Chapter Four

1
Chapter Four
2
Objectives

• Identify common cost behavior patterns.
• Estimate the relation between cost and activity
  using account analysis and the high-low method.
• Perform cost-volume-profit-analysis for single
  products.
• Perform cost-volume-profit-analysis for multiple
  products.

3
Objectives (continued)

• Discuss the effect of operating leverage.
• Use the contribution margin per unit of the
  constraint to analyze situations involving a
  resource constraint.

4
Cost Behavior Patterns

• Refer to the way costs change when the volume
• of units produced during a period changes.
• Variable Costs are costs that change
• proportional to units produced.
• Fixed Costs are costs that do not change at all
  
• when the number of units produced is increased
• or decreased.
• Mixed Costs are costs that can be analyzed into
  
• fixed and variable components.
• Step Costs are fixed for a range of volume but
• then increase to a higher level for the next
  range etc.
• They increase by steps.

5
Variable Costs
6
Fixed Costs
7
Analysis of fixed costs

• Fixed Costs may be analyzed into
• Committed Fixed Costs
• These costs cannot be changed in the short run.
• Discretionary Fixed Costs
• These costs can be changed in the short run
  but they are independent of production or sales
  volume

8
Mixed Costs total production costs contain
fixed and variable elements but many individual
costs such as electricity or indirect labor are
also mixed costs.
9
Step costs

• Many costs increase by steps as shown in
  illustration 4-4 on page 115.
• You cant hire half a production supervisor or
  buy half a truck.

10
Cost Estimation Methods

• Cost Estimation Methods are frequently required
  to separate the fixed and variable components of
  a total cost pool. Methods include

• Account Analysis each cost is defined as fixed,
  variable or mixed based on judgment. Consider
  exercise 4-10.
• 2. Estimation of fixed and variable components
  using data from the recent past by means of
• a. Scattergraph.
• b. High-Low Method
• c. Regression

11
Scattergraph
The slope of the line is the variable cost per
unit. The intercept is the fixed cost
12
High-Low Method

• Uses the highest volume activity level and the
  lowest volume activity level to determine the
  intercept and slope
• Example In the illustrated case presented on
  page 118, the cost at 500 units of output is
  150,000 and at 3,000 units of output is
  400,000. Calculate variable and fixed costs,
  respectively.

13
High-Low Method

• Solution High Low Change
• Costs 400,000 150,000 250,000
• Units 3,000 500 2,500
• Calculate Variable Cost Per Unit
• 250,000/2,500 100
• Calculate Total Fixed Costs
• 400,000 (3,000 x 100) 100,000

14
High-Low Method
The line connects the high activity and low
activity points. Other points are ignored
15
Regression Analysis
A mathematical program draws the line minimizing
the sum of squared vertical distances between
the line and all the points
16
The Relevant Range
is the range of activity within which the
estimate of fixed and variable costs are valid.
Costs are assumed to be linear within the
relevant range
17
Cost-Volume-Profit Analysis

• Uses information about fixed and variable costs
  to study the relationships between costs, volume
  and profit within the relevant range.
• Useful for planning, presentation and evaluation
  of alternatives, and decision making.

18
Cost-Volume-Profit Analysis

• The Profit Equation
• Contribution Margin
• Contribution Margin Ratio
• Breakeven Point
• Margin of Safety
• What-if Analysis

19
The Profit Equation

• Let
• Q Quantity of units produced and sold
• SP Selling price per unit
• VC Variable cost per unit
• TFC Total fixed cost
• Then
• Profit SP x Q VC x Q TFC
• or Profit (SP-VC) x Q - TFC

20
Contribution Margin

• But it is simpler to think of the difference
  between selling price and variable cost per unit
  as the contribution margin per unit.
• or SP VC CMU

21
Contribution Margin Ratio

• Another useful concept is the contribution margin
  ratio which shows the contribution margin per
  unit as a of the selling price.
• CMU / SP CMR
• Even if we only know total Sales and total
  variable costs, we can still derive the
  contribution margin ratio as
• Sales Variable Costs CMR
• Sales

22
Break-Even Point

• The break even point is the number of units Q or
  Sales we need to sell to exactly break even.
• Profit 0 CMU x Q - TFC
• Therefore TFC CMU x Q
• TFC/CMU Q
• Similarly 0 CMR x Sales - TFC
• So TFC/CMR Sales

23
Break-Even Point
24
Some extensions of CVP analysis

• Target profit. How many units must be sold to
  achieve a target profit?
• Margin of Safety. By how many units or by what
  can sales decrease without losing money?
• What is the lowest price we can charge and still
  break even if we sell a certain volume.

