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
Contribution Margin Income Statement
For Year Ended December 31, 2017
Sales	\(1,000,000
Variable cost	800,000
Contribution margin	200,000
Fixed cost	250,000
Net loss	(\)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 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.

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. Round answers to whole dollars and whole units.

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.

Short answer

Answer

• Break-even point:$1,250,000.

• Predicted break-even point:$750,000.

• Forecasted net income:$150,000.

• Targeted sales:$1,083,333 and 21,667 units.

Forecasted net income: $233,333.

Step-by-step solution

Step-By-Step SolutionStep 1: Definition of Contribution margin

If a business entity generates Profit from sales after adjusting the amount of variable cost is known as contribution margin. It is used as a cost, volume, and profit analysis tool.

Calculation of break-even point

$$\begin{gathered} Contributionmarginratio=\frac{Contributionmargin}{Sales} \\ =\frac{\$200,000}{\$1,000,000} \\ =0.20 \end{gathered}$$

$$\begin{gathered} Break-evenpoint\left(indollars\right)=\frac{Fixed\cos t}{Contributionmarginratio} \\ =\frac{\$250,000}{0.20} \\ =\$1,250,000 \end{gathered}$$

Predicted break-even point

$$\begin{gathered} Contributionmarginratio=\frac{Contributionmargin}{Sales} \\ =\frac{\$600,000}{\$1,000,000} \\ =0.60 \end{gathered}$$

$$\begin{gathered} Break-evenpoint\left(indollars\right)=\frac{Fixed\cos t}{Contributionmarginratio} \\ =\frac{\$250,000+\$200,000}{0.60} \\ =\$750,000 \end{gathered}$$

Working note:

Calculation of new variable cost:

Particular	Amount $
Variable cost	$800,000
Less: Reduction in cost @ 50%	(400,000)
New variable cost	$400,000

Calculation of new contribution margin:

Particular	Amount $
Sales	$1,000,000
Less: Variable cost	(400,000)
Contribution margin	$600,000

Forecasted contribution margin income statement

Particular	Amount $
Sales	$1,000,000
Less: variable cost	(400,000)
Contribution margin	600,000
Less: Fixed cost	($450,000)
Net income	$150,000

Targeted sales

$$\begin{gathered} Targeteddollarsales=\frac{Fixed\cos t+Targetedprofit}{Contributionmarginratio} \\ =\frac{\$450,000+\$200,000}{0.60} \\ =\$1,083,333 \end{gathered}$$

$$\begin{gathered} Priceperunit=\frac{Totaldollarsales}{Totalsalesinunit} \\ =\frac{\$1,000,000}{20,000} \\ =\$50 \end{gathered}$$

$$\begin{gathered} Targetedunitsales=\frac{Targeteddollarsales}{Priceperunit} \\ =\frac{\$1,083,333}{\$50} \\ =21,667units \end{gathered}$$

Forecasted contribution margin income statement

Particular	Amount $
Sales	$1,083,333
Less: variable cost	(400,000)
Contribution margin	$683,333
Less: Fixed cost	(450,000)
Net income	$233,333