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 2016’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
Contribution Margin Income Statement
For Year Ended December 31, 2015
Sales $ 1,000,000
Variable costs 800,000
Contribution margin 200,000
Fixed costs 250,000
Net loss $ (50,000 )
1. Compute the break-even point in dollar sales for year 2015.
2. Compute the predicted break-even point in dollar sales for year 2016 assuming the machine is installed and there is no change in the unit selling price.
3. Prepare a forecasted contribution margin income statement for 2016 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.
4. Compute the sales level required in both dollars and units to earn $200,000 of target pre-tax income income in 2016 with the machine installed and no change in unit sales price.

Answer 1

Answer:

Required 1.

Break even point (dollar sales) =   $750,000

Required 2.

Break even point (dollar sales) = $1,250,000

Required 3.

ASTRO COMPANY

Forecasted Contribution Margin Income Statement

For Year Ended December 31, 2016

Sales                             $ 1,000,000

Variable costs               ($ 400,000 )

Contribution margin      $ 600,000

Fixed costs                    ($ 450,000 )

Net loss                           $ 150,000

Required 4.

Sales to meet target profit (dollar sales) = $1,833,333

Sales to meet target profit (unit sales) = 73,334

Explanation:

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

Break even point (dollar sales) = Fixed Cost / Contribution Margin Ratio

Where,

Contribution Margin Ratio = Contribution / Sales

                                           = $ 200,000 / $ 1,000,000

                                           = 0.20

Therefore,

Break even point (dollar sales) = $250,000 / 0.20

                                                   = $1,250,000

Assuming the machine is installed

Contribution Margin Ratio = ($ 1,000,000 - $400,000) / $ 1,000,000

                                           = $600,000 / $1,000,000

                                           = 0.60

Therefore,

Break even point (dollar sales) = ($250,000 + $200,000) / 0.60

                                                   = $750,000

Sales to meet target profit of $200,000

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

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

                                                                  = $1,833,333

Sales to meet target profit (unit sales) = $1,833,333 / $25

                                                               = 73,334