Concept explainers
Rivera Co. sold 20,000units 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 2016’s activities, the production manager notes that variable costs can be reduced 50% by installing a machine that automates several operations. To obtain these saving, 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 31.2015
Required
- Compute the break-even points in dollar sales for year 2015.
- Compute the predicted break-even point in dollar sales for year 2016 assuming the machine is installed and no change occurs in the unit selling price. (Round the change in variable costs to a whole number.)
- Prepare a
forecasted contribution margin income statement for 2016 that show 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. - Compute the sales level required in both dollars and units to earn $200,000 of target pretax income in 2016 with the machine installed and no change in unit sales price. (Round answer to whole dollars and whole units.)
- Prepare a forecasted contribution margin income statement that shows the results at the sales level computed in part 4. Assume no income taxex will be due.
Concept introduction:
Break-Even Point: The level of sales at which profits are zero refers to break-even point. In other words, it is the point where total revenue equals total cost and total contribution margin equals total fixed cost.
Contribution Margin Ratio: The ratio that indicates the percentage of sales that is available with the company to cover its fixed expenses and profit refers to contribution margin ratio. The ratio is used to determine the profits from various levels of sales.
Requirement 1:
To compute:
The break-even point in dollar sales Rivera Co. for the year 2016.
Answer to Problem 4PSB
Break-even point in dollar sales of Rivera Co. is $1, 000, 000.
Explanation of Solution
Break-even point in sales dollars is computed by using the formula,
Break-even point (in dollars) = Fixed Costs/Contribution Margin Ratio:
Where Contribution Margin Ratio = Contribution Margin per unit/ Sales per unit
Contribution Margin per unit = Selling price per unit-Variable cost per unit
Given,
Sales: $750, 000
Sales unit: 20, 000
Selling price per unit = $750, 000/20, 000 units
Selling price per unit = $37.50
Variable costs: $600, 000
Sales unit: 20, 000
Variable cost per unit = $600, 000/20, 000
Variable cost per unit = $30.00
Contribution Margin per unit is computed as in the below table:
Contribution Margin per unit | ($) per unit. |
Selling Price per unit | 37.50 |
Less: Variable Cost per unit | (30.00) |
Contribution Margin per unit | 7.50 |
Therefore Contribution Margin Ratio = $7.50/$37.50
Contribution Margin Ratio = 20%
Break-even point in dollars is computed by using the formula as below:
Break-even point (in dollars) = $200, 000/20%
Break-even point (in dollars) = $1, 000, 000
Concept introduction:
Break-Even Point: The level of sales at which profits are zero refers to break-even point. In other words, it is the point where total revenue equals total cost and total contribution margin equals total fixed cost.
Contribution Margin Ratio: The ratio that indicates the percentage of sales that is available with the company to cover its fixed expenses and profit refers to contribution margin ratio. The ratio is used to determine the profits from various levels of sales.
Requirement 2:
To compute:
The predicted break-even point in dollar sales for the year 2016 assuming the machine is installed and there is no change in unit selling price.
Answer to Problem 4PSB
The break-even point in dollar sales of Rivera Co. after installation of machine with no change in selling price per unit would be $583, 333.
Explanation of Solution
Break-even point in sales dollars is computed by using the formula,
Break-even point (in dollars) = Fixed Costs/Contribution Margin Ratio:
Where Contribution Margin Ratio = Contribution Margin per unit/ Sales per unit
Contribution Margin per unit = Selling price per unit-Variable cost per unit
Contribution Margin per unit is computed as in the below table:
Contribution Margin | ($) Per Unit |
Sales | 37.50 |
Less: Variable Cost | (15) |
Contribution Margin | 22.50 |
Therefore Contribution Margin Ratio = $22.50/$37.50
Contribution Margin Ratio = 60%
Break-even point in dollars is computed by using the formula as below:
Break-even point (in dollars) = $350, 000/60%
Break-even point (in dollars) = $583, 333
Note 1: Annual fixed costs is increased by $200, 000 as given in the problem. So now the fixed costs would be $200, 000+$150, 000=$350, 000.
Note 2: Variable cost is reduced by 50% by installing a machine
Concept introduction:
Break-Even Point: The level of sales at which profits are zero refers to break-even point. In other words, it is the point where total revenue equals total cost and total contribution margin equals total fixed cost.
Contribution Margin Ratio: The ratio that indicates the percentage of sales that is available with the company to cover its fixed expenses and profit refers to contribution margin ratio. The ratio is used to determine the profits from various levels of sales.
