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Techniques for Estimating Fixed and Variable Costs

LO1: Prepare a contribution margin income statement.

Contribution Margin Statement

- Traditional statement mingles controllable and non-controllable costs
- In short-term, variable costs are usually controllable and fixed costs are not
- Contribution margin statement separates fixed and variable costs
- Some Terms
- Contribution margin: Revenues less variable costs
- Include both manufacturing and marketing costs
- Unit Contribution Margin: The contribution margin from one unit

LO1: Prepare a contribution margin income statement.

Contribution Margin Statement

How does this help Tom and Lynda’s decision?

LO1: Prepare a contribution margin income statement.

Application to Hercules

- Can also be computed directly as:

LO1: Prepare a contribution margin income statement.

Hercules’ rental cost does not change by offering yoga. Hercules will incur this cost regardless of Tom and Lynda’s decision. The decrease in salaries paid would be a benefit. We would include the amount as a controllable fixed cost with a negative value.

- Bill and Ted recently opened a plumbing business. The business currently has $500 monthly depreciation for its two trucks as its only fixed costs. During the first month, the company had 10 service calls each earning $99 revenue per call and variable costs amounting to $20 per call for plumbing supplies and gas. How much is Bill and Ted’s contribution margin for its first month?
- a) $990
- b) $790
- c) $490
- d) $700

- Bill and Ted recently opened a plumbing business. The business currently has $500 monthly depreciation for its two trucks as its only fixed costs. During the first month, the company had 10 service calls each earning $99 revenue per call and variable costs amounting to $20 per call for plumbing supplies and gas. How much is Bill and Ted’s contribution margin for its first month?
- a) $990
- b) $790
- c) $490
- d) $700

Contribution margin equals revenue less variable costs or ($99 x 10) – ($20 x 10) = $790.

How to Construct CM Statement?

- Two step process
- Form “model” of underlying relations
- Estimate model using historical data
- Use model to project future costs and benefits
- Confidence in estimate depends on
- Traceability
- Relevant range for the model

LO1: Prepare a contribution margin income statement.

Using Historical Data to Estimate Cost Structure

LO1: Prepare a contribution margin income statement.

Benefits to Plotting Data

- Obtain visual confirmation of expected relation
- Help determine cost driver
- Identify unusual patterns
- Curvilinear, Steps
- Identify outliers
- Eliminate from further analysis
- Help determine relevant range

LO1: Prepare a contribution margin income statement.

LO1: Prepare a contribution margin income statement.

Account Classification

- Analyze each account / type of cost to determine controllability for given decision
- We calculate the change in variable costs as:
- Sum the costs classified as variable to obtain the total variable costs for the most recent period.
- Divide the amount in (1) by the volume of activity for the corresponding period to estimate the unit variable cost (e.g., variable cost per member).
- Multiply (2) by the change in activity to estimate the total controllable variable cost.
- We add up the change in the accounts classified as “fixed”

LO2: Use the account classification method to identify fixed and variable costs.

Application to Hercules

- We can calculate
- Total revenue = $80,000 or $80 per member per month
- Total variable costs = $30,000 or $30 per member per month
- Contribution is $50 per month per member
- The change in the fixed cost is $12,000 per month
- Change in profit = 30 members * 12 months * $50 - $12,000 = $6,000

LO2: Use the account classification method to identify fixed and variable costs.

Account Classification: Evaluation

- Benefits
- Accurate if done well
- Allows for entire cost hierarchy
- Costs
- Time consuming and subjective
- Based on expertise of person doing the task
- Maybe best suited for “new” operations where historical patterns are not likely to occur.

LO2: Use the account classification method to identify fixed and variable costs.

High-Low Method

- Construct model that classifies all costs as being fixed or variable
- Need to estimate two parameters
- Fixed cost and unit variable cost
- Pick two points (highest and lowest activity level) to estimate

LO3: Compute fixed and variable costs using the high-low method.

Graphical Illustration

LO3: Compute fixed and variable costs using the high-low method.

Numerical Example

Fixed cost per month

= $78,000 – (1,250 members ×$32 per member)

= $38,000

LO3: Compute fixed and variable costs using the high-low method.

High-Low Method: Evaluation

- Advantages
- Simple, easy to implement
- Can easily try out alternate drivers
- Drawbacks
- Assumes simple cost structure
- Ignores information in other data
- Caveats
- Be sure to plot. Identify outliers, unusual patterns
- Use high and low activity (to maximize relevant range) and not the high and low cost

LO3: Compute fixed and variable costs using the high-low method.

