Chapter 18: Break-even Points, Contribution Margin Income Statement

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.

Required:

1. Compute the break-even point in dollar sales for year 2017.

Explanation:

Calculation of contribution margin ratio 20%

Sales price per unit ($100,000 / 20,000)                       $ 50.00
Variable costs per unit ($800,000 / 20,000)                  $ 40.00
Contribution margin ratio (50.00 – $40.00) / $50.00)   20 %

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.

Explanation:

		Fixed costs
break-even point in dollars	=
		Contribution margin ratio

  

2016 break-even in sales dollars	=	Fixed costs / Contribution margin ratio
	=	$450,000* / 60%**
	=	$750,000

*To compute predicted fixed costs

2015 fixed costs plus 2016 increase ($250,000 + $ 200,000) = $450,000

**To compute predicted contribution margin ratio

Predicted sales price per unit (no change in sales price)	$	50.00
Predicted variable costs per unit (($800,000 × 50%) / 20,000)	$	20.00
Predicted contribution margin ratio ($50.00 – $20.00) / $50.00)		60	%

3. Prepare a 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.

Explanation:

Sales: 20,000 × $50.00 = $100,000

Variable costs: 20,000 × $20.00 = $400,000

Contribution margin: 20,000 × $30.00 = $600,000

4. Compute the sales level required in both dollars and units to earn $200,000 of target pretax income in 2018 with the machine installed and no change in unit sales price.

Explanation:

		Fixed costs + Target pretax income
Required sales in dollars	=
		Contribution margin ratio

Required sales in dollars	=	($450,000* + $200,000) / 60%***
	=	$650,000 / 60%
	=	$1,083,333

		Fixed costs + Target pretax income
Required sales in units	=
		Contribution margin per unit

Required sales in units	=	($450,0000 + $200,000) / $30.00
	=	21,666 units (rounded up to whole units)

* 2015 fixed costs plus 2016 increase ($450,000 + $200,000)

$

650,000

   

***Predicted contribution margin ratio ($50.00 – $20.00) / $50.00)— from Part 2

60%

5. Prepare a forecasted contribution margin income statement that shows the results at the sales level computed in part 4. Assume no income taxes will be due. (Round your intermediate calculation and final answer to the nearest whole dollar.)

Explanation:

Sales: 21,666 units × $50.00 = $1,083,333
Variable costs: 21,667 units × $20= $433,333
Contribution margin: 31,938 units × $20.90 = $667,504

Income before income taxes is slightly greater than the targeted $250,000 income due to rounding of units.