Question

Astro Co.sold 20,000 units of its only product and incurred a $50,000 loss (ignoring taxes) for the current year as shown here. During a planning session for year 2018's activities, the production manager notes that variable costs can be reduced 50% by installing a machine that automates several operations. To obtain these savings, the company must increase its annual fixed costs by $200,000. The maximum output capacity of the company is 40,000 units per year.
ASTRO COMPANY
Contributed Margin Income Statement
For Year Ended December 31, 2017
Sales $ 1,000,000
Variable costs 800,000
Contribution margin 200,000
Fixed costs 250,000
Net loss $ (50,000)
Required:
1. Compute the break-even point in dollar sales for year 2017.
2. Compute the predicted break-even point in dollar sales for year 2018 assuming the machine is installed and there is no change in the unit selling price.
3. Prepare the forecasted contribution margin income statement for 2018 that shows the expected results with the machine installed. Assume that the unit selling price and the number of units sold will not change, and no income taxes will be due.
Compute the sales level required in both dollars and units to earn $200,000 of target pretax income for 2018 with the machine installed and no change in unit sales price.
4. Prepare a forecasted contribution margin income statement that shows the results at the sales level computed in part 5. Assume no income taxes will be due. (Round your intermediate calculation and final answer to the nearest whole dollar.)

Answer 1

Answer:

1. $1,250,000

2. $750,000

3. Forecasted contribution margin income statement for 2018

Sales                                                    $ 1,000,000

Variable costs                                       ($400,000 )

Contribution margin                              $600,000

Fixed costs ($250,000  + $200,000)  ($450,000)

Net Income /( loss)                                 $150,000    

Sales to meet target profit (dollars) = $1,083,333

4. Forecasted contribution margin income statement

Sales                                                      $1,083,333

Variable costs                                       ($400,000 )

Contribution margin                               $683,333

Fixed costs ($250,000  + $200,000)  ($450,000)

Net Income /( loss)                                 $233,333

Explanation:

Break even point is the level of activity where a firm neither makes a profit nor a loss.

Break-even point in dollar sales = Fixed Cost ÷ Contribution Margin Ratio

Where, Contribution Margin Ratio = Contribution margin ÷ Sales

                                                        = $200,000 ÷ $ 1,000,000

                                                        = 0.20

Thus, Break-even point in dollar sales = $250,000 ÷ 0.20

                                                               = $1,250,000

Predicted break-even point in dollar sales for year 2018

New Contribution Margin :

Sales                                                        $ 1,000,000

Less Variable Cost $800,000 × 50%     ($400,000)

New Contribution Margin                         $600,000

New Contribution Margin Ratio

New Contribution Margin Ratio =   $600,000 ÷ $ 1,000,000

                                                    =   0.60

New Break-even point in dollar sales

Break-even point in dollar sales = ($250,000 + $200,000) ÷ 0.60

                                                     = $750,000

Sales to meet target profit = (Fixed Cost + Target Profit) ÷ Contribution Margin Ratio

                                            = ($450,000 + $200,000) ÷ 0.60

                                            = $1,083,333

Forecasted contribution margin income statement

Sales                                                      $1,083,333

Variable costs                                       ($400,000 )

Contribution margin                               $683,333

Fixed costs ($250,000  + $200,000)  ($450,000)

Net Income /( loss)                                 $233,333