Chapter 5, Problem 4PSA

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 2016’s activities, the production manager notes that variable costs can be reduced 50% by installing machine that automates several operation. 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 31.2015 Sales……………………………………….. $1,000,000 Variable costs………………………….. 800,000 Contribution margin……………….. 200,000 Fixed costs……………………………… 250,000 Net loss…………………………………. $ (50,000)

Required

1. Compute the break-even point in dollar sales for year 2015.
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.
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.
4. 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 answers to whole dollars and whole units.
5. Prepare a forested contribution margin income statement that shows the results aat the sales level computed in part 4. Assume no income taxes will be due.

To determine

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 Astro Co. for the year 2016.

Answer to Problem 4PSA

Break-even point in dollar sales of Astro Co. is $1, 250, 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: $1, 000, 000

Sales unit: 20, 000

Selling price per unit = $1, 000, 000/20, 000 units

Selling price per unit = $50

Variable costs: $800, 000

Sales unit: 20, 000

Variable cost per unit = $800, 000/20, 000

Variable cost per unit = $40

Contribution Margin per unit is computed as in the below table:

Contribution Margin per unit	($) per unit.
Selling Price per unit	50
Less: Variable Cost per unit	(40)
Contribution Margin per unit	10

Therefore Contribution Margin Ratio = $10/$50

Contribution Margin Ratio = 20%

Break-even point in dollars is computed by using the formula as below:

Break-even point (in dollars) = $250, 000/20%

Break-even point (in dollars) = $1, 250, 000

To determine

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 4PSA

The break-even point in dollar sales of Astro Co. after installation of machine with no change in selling price per unit would be $750, 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

Contribution Margin per unit is computed as in the below table:

Contribution Margin	($) Per Unit
Sales	50
Less: Variable Cost	(20)
Contribution Margin	30

Therefore Contribution Margin Ratio = $30/$50

Contribution Margin Ratio = 60%

Break-even point in dollars is computed by using the formula as below:

Break-even point (in dollars) = $450, 000/60%

Break-even point (in dollars) = $750, 000

Note 1: Annual fixed costs is increased by $200, 000 as given in the problem. So now the fixed costs would be $250, 000+$200, 000=$450, 000.

Note 2: Variable cost is reduced by 50% by installing a machine.

To determine

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 Astro Co. for the year 2016 showing the expected results with the machine installed.

Answer to Problem 4PSA

Astro Co. Forecasted Contribution Margin Income Statement for the year 2016
	Amount in $
Sales	1, 000, 000
Less: Variable costs	(400, 000)
Contribution Margin	600, 000
Less: Fixed costs	(450, 000)
Net income	150, 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: $20

Variable costs = 20, 000*$20

Variable costs = $400, 000

Note: Variable costs is reduced by 50% by installing a machine.

Computation of total fixed costs:

Fixed Costs in 2015: $250, 000

Increase in annual costs of 2016: $200, 000

Total fixed costs = $250, 000 + $200, 000

Total fixed Costs = $450, 000

To determine

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 4PSA

Sales level required in dollars to earn $200, 000 of target pretax income would be $1, 083, 333.

Sales level required in units to earn $200, 000 of target pretax income would be 21, 667 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 = [$450, 000+$200, 000]/60%

Required sales in dollars = $650, 000/60%

Required sales in dollars = $1, 083, 333

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 = [$450, 000+$200, 000]/$30

Required sales in units = 21, 666.66 units i.e. 21, 667 units (Rounded up to whole units)

Note 1: Fixed costs of $250, 000 and increase in annual fixed costs of $200, 000 is added.

Note 2: Contribution Margin per unit is $30 computed in Requirement 2.

To determine

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 $1, 083, 333 and unit sales level of 21, 666 assuming no income taxes due.

Answer to Problem 4PSA

Astro Co. Forecasted Contribution Margin Income Statement For Year Ended December 2016
	$ per unit	$
Sales	50	1, 083, 333
Less: Variable costs	20	433, 333
Contribution Margin	30	650, 000
Less: Fixed Costs		450, 000
Income before taxes		200, 000

Explanation of Solution

Computation of sales:

Sales unit [As computed in Requirement 4]: 21, 666 units

Selling price per unit: $50

Sales = 21, 666*$50

Sales = $1, 083, 333

Computation of variable costs:

Sales unit [As computed in Requirement 4]: 21, 666 units

Variable costs per unit: $20

Variable costs = 21, 666*$20

Variable costs = $433, 333