CostVolumeProfit Relationships

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Cost-Volume-Profit Relationships
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LEARNING OBJECTIVES
After studying this chapter, you should be able
to

• 1. Explain how changes in activity affect
  contribution margin and net operating income.
• 2. Prepare and interpret a cost-volume-profit
  (CVP) graph.
• 3. Use the contribution margin (CM) ratio to
  compute changes in contribution margin and net
  operating income resulting from changes in sales
  volume.
• 4. Show the effects on contribution margin of
  changes in variable costs, fixed costs, selling
  price, and volume.
• 5. Compute the break-even point.

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LEARNING OBJECTIVES
After studying this chapter, you should be able
to

• 6. Determine the level of sales needed to
  achieve a desired target profit.
• 7. Use the margin of safety and explain its
  significance.
• 8. Compute the degree of operating leverage at a
  particular level of sales and explain how the
  degree of operating leverage can be used to
  predict changes to net operating income.
• 9. Compute the break-even point for a
  multiple-product company and explain the effects
  of shifts in the sales mix on contribution margin
  and the break-even point.
• 10. (Appendix 6A) Understand cost-volume-profit
  with uncertainty.

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The Basics of Cost-Volume-Profit (CVP) Analysis
Contribution Margin (CM) is the amount remaining
from sales revenue after variable expenses have
been deducted.
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The Basics of Cost-Volume-Profit (CVP) Analysis
CM is used to cover fixed expenses.
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The Basics of Cost-Volume-Profit (CVP) Analysis
After covering fixed costs, any remaining CM
contributes to income.
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The Contribution Approach

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

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The Contribution Approach

• Each month Wind must generate at least 80,000 in
  total CM to break even.

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The Contribution Approach

• If Wind sells 400 units in a month, it will be
  operating at the break-even point.

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The Contribution Approach

• If Wind sells one additional unit (401
  bikes), net income will increase by 200.

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The Contribution Approach

• The break-even point can be defined either as
• The point where total sales revenue equals total
  expenses (variable and fixed).
• The point where total contribution margin equals
  total fixed expenses.

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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
  Wind Co.

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CVP Graph
Total Expenses
Dollars
Fixed expenses
Units
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CVP Graph
Total Sales
Dollars
Units
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CVP Graph
Profit Area
Dollars
Break-even point
Loss Area
Units
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Contribution Margin Ratio

• The contribution margin ratio isFor Wind
  Bicycle Co. the ratio is

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Contribution Margin Ratio

• At Wind, each 1.00 increase in sales revenue
  results in a total contribution margin increase
  of 40.
• If sales increase by 50,000, what will be the
  increase in total contribution margin?

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Contribution Margin Ratio
A 50,000 increase in sales revenue
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Contribution Margin Ratio
A 50,000 increase in sales revenue results in a
20,000 increase in CM or (50,000 40
20,000)
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Changes in Fixed Costs and Sales Volume

• Wind 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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Changes in Fixed Costs and Sales Volume
80,000 10,000 advertising 90,000
Sales increased by 20,000, but net income
decreased by 2,000.
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Changes in Fixed Costs and Sales Volume

• The Shortcut Solution

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APPLICATIONS OF CVP

• Consider the following basic data
• Per unit Percent
• Sales Price 250 100
• Less Variable cost 150 60
• Contribution margin 100 40
• Fixed costs total 35,000

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Change in Fixed Cost and Sales Volume

• Current sales are 100,000. Sales manager feels
  10,000 increase in sales budget will provide
  30,000 increase in sales. Should the budget be
  changed?
• Incremental CM approach
• 30,000 x 40 CM ratio 12,000
• Additional advertising expense 10,000
• Increase in net income 2,000

YES
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Change in Variable Cost and Sales Volume

• Management is considering increasing quality of
  speakers at an additional cost of 10 per speaker
  and plan to sell 80 more units. Should management
  increase quality?
• Expected total CM
• (480 speakers x 90) 43,200
• Present total CM
• (400 speakers x 100) 40,000
• Increase in total contribution margin 3,200
  (and net income)

