Astro Co. sold 20,500 units of its only product and incurred a $67,750 loss (ignoring taxes) for the current year as shown here. During a planning session for year 2016’s activities

Astro Co. sold 20,500 units of its only product and incurred a $67,750 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 40% by installing a machine that automates several operations. To obtain these savings, the company must increase its annual fixed costs by $155,000. 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           $     779,000          
  Variable costs                 584,250          
                       
  Contribution margin                 194,750          
  Fixed costs                 262,500          
                       
  Net loss           $     (67,750     )    
                       
Required:
1.     Compute the break-even point in dollar sales for year 2015.

Explanation:

Calculation of contribution margin ratio 25%

  

Sales price per unit ($779,000 / 20,500)	$	38.00
Variable costs per unit ($584,250 / 20,500)	$	28.50
Contribution margin ratio ($38.00 – $28.50) / $38.00)		25	%

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.

Explanation:

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

  

2016 break-even in sales dollars	=	Fixed costs / Contribution margin ratio
	=	$417,500* / 55%**
	=	$759,091

*To compute predicted fixed costs

 

2015 fixed costs plus 2016 increase ($262,500 + $155,000) = $417,500

 

**To compute predicted contribution margin ratio

 

Predicted sales price per unit (no change in sales price)	$	38.00
Predicted variable costs per unit (($584,250 × 60%) / 20,500)	$	17.10
Predicted contribution margin ratio ($38.00 – $17.10) / $38.00)		55	%

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.

Explanation:

Sales: 20,500 × $38.00 = $779,000

Variable costs: 20,500 × $17.10 = $350,550

Contribution margin: 20,500 × $20.90 = $428,450

4.     Compute the sales level required in both dollars and units to earn $250,000 of target pretax income in 2016 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	=	($417,500* + $250,000) / 55%***
	=	$667,500 / 55%
	=	$1,213,636

 

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

 

Required sales in units	=	($417,500 + $250,000) / $20.90
	=	31,938 units (rounded up to whole units)

* 2015 fixed costs plus 2016 increase ($262,500 + $155,000)

$

417,500

   

***Predicted contribution margin ratio ($38.00 – $17.10) / $38.00)— from Part 2

55%

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.

Explanation:

Sales: 31,938 units × $38.00 = $1,213,644

Variable costs: 31,938 units × $17.10 = $546,140

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.