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Assumptions of CVP Analysis

- Selling price is constant.
- Costs are linear.
- In multi-product companies, the sales mix is constant.
- In manufacturing companies, inventories do not change (units produced = units sold).

The Basics of Cost-Volume-Profit (CVP) Analysis

Contribution Margin (CM) is the amount remaining from sales revenue after variable expenses have been deducted.

The Contribution Approach

For each additional unit Wind sells, $200 more in contribution margin will help to cover fixed expenses and profit.

The Variable Expense Ratio

The variable expense ratio is the ratio of variable expenses to sales. It can be computed by dividing the total variable expenses by the total sales, or in a single product analysis, it can be computed by dividing the variable expenses per unit by the unit selling price.

Unit selling price

CM Ratio =

$200

$500

= 40%

Contribution Margin RatioIn terms of contibution margin per unit, the contribution margin ratiois:

For Wind Bicycle Co. the ratio is:

Total sales

CM Ratio =

$100,000

$250,000

= 40%

Contribution Margin RatioThe contribution margin ratiousing

totaldollars is:For Wind Bicycle Co. the ratio is:

Break-Even Analysis

Break-even analysis can be approached in three ways:

- Graphical analysis.
- Equation method.
- Contribution margin method.

B/E Relationships in Graphic Form

Viewing CVP relationships in a graph is often helpful. Consider the following information for Wind Co.:

Break-Even Analysis (cont’d)

Here is information from Wind Bicycle Co.:

Equation Method

- We calculate the break-even point in units as follows:

Sales = Variable expenses + Fixed expenses + Profits

$500Q = $300Q + $80,000 + $0

$200Q = $80,000

Q = $80,000 ÷ $200 per bike

Q = 400 bikes

Equation Method

- We can also use the following equation to compute the break-even point in sales dollars.

Sales = Variable expenses + Fixed expenses + Profits

X = 0.60X + $80,000 + $0

0.40X = $80,000

X = $80,000 ÷ 0.40

X = $200,000

in units sold

Fixed expenses

Unit contribution margin

=

Contribution Margin MethodThe contribution margin method is a variation of the equation method.

Break-even point in

total sales dollars

Fixed expenses

CM ratio

=

Target Profit Analysis

Suppose Wind Co. wants to know how many bikes must be sold to earn a profit of $100,000.

We can use either the Equation or Contribution Margin approaches to determine the sales volume needed to achieve a target net profit.

Equation Method

We calculate the target profit in units as follows:

Sales = Variable expenses + Fixed expenses + Profits

$500Q = $300Q + $80,000 + $100,000

$200Q = $180,000

Q = $180,000 ÷ $200 per bike

Q = 900 bikes

Equation Method

We can also use the following equation to compute the target profit in sales dollars.

Sales = Variable expenses + Fixed expenses + Profits

X = 0.60X + $80,000 + $100,000

0.40X = $180,000

X = $180,000 ÷ 0.40

X = $450,000

the target profit

Fixed expenses + Target profit

Unit contribution margin

=

$80,000 + $100,000

$200 per bike

= 900 bikes

The Contribution Margin MethodWe can determine the number of bikes that must be sold to earn a target profit of $100,000 using the contribution margin approach.

The Contribution Margin Method

We can determine the sales needed to earn a target profit of $100,000 using the contribution margin approach.

Sales to attain

the target profit

Fixed expenses + Target profit

Contribution Margin Ratio

=

$80,000 + $100,000

40%

= $450,000

The margin of safety is the excess of budgeted (or actual) sales over the break-even volume of sales.

The Margin of SafetyMargin of safety = Total sales - Break-even sales

Degree of sales over the break-even volume of sales.

operating leverage

Contribution margin

Net operating income

=

Operating Leverage- A measure of how sensitive net operating income is to percentage changes in sales.
- With high operating leverage, a small percentage increase in sales can produce a much larger percentage increase in net operating income.

Operating Leverage sales over the break-even volume of sales.

10% increase in sales from

$250,000 to $275,000 . . .

. . . results in a 50% increase in

income from $20,000 to $30,000.

Operating Leverage sales over the break-even volume of sales.

With an operating leverage of 5, if Wind increases its sales by 10%, net operating income would increase by 50%.

Here’s the verification!

The Concept of Sales Mix sales over the break-even volume of sales.

- Sales mix is the relative proportion in which a company’s products are sold.
- Different products have different selling prices, cost structures, and contribution margins.
- When a company sells more than one product, break-even analysis becomes more complex as the following example illustrates.

$265,000 sales over the break-even volume of sales.

$550,000

= 48.2% (rounded)

Multi-Product Break-Even AnalysisBikes comprise 45% of RBC’s total sales revenue and carts comprise the remaining 55%. RBC provides the following information:

Multi-Product Break-Even Analysis sales over the break-even volume of sales.

$170,00048.2%

Dollar sales tobreak even

= $352,697

=

Dollar sales to break even

Fixed expenses

CM ratio

=

End of Chapter 5 sales over the break-even volume of sales.

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