Chapter 5
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Chapter 5. 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.

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Chapter 5

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Chapter 5

Chapter 5


Assumptions of cvp analysis

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

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

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

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.


Contribution margin ratio

Unit CM

Unit selling price

CM Ratio =

$200

$500

= 40%

Contribution Margin Ratio

In terms of contibution margin per unit, the contribution margin ratiois:

For Wind Bicycle Co. the ratio is:


Contribution margin ratio1

Total CM

Total sales

CM Ratio =

$100,000

$250,000

= 40%

Contribution Margin Ratio

The contribution margin ratiousing

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


Break even analysis

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

B/E Relationships in Graphic Form

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


B e graph

Break-even point

B/E Graph

Profit Area

Dollars

Loss Area

Units


Break even analysis cont d

Break-Even Analysis (cont’d)

Here is information from Wind Bicycle Co.:


Equation method

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 method1

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


Contribution margin method

Break-even point

in units sold

Fixed expenses

Unit contribution margin

=

Contribution Margin Method

The contribution margin method is a variation of the equation method.

Break-even point in

total sales dollars

Fixed expenses

CM ratio

=


Target profit analysis

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 method2

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 method3

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 contribution margin method

Unit sales to attain

the target profit

Fixed expenses + Target profit

Unit contribution margin

=

$80,000 + $100,000

$200 per bike

= 900 bikes

The Contribution Margin Method

We 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 method1

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

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

The Margin of Safety

Margin of safety = Total sales - Break-even sales


Operating leverage

Degree of

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 leverage1

Operating Leverage

10% increase in sales from

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

. . . results in a 50% increase in

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


Operating leverage2

Operating Leverage

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

The Concept of Sales Mix

  • 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.


Multi product break even analysis

$265,000

$550,000

= 48.2% (rounded)

Multi-Product Break-Even Analysis

Bikes comprise 45% of RBC’s total sales revenue and carts comprise the remaining 55%. RBC provides the following information:


Multi product break even analysis1

Multi-Product Break-Even Analysis

$170,00048.2%

Dollar sales tobreak even

= $352,697

=

Dollar sales to break even

Fixed expenses

CM ratio

=


End of chapter 5

End of Chapter 5


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