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Chapter 4. Techniques for Estimating Fixed and Variable Costs. Traditional Income Statement. LO1: Prepare a contribution margin income statement. Contribution Margin Statement. Traditional statement mingles controllable and non-controllable costs

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## Chapter 4

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**Chapter 4**Techniques for Estimating Fixed and Variable Costs**Traditional Income Statement**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.**Test Your Knowledge!**• 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**Test Your Knowledge!**• 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.**Cost Patterns**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.**$3,000**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.**Test Your Knowledge!**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.**Test Your Knowledge!**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.**$29.30**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.**Segment Contribution Margin**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**Graphical Representation**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.**Exercise 4.32 (Continued)**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.**Exercise 4.32 (Concluded)**The following is the contribution margin statement.

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