Question

Riveria 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.

Riveria Company Contribution Margin Income Statement For Year Ended Dec. 31,2017

Sales.............................$750,000

Variable costs................60,000

Contribution Margin......150,000

Fixed costs...................200,000

Net loss........................$(50,000)

Required: 1. Compute the break-even point in dollar sales for 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.

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.

Answer 1

Answer to Requirement 1:

Selling Price per unit = Sales / Units Sold
Selling Price per unit = $750,000 / 20,000
Selling Price per unit = $37.50

Variable Cost per unit = Variable Costs / Units Sold
Variable Cost per unit = $600,000 / 20,000
Variable Cost per unit = $30.00

Contribution Margin Ratio = (Selling Price per unit - Variable Cost per unit) / Selling Price per unit
Contribution Margin Ratio = ($37.50 - $30.00) / $37.50
Contribution Margin Ratio = 0.20

Breakeven Point in dollar sales = Fixed Costs / Contribution Margin Ratio
Breakeven Point in dollar sales = $200,000 / 0.20
Breakeven Point in dollar sales = $1,000,000

Answer to Requirement 2:

Selling Price per unit = $37.50

Variable Cost per unit = $30.00 - 50% * $30.00
Variable Cost per unit = $15.00

Fixed Costs = $200,000 + $150,000
Fixed Costs = $350,000

Contribution Margin Ratio = (Selling Price per unit - Variable Cost per unit) / Selling Price per unit
Contribution Margin Ratio = ($37.50 - $15.00) / $37.50
Contribution Margin Ratio = 0.60

Breakeven Point in dollar sales = Fixed Costs / Contribution Margin Ratio
Breakeven Point in dollar sales = $350,000 / 0.60
Breakeven Point in dollar sales = $583,333

Answer to Requirement 3:

$ $ Income Statement Sales (20,000 * $37.50) Variable costs (20,000 * $15.00) Contribution margin Fixed costs Net income $ 750,000 300,000 450,000 350,000 100,000 $ $

Answer to Requirement 4:

Required Sales in dollars = (Fixed Costs + Target Profit) / Contribution Margin Ratio
Required Sales in dollars = ($350,000 + $200,000) / 0.60
Required Sales in dollars = $916,667

Required Sales in units = Required Sales in dollars / Selling Price per unit
Required Sales in units = $916,667 / $37.50
Required Sales in units = 24,445

Answer to Requirement 5:

Income Statement Sales (24,445 * $37.50) Variable costs (24,445 * $15.00) Contribution margin Fixed costs Net income $ $ $ $ $ 916,688 366,675 550,013 350,000 200,013