of desired sales if desired operating profit is $195300

Desired sales in unit = Fixed cost+desired profit

                                           Contribution per unit

                                        = (5411700+195300)/43.56 = 128719

6. Calculation of Maximum income possible with the expanded plant

Existing Unit                                          = 125550

Increase unit due to expanded          = 1100

(138600/126)

Total no of unit sales after expanded= 126650

Contribution per unit = $43.56

                                                                 Income statement

Revenue (126650X126)                     =                        15957900

Contribution (126650X43.56)            = 5516874

Less: Fixed cost                                  =                         5411700

Net Income after expanded                =                         105174

7. If the proposal is accepted and sales is remain current level. calculation of income or loss

Existing no of unit sales   = 125550

Contribution margin (125550X43.56)       = 5468958

Fixed cost                                                       = (5411700)

Net income after expanded                        =   57258

8. Comment: Reject the proposal because the sales necessary to maintain the current income from operations would be below the current year sales.

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