Requirement 3:
To prepare:
The forecasted contribution margin income statement for Rivera Co. for the year 2016 showing the expected results with the machine installed.
Answer to Problem 4PSB
Rivera Co. Forecasted Contribution Margin Income Statement for the year 2016 | |
Amount in $ | |
Sales | 750, 000 |
Less: Variable costs | (300, 000) |
Contribution Margin | 450, 000 |
Less: Fixed costs | (350, 000) |
Net income | 100, 000 |
Explanation of Solution
Computation of Contribution Margin:
Given,
Sales: 20, 000 units * $50 = $1, 000, 000
Variable costs: 20, 000 units * $20 = $400, 000
Contribution Margin is computed by using the formula,
Contribution Margin = Sales-Variable costs:
Contribution Margin = $1, 000, 000-$400, 000
Contribution Margin = $600, 000
Computation of Variable costs:
Sales Units: 20, 000
Variable costs: $15
Variable costs = 20, 000*$15
Variable costs = $300, 000
Note: Variable costs is reduced by 50% by installing a machine.
Computation of total fixed costs:
Fixed Costs in 2015: $200, 000
Increase in annual costs of 2016: $150, 000
Total fixed costs = $200, 000 + $150, 000
Total fixed Costs = $350, 000
Concept introduction:
Break-Even Point: The level of sales at which profits are zero refers to break-even point. In other words, it is the point where total revenue equals total cost and total contribution margin equals total fixed cost.
Contribution Margin Ratio: The ratio that indicates the percentage of sales that is available with the company to cover its fixed expenses and profit refers to contribution margin ratio. The ratio is used to determine the profits from various levels of sales.
Requirement 4:
To compute:
The sales level required in both dollars and units to earn $200, 000 of target pretax income in 2016 with the machine installed and no change in unit sales price.
Answer to Problem 4PSB
Sales level required in dollars to earn $200, 000 of target pretax income would be $916, 667.
Sales level required in units to earn $200, 000 of target pretax income would be 24, 445 units.
Explanation of Solution
Required sales in dollars:
Required sales in dollars is computed by using the formula,
Required sales in dollars = [Fixed costs + Target pretax income]/Contribution Margin Ratio
Required sales in dollars = [$350, 000+$200, 000]/70%
Required sales in dollars = $550, 000/60%
Required sales in dollars = $916, 667
Note: Contribution Margin Ratio is 60% as computed in Requirement 2.
Required sales in units:
Required sales in units is computed by using the formula,
Required sales in units = [Fixed costs + Target pretax income]/Contribution Margin per unit
Required sales in units = [$350, 000+$200, 000]/$22.50
Required sales in units = 24, 444.44 units i.e. 24, 445 units (Rounded up to whole units)
Note 1: Fixed costs of $200, 000 and increase in annual fixed costs of $150, 000 is added.
Note 2: Contribution Margin per unit is $22.50 computed in Requirement 2.
Concept introduction:
Break-Even Point: The level of sales at which profits are zero refers to break-even point. In other words, it is the point where total revenue equals total cost and total contribution margin equals total fixed cost.
Contribution Margin Ratio: The ratio that indicates the percentage of sales that is available with the company to cover its fixed expenses and profit refers to contribution margin ratio. The ratio is used to determine the profits from various levels of sales.
Requirement 5:
To prepare:
The forecasted contribution margin income statement that shows the results at the dollar sales level of $916, 667and unit sales level of 24, 445 assuming no income taxes due.
Answer to Problem 4PSB
Rivera Co. Forecasted Contribution Margin Income Statement For Year Ended December 2016 | ||
$ per unit | $ | |
Sales | 37.50 | 916, 688 |
Less: Variable costs | 15 | 366, 675 |
Contribution Margin | 22.50 | 550, 013 |
Less: Fixed Costs | 350, 000 | |
Income before taxes | 200, 013 |
Explanation of Solution
Computation of sales:
Sales unit [As computed in Requirement 4]: 24, 445 units
Selling price per unit: $37.50
Sales = 24, 445*$37.50
Sales = $916, 687.5.5 i.e. 916, 688 (Rounded up to whole number)
Computation of variable costs:
Sales unit [As computed in Requirement 4]: 24, 445 units
Variable costs per unit: $15
Variable costs = 24, 445*$15
Variable costs = $366, 675
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