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Principles of Accounting, Volume 2: Managerial Accounting

2.3 Estimate a Variable and Fixed Cost Equation and Predict Future Costs

Principles of Accounting, Volume 2: Managerial Accounting2.3 Estimate a Variable and Fixed Cost Equation and Predict Future Costs
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  1. Preface
  2. 1 Accounting as a Tool for Managers
    1. Why It Matters
    2. 1.1 Define Managerial Accounting and Identify the Three Primary Responsibilities of Management
    3. 1.2 Distinguish between Financial and Managerial Accounting
    4. 1.3 Explain the Primary Roles and Skills Required of Managerial Accountants
    5. 1.4 Describe the Role of the Institute of Management Accountants and the Use of Ethical Standards
    6. 1.5 Describe Trends in Today’s Business Environment and Analyze Their Impact on Accounting
    7. Key Terms
    8. Summary
    9. Multiple Choice
    10. Questions
    11. Exercise Set A
    12. Exercise Set B
    13. Thought Provokers
  3. 2 Building Blocks of Managerial Accounting
    1. Why It Matters
    2. 2.1 Distinguish between Merchandising, Manufacturing, and Service Organizations
    3. 2.2 Identify and Apply Basic Cost Behavior Patterns
    4. 2.3 Estimate a Variable and Fixed Cost Equation and Predict Future Costs
    5. Key Terms
    6. Summary
    7. Multiple Choice
    8. Questions
    9. Exercise Set A
    10. Exercise Set B
    11. Problem Set A
    12. Problem Set B
    13. Thought Provokers
  4. 3 Cost-Volume-Profit Analysis
    1. Why It Matters
    2. 3.1 Explain Contribution Margin and Calculate Contribution Margin per Unit, Contribution Margin Ratio, and Total Contribution Margin
    3. 3.2 Calculate a Break-Even Point in Units and Dollars
    4. 3.3 Perform Break-Even Sensitivity Analysis for a Single Product Under Changing Business Situations
    5. 3.4 Perform Break-Even Sensitivity Analysis for a Multi-Product Environment Under Changing Business Situations
    6. 3.5 Calculate and Interpret a Company’s Margin of Safety and Operating Leverage
    7. Key Terms
    8. Summary
    9. Multiple Choice
    10. Questions
    11. Exercise Set A
    12. Exercise Set B
    13. Problem Set A
    14. Problem Set B
    15. Thought Provokers
  5. 4 Job Order Costing
    1. Why It Matters
    2. 4.1 Distinguish between Job Order Costing and Process Costing
    3. 4.2 Describe and Identify the Three Major Components of Product Costs under Job Order Costing
    4. 4.3 Use the Job Order Costing Method to Trace the Flow of Product Costs through the Inventory Accounts
    5. 4.4 Compute a Predetermined Overhead Rate and Apply Overhead to Production
    6. 4.5 Compute the Cost of a Job Using Job Order Costing
    7. 4.6 Determine and Dispose of Underapplied or Overapplied Overhead
    8. 4.7 Prepare Journal Entries for a Job Order Cost System
    9. 4.8 Explain How a Job Order Cost System Applies to a Nonmanufacturing Environment
    10. Key Terms
    11. Summary
    12. Multiple Choice
    13. Questions
    14. Exercise Set A
    15. Exercise Set B
    16. Problem Set A
    17. Problem Set B
    18. Thought Provokers
  6. 5 Process Costing
    1. Why It Matters
    2. 5.1 Compare and Contrast Job Order Costing and Process Costing
    3. 5.2 Explain and Identify Conversion Costs
    4. 5.3 Explain and Compute Equivalent Units and Total Cost of Production in an Initial Processing Stage
    5. 5.4 Explain and Compute Equivalent Units and Total Cost of Production in a Subsequent Processing Stage
    6. 5.5 Prepare Journal Entries for a Process Costing System
    7. Key Terms
    8. Summary
    9. Multiple Choice
    10. Questions
    11. Exercise Set A
    12. Exercise Set B
    13. Problem Set A
    14. Problem Set B
    15. Thought Provokers
  7. 6 Activity-Based, Variable, and Absorption Costing
    1. Why It Matters
    2. 6.1 Calculate Predetermined Overhead and Total Cost under the Traditional Allocation Method
    3. 6.2 Describe and Identify Cost Drivers
    4. 6.3 Calculate Activity-Based Product Costs
    5. 6.4 Compare and Contrast Traditional and Activity-Based Costing Systems
    6. 6.5 Compare and Contrast Variable and Absorption Costing
    7. Key Terms
    8. Summary
    9. Multiple Choice
    10. Questions
    11. Exercise Set A
    12. Exercise Set B
    13. Problem Set A
    14. Problem Set B
    15. Thought Provokers
  8. 7 Budgeting
    1. Why It Matters
    2. 7.1 Describe How and Why Managers Use Budgets
    3. 7.2 Prepare Operating Budgets
    4. 7.3 Prepare Financial Budgets
    5. 7.4 Prepare Flexible Budgets
    6. 7.5 Explain How Budgets Are Used to Evaluate Goals
    7. Key Terms
    8. Summary
    9. Multiple Choice
    10. Questions
    11. Exercise Set A
    12. Exercise Set B
    13. Problem Set A
    14. Problem Set B
    15. Thought Provokers
  9. 8 Standard Costs and Variances
    1. Why It Matters
    2. 8.1 Explain How and Why a Standard Cost Is Developed
    3. 8.2 Compute and Evaluate Materials Variances
    4. 8.3 Compute and Evaluate Labor Variances
    5. 8.4 Compute and Evaluate Overhead Variances
    6. 8.5 Describe How Companies Use Variance Analysis
    7. Key Terms
    8. Summary
    9. Multiple Choice
    10. Questions
    11. Exercise Set A
    12. Exercise Set B
    13. Problem Set A
    14. Problem Set B
    15. Thought Provokers
  10. 9 Responsibility Accounting and Decentralization
    1. Why It Matters
    2. 9.1 Differentiate between Centralized and Decentralized Management
    3. 9.2 Describe How Decision-Making Differs between Centralized and Decentralized Environments
    4. 9.3 Describe the Types of Responsibility Centers
    5. 9.4 Describe the Effects of Various Decisions on Performance Evaluation of Responsibility Centers
    6. Key Terms
    7. Summary
    8. Multiple Choice
    9. Questions
    10. Exercise Set A
    11. Exercise Set B
    12. Problem Set A
    13. Problem Set B
    14. Thought Provokers
  11. 10 Short-Term Decision Making
    1. Why It Matters
    2. 10.1 Identify Relevant Information for Decision-Making
    3. 10.2 Evaluate and Determine Whether to Accept or Reject a Special Order
    4. 10.3 Evaluate and Determine Whether to Make or Buy a Component
    5. 10.4 Evaluate and Determine Whether to Keep or Discontinue a Segment or Product
    6. 10.5 Evaluate and Determine Whether to Sell or Process Further
    7. 10.6 Evaluate and Determine How to Make Decisions When Resources Are Constrained
    8. Key Terms
    9. Summary
    10. Multiple Choice
    11. Questions
    12. Exercise Set A
    13. Exercise Set B
    14. Problem Set A
    15. Problem Set B
    16. Thought Provokers
  12. 11 Capital Budgeting Decisions
    1. Why It Matters
    2. 11.1 Describe Capital Investment Decisions and How They Are Applied
    3. 11.2 Evaluate the Payback and Accounting Rate of Return in Capital Investment Decisions
    4. 11.3 Explain the Time Value of Money and Calculate Present and Future Values of Lump Sums and Annuities
    5. 11.4 Use Discounted Cash Flow Models to Make Capital Investment Decisions
    6. 11.5 Compare and Contrast Non-Time Value-Based Methods and Time Value-Based Methods in Capital Investment Decisions
    7. Key Terms
    8. Summary
    9. Multiple Choice
    10. Questions
    11. Exercise Set A
    12. Exercise Set B
    13. Problem Set A
    14. Problem Set B
    15. Thought Provokers
  13. 12 Balanced Scorecard and Other Performance Measures
    1. Why It Matters
    2. 12.1 Explain the Importance of Performance Measurement
    3. 12.2 Identify the Characteristics of an Effective Performance Measure
    4. 12.3 Evaluate an Operating Segment or a Project Using Return on Investment, Residual Income, and Economic Value Added
    5. 12.4 Describe the Balanced Scorecard and Explain How It Is Used
    6. Key Terms
    7. Summary
    8. Multiple Choice
    9. Questions
    10. Exercise Set A
    11. Exercise Set B
    12. Problem Set A
    13. Problem Set B
    14. Thought Provokers
  14. 13 Sustainability Reporting
    1. Why It Matters
    2. 13.1 Describe Sustainability and the Way It Creates Business Value
    3. 13.2 Identify User Needs for Information
    4. 13.3 Discuss Examples of Major Sustainability Initiatives
    5. 13.4 Future Issues in Sustainability
    6. Key Terms
    7. Summary
    8. Multiple Choice
    9. Questions
    10. Thought Provokers
  15. Financial Statement Analysis
  16. Time Value of Money
  17. Suggested Resources
  18. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
    11. Chapter 11
    12. Chapter 12
    13. Chapter 13
  19. Index