25
What If Analysis

• Considers the effects on volume and profit of
  changes in
• Selling price per unit
• Variable cost per unit
• Total fixed cost

26
Multiproduct Analysis

• C-V-P may be applied to multiple products.
• An Average Contribution Margin Approach (used
  for similar products).
• Contribution Margin Ratio Approach (used for
  substantially different products).

27
Average Contribution Margin Approach

• Example the contribution margin of product A is
  8 and B is 5. Two units of B are sold for each
  unit of A. The Weighted Average Contribution
  Margin is 6.00.
• 2/3 5 1/3 8 10/3 8/3 18/3
• To use this approach we must assume the MIX of
  sales between B and A i.e. 2 to 1 is fixed.

28
Contribution Margin Ratio Approach

• Retail Stores sell a wide variety of products
  with different unit contribution margins. But
  the mark-up may be the same for all products.
  In that case the CMR will be the same, so we can
  use the CMR to find break even or target profit
  volume in sales
• Or if the retailer has higher mark-up and lower
  mark-up items and the MIX is known then an
  average CMR can be used as in illustration 4-14

29
Major Assumptions in C-V-P Analysis

• Costs can be accurately separated into variable
  and fixed components.
• Fixed costs remain fixed and variable costs per
  unit do not change over the relevant range.
• 3. If an average contribution margin is used then
  the mix must be constant.

30
Operating Leverage

• Total contribution margin divided by profit at
  any level of volume is called operating leverage.
  
• Firms whose costs are mostly fixed have high
  operating leverage because a small change in
  sales produces a relatively high change in
  profits
• Operating leverage is used to determine the
  sensitivity of profits to a change in sales.
• The change in profits is to the change in
  sales multiplied times the operating leverage.

31
Operating Leverage

• Example of Operating Leverage
• Firm 1 Firm 2
• Sales 10,000,000 10,000,000
• VC 5,000,000 7,000,000
• CM 5,000,000 3,000,000
• FC 3,000,000 1,000,000
• Profit 2,000,000 2,000,000
• Which firm has more operating leverage?
• By what will profits increase if sales
  increase by 10 for each firm?

32
Constraints

• A reference to scarce resources.
• Examples of constraints include manufacturing
  space, labor, parts and materials etc..
• The focus shifts from Contribution Margin per
  unit of product to the contribution margin per
  unit of scarce resource or constraint.
• 4. Look for products which yield the highest
  contribution margin per unit of scarce resource

33
Quick Review Question 1

• At Winford Corp., the selling price per unit for
  lawn mowers is 120, variable cost per unit is
  55. Fixed costs are 130,000. Contribution
  Margin per unit is?
• 65
• 75
• 175
• 30

34
Quick Review Question 1

• At Winford Corp., the selling price per unit for
  lawn mowers is 120, variable cost per unit is
  55. Fixed costs are 130,000. Contribution
  Margin per unit is?
• 65
• 75
• 175
• 30

35
Quick Review Question 2

• At Winford Corp., the selling price per unit for
  lawn mowers is 120, variable cost per unit is
  55. Fixed costs are 130,000. Break-Even Point
  is?
• 1,000 units
• 1,083 units
• 2,000 units
• None of these

36
Quick Review Question 2

• At Winford Corp., the selling price per unit for
  lawn mowers is 120, variable cost per unit is
  55. Fixed costs are 130,000. Break-Even Point
  is?
• 1,000 units
• 1,083 units
• 2,000 units
• None of these

37
Quick Review Question 3

• At Winford Corp., the selling price per unit for
  lawn mowers is 120, variable cost per unit is
  55. Fixed costs are 130,000. Expected sales are
  4,200 units. The Margin of Safety is?
• 264,000
• 384,000
• 143,000
• 121,000

38
Quick Review Question 3

• At Winford Corp., the selling price per unit for
  lawn mowers is 120, variable cost per unit is
  55. Fixed costs are 130,000. Expected sales are
  4,200 units. The Margin of Safety is?
• 264,000
• 384,000
• 143,000
• 121,000

39
Quick Review Question 4

• At Winford Corp., the selling price per unit for
  lawn mowers is 120, variable cost per unit is
  55. Fixed costs are 130,000. Expected sales are
  4,200 units. What is profit expected to be?
• Answer here _________________

40
Quick Review Question 4

• At Winford Corp., the selling price per unit for
  lawn mowers is 120, variable cost per unit is
  55. Fixed costs are 130,000. Expected sales are
  4,200 units. What is profit expected to be?
• Answer here 143,000