YES
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Change in Fixed Cost, Sales Price and Sales
Volume

• Management advises that if selling price dropped
  20 per speaker and advertising increased by
  15,000/month, sales would increase 50. Good
  idea?
• Expected total CM
• (400 x 150 x 80) 48,000
• Present total CM (400 x 100) 40,000
• Incremental CM 8,000
• Additional advertising cost 15,000
• Reduction in net income (7,000)

NO
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Changes in Variable Cost, Fixed Cost, and Sales
Volume

• A plan to switch salespeople from flat salary
  (6,000 per month) to a sales commission of 15
  per speaker could increase sales by 15. Good
  idea?
• Expected total CM (400x115x85) 39,100
• Current total CM (400 x 100) 40,000
• Decrease in total CM (900)
• Salaries avoided if commission paid 6,000
• Increase in net income 5,100

YES
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Change in Regular Sales Price

• A wholesaler is willing to buy 150 speakers if we
  will give him a discount off our price. The sale
  will not disturb regular sales and will not
  change fixed costs. We want to make 3,000 on
  this sale. What price should we quote?
• Variable cost per speaker 150
• Desired profit on order (3,000/150) 20
• Quoted price per speaker 170

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Break-Even Analysis

• Break-even analysis can be approached in two
  ways
• Equation method
• Contribution margin method.

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Equation Method
Profits Sales (Variable expenses Fixed
expenses)
OR
Sales Variable expenses Fixed expenses
Profits
At the break-even point profits equal zero.
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Equation Method

• Here is the information from Wind Bicycle Co.

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Equation Method

• We calculate the break-even point as follows

Sales Variable expenses Fixed expenses
Profits
500Q 300Q 80,000 0 Where Q
Number of bikes sold 500 Unit sales
price 300 Unit variable expenses 80,000
Total fixed expenses
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Equation Method

• We calculate the break-even point as follows

Sales Variable expenses Fixed expenses
Profits
500Q 300Q 80,000 0 200Q 80,000
Q 400 bikes
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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
Where X Total sales dollars 0.60
Variable expenses as a percentage
of sales 80,000 Total fixed expenses
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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 200,000
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Contribution Margin Method

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

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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 our CVP formula to determine the sales
  volume needed to achieve a target net profit
  figure.

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The CVP Equation
Sales Variable expenses Fixed expenses
Profits
500Q 300Q 80,000 100,000 200Q
180,000 Q 900 bikes
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The Contribution Margin Approach

• We can determine the number of bikes that must
  be sold to earn a profit of 100,000 using the
  contribution margin approach.

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The Margin of Safety

• Excess of budgeted (or actual) sales over the
  break-even volume of sales. The amount by which
  sales can drop before losses begin to be incurred.

Margin of safety Total sales - Break-even
sales
Lets calculate the margin of safety for Wind.
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The Margin of Safety

• Wind 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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The Margin of Safety

• The margin of safety can be expressed as 20
  percent of sales.(50,000 250,000)

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Operating Leverage

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

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Operating Leverage
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Operating Leverage

• With a measure of operating leverage of 5, if
  Wind increases its sales by 10, net income
  would increase by 50.

Heres the proof!
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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.
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The Concept of Sales Mix

• Sales mix is the relative proportions in which a
  companys products are sold.
• Different products have different selling prices,
  cost structures, and contribution margins.
• Lets assume Wind sells bikes and carts and see
  how we deal with break-even analysis.

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The Concept of Sales Mix

• Wind Bicycle Co. provides us with the following
  information

265,000 550,000
48 (rounded)
Break-even point in sales dollars
170,000 0.48
354,167 (rounded)
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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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Cost-Volume-Profitwith Uncertainty
Appendix6A
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CVP with Uncertainty

• Use a decision tree to simplify calculations
• The decision tree is used to calculate profits
  under various alternatives
• A second decision tree can be used to calculate
  the probabilities of the various scenarios to
  further determine a reasonable estimate of profit
• A computer can be used to save time

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End of Chapter 6