CostVolumeProfit CVP Analysis

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Cost-Volume-Profit (CVP) Analysis

• CVP analysis is a short-run planning tool which
  is based on the relationships among

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Three Approaches to CVP

• Contribution Margin Income Statement
• Profit Equation Approach
• Graphical approach

All techniques will give same answer. Which is
appropriate depends on decision context as well
as personal preference. Ex. Graphical approach
wont be as precise, but may be more useful for
explaining relationships.
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The Contribution Margin Income Statement

• Consider the following information for Nord, a
  bicycle manufacturing company

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Questions

• How much does each bicycle sold contribute
  toward fixed costs, taxes and profit?
• How much total contribution margin does Nord need
  to break-even?
• How many bicycles must they sell to break-even?
• If Nord sell 50 bicycles more than needed to
  break-even, how much pre-tax profit will be
  earned?

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Break-even formula
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But what if we want to do more than break-even?

• Target CM must cover fixed costs plus pre-tax
  profit objective.
• Ex. Suppose Nord wants to earn a pre-tax profit
  of 100,000. How many bicycles must they sell?

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How to incorporate taxes?
After-tax profit
Pre-tax profit
(1-tax rate)
How many bicycles must Nord sell to earn 66,000,
after taxes of 40? What level of sales
() is required to earn 66,000 after tax?
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Contribution Margin Ratio ()

• The contribution margin can also be stated as a
  percentage of sales.

What does Nords CM tell us?
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Question?

• Nord is currently selling 500 bikes per month.
• The companys sales manager believes that an
  increase of 10,000 in the monthly advertising
  budget, would increase bike sales to 540 units.
• Should we authorize the requested increase in the
  advertising budget?

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Contribution Margin Ratio

• The CM ratio can be used to calculate the total
  sales dollars needed to earn a target profit

How much total sales () must Nord generate to
earn 90,000 after taxes of 40?
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Equation Method
Sales (Variable expenses Fixed expenses)
Pre-Tax Profits
OR
Sales Variable expenses Fixed expenses
Pre-Tax Profits
At the break-even point profits and taxes equal
zero.
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Equation Method

• For example, Nords break-even point can be found
  by solving the following equation

Sales Variable expenses Fixed expenses
Pre-tax Profits
500X 300X 80,000 0 Where X Number
of bikes sold 500 Unit sales price 300
Unit variable expenses 80,000 Total
fixed expenses
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Solving for X (number of bikes)
500X 300X 80,000 0 200X 80,000
X 400 units
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Equation Method

• We can also use the following equation to compute
  sales dollars needed to earn a target pre-tax
  profit of 100,000

Sales Variable expenses Fixed expenses
Pre-Tax Profits
X .60X 80,000 100,000
Where X Total sales dollars .60
Variable expenses as a percentage of
sales 80,000 Total fixed expenses
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Solving for X (Total Sales )
Sales Variable expenses Fixed expenses
Pre-Tax Profits
X .60X 80,000 100,000
.40X 180,000 X 450,000
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CVP Relationships in Graphic Form

• Viewing CVP relationships in a graph gives
  managers a perspective that can be obtained in no
  other way.
• Consider the following information for Nord Co.

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CVP Graph
Total Costs
Dollars
Units
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CVP Graph
Total Sales
Dollars
Units
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CVP Graph
Profit Area
Dollars
Break-even point 400 units or 200,000 sales.
Loss Area
Units
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The Margin of Safety

• Excess of budgeted (or actual) sales over the
  break-even level of sales.
• Can be stated in either units or sales ()
• Amount by which sales can drop before losses
  begin to be incurred.What is Nords margin of
  safety if current sales is 500 bikes (250,000)

Margin of Safety Current sales - Break-even
sales
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The Margin of Safety

• Nord has a break-even point of 200,000. If
  actual sales are 250,000, the margin of safety
  is 50,000 or 100 bikes.

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Degree of Operating Leverage (DOL)

• A measure of the extent to which fixed costs are
  being used in an organization.
• Operating leverage is . . .
• greatest in companies that have a high proportion
  of fixed costs in relation to variable costs.
• lowest in companies that have a low proportion of
  fixed costs in relation to variable costs.

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Nord Bicycle Company
What is Nords degree of operating leverage
(DOL)? What does this tell us about Nords
operating risk compared to a company that has a
DOL of 3?
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What does DOL mean?

• DOL tells us how a change in sales will
  translate into a change in profits.If Nord
  increases its sales by 5, what will happen to
  profits?
• If Nords sales drop by 10, how much will
  profits drop?

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Multi-Product CVP

• Most companies sell more than one product.
• Different products are likely to have different
  selling prices, cost structures, and contribution
  margins.
• Key to multi-product CVP is to maintain a
  constant product or sales mix.
• Apply previous approach using average CM per unit
  or average CM.

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Average CM and CM per unit
Total CM
Average CM
Total Sales
Assumes a constant sales () mix.
Total CM
Average CM per unit
Total of units
Assumes a constant mix in terms of units.
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Now assume that Nord sells two products bikes
and carts.
What is the sales () mix? What is the average
CM? What is the total sales level required to
break-even? What sales () are required for each
product line? What will happen if cart sales are
300,000 and bike sales are 100,000?
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Now assume that Nord sells two products bikes
and carts.
How many bikes and carts are currently being
sold? What is the average CM per unit? How many
bikes and carts must be sold to earn a
pre-tax net income 129,000?
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Assumptions of CVP Analysis

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

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End of Chapter 10
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