Question

Problem 18-4B Break-even analysis; income targeting and forecasting C2 P2 A1

Rivera 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 $150,000. The maximum output capacity of the company is 40,000 units per year.

RIVERA COMPANY Contribution Margin Income Statement For Year Ended December 31, 2017
Sales	$750,000
Variable costs	600,000
Contribution margin	150,000
Fixed costs	200,000
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 no change occurs in the unit selling price. (Round the change in variable costs to a whole number.)
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.

Check (3) Net income, $100,000

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. (Round answers to whole dollars and whole units.)

(4) Required sales, $916,667 or 24,445 units (both rounded)

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.

Answer 1

1. Break-even point in dollar sales = Fixed costs/Contribution margin ratio

Contribution margin ratio = Contribution margin/Sales = $150000/$750000 = 20%

Break-even point in dollar sales for year 2017 = $200000/20% = $1000000

2. Fixed costs for 2018 = $200000 + $150000 = $350000

Variable costs = $600000 - (50% x $600000) = $300000

Contribution margin = $750000 - $300000 = $450000

Contribution margin ratio = $450000/$750000 = 60%

Predicted break-even point in dollar sales for year 2018 = $350000/60% = $583333

3.

Forecasted Contribution Margin Income Statement
For Year Ended December 31, 2018
Sales	750000
Variable costs	300000
Contribution margin	450000
Fixed costs	350000
Net income	100000

4. Sales level required in dollars = (Fixed costs + Target income)/Contribution margin ratio = ($350000 + $200000)/60% = $550000/60% = $916667

Sales level required in units = (Fixed costs + Target income)/Contribution margin per unit = ($350000 + $200000)/($450000/20000) = $550000/$22.50 = 24444.44 = 24445

5.

Forecasted Contribution Margin Income Statement
For Year Ended December 31, 2018
Sales	916667
Variable costs	366667
Contribution margin	550000
Fixed costs	350000
Net income	200000