1

100

2

$30

3

$40,000

4

Difference in total costs = $76,000 - $73,000 = $3,000

1

Difference in activity volume = 1,200 - 1,100 = 100 members

2

Variable cost per member = $3,000/1,000 = $30

3

Fixed costs per month = $76,000 - ($30 x 1,200) = $40,000

4

Regression Analysis

- Statistical method to find line that best fits the data
- Defined criterion for “best fit”
- Difficult to do by hand
- Spreadsheet programs
- Statistical software

LO4: Perform regression analysis to estimate fixed and variable costs.

Regression: Inputs into Excel

LO4: Perform regression analysis to estimate fixed and variable costs.

Regression Output in Excel

LO4: Perform regression analysis to estimate fixed and variable costs.

Which of the following is correct with regard to using regression analysis to estimate fixed and variable costs?

- Using the p-value of .05 versus .01 indicates a much better confidence in an estimate.
- Regression makes a number of assumptions about the data used in its analysis.
- Regression is usually limited to one or fewer observations.
- There will always be x, y, and z coordinates using regression analysis.

Which of the following is correct with regard to using regression analysis to estimate fixed and variable costs?

- Using the p-value of .05 versus .01 indicates a much better confidence in an estimate.
- Regression makes a number of assumptions about the data used in its analysis.
- Regression is usually limited to one or fewer observations.
- There will always be x, y, and z coordinates using regression analysis.

Regression uses a number of assumptions about data including that some data do not have variability over a period of time.

1

2

$29,300

$40,715.88

3

$70,015.88

4

Unit variable cost = $29.30

1

Total variable costs = $29.30 x 1,000 = $29,300

2

Fixed costs = $40,715.88

3

Total costs = $29,300 + $40,715.88 = $70,015.88

4

Regression: Evaluation

- Benefits
- Uses all available data
- Precise statements possible
- Can use many drivers
- Costs
- Makes many assumptions regarding data
- Applying technique well requires extensive training and considerable work
- Best suited when historical cost patterns are complex and are likely to continue

LO4: Perform regression analysis to estimate fixed and variable costs.

Choosing the Best Method

- No one method is always best
- Account classification is best when historical patterns may not continue
- High-low may be preferred for quick and simple estimates
- Regression might be called for when cost patterns are complex and we expect historical relations to continue
- Estimates are only valid under relevant range

LO4: Perform regression analysis to estimate fixed and variable costs.

Segmented Statements

- Firms often prepare contribution margin statements for individual products / markets
- Such a presentation helps with decision making
- Can assign traceable fixed costs to get:
- Segment contribution
- Product contribution
- Can extend to customer groupings, if needed
- We do not allocate common fixed costs to segments

LO5: Construct segmented contribution margin statements.

LO5: Construct segmented contribution margin statements.

Total variable costs are: $16,422,000 + $901,600 + $418,600 = $17,742,200

- Thus, each desk has a variable cost of:($17,742,200/32,200) = $551
- In turn, Office Gallery would experience a negative contribution of $26 per desk that it sells for $525.
- At a volume of 1,000 desks, Office Gallery would lose $26,000. Notice that fixed costs are not controllable for this decision.

Learning Effects

- Empirical phenomenon
- Most applicable to labor costs
- Strong effects in assembly operations
- People learn and become more efficient over time
- The reduction is predictable

Appendix : Learning Curves

Appendix : Learning Curves

Doubling Approach

Appendix : Learning Curves

Exercise 4.32

Contribution margin statement (LO1)

Suppose a firm provides you with the following information for the most recent period of operations: (a) Sales = 500 units; (b) Revenues = $15,000; (c) Variable manufacturing costs = $5,000; (d) Variable selling and administrative costs = $1,000; (e) Fixed manufacturing costs = $6,000, and; (f) Fixed selling and administrative costs = $2,000.

Required:

Calculate both the unit contribution margin and contribution margin, and prepare a contribution margin statement.

Unit contribution margin = Price – all variable costs

We first calculate price = ($15,000 revenue/500 units) = $30 per unit. Given that variable manufacturing costs = $10 per unit and variable selling costs = $2 per unit, then unit contribution margin = $30 - $10 - $2 = $18 per unit.

Contribution margin = number of units × unit contribution margin

Thus, contribution margin = 500 units × $18/unit = $9,000.

The following is the contribution margin statement.

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