Sometimes, a business will need to use cost estimation techniques, particularly in the case of mixed costs, so that they can separate the fixed and variable components, since only the variable components change in the short run. Estimation is also useful for using current data to predict the effects of future changes in production on total costs. Three estimation techniques that can be used include the scatter graph, the high-low method, and regression analysis. Here we will demonstrate the scatter graph and the high-low methods (you will learn the regression analysis technique in advanced managerial accounting courses.

Functions of Cost Equations

The cost equation is a linear equation that takes into consideration total fixed costs, the fixed component of mixed costs, and variable cost per unit. Cost equations can use past data to determine patterns of past costs that can then project future costs, or they can use estimated or expected future data to estimate future costs. Recall the mixed cost equation:

alt text

where Y is the total mixed cost, a is the fixed cost, b is the variable cost per unit, and x is the level of activity.

Let’s take a more in-depth look at the cost equation by examining the costs incurred by Eagle Electronics in the manufacture of home security systems, as shown in Table 2.9.

Cost Information for Eagle Electronics
Cost Incurred Fixed or Variable Cost
Lease on manufacturing equipment Fixed $50,000 per year
Supervisor salary Fixed $75,000 per year
Direct materials Variable $50 per unit
Direct labor Variable $20 per unit
Table 2.9

By applying the cost equation, Eagle Electronics can predict its costs at any level of activity (x) as follows:

  1. Determine total fixed costs: $50,000 + $75,000 = $125,000
  2. Determine variable costs per unit: $50 + $20 = $70
  3. Complete the cost equation: Y = $125,000 + $70x

Using this equation, Eagle Electronics can now predict its total costs (Y) for any given level of activity (x), as in Figure 2.27:

Units Produced, Cost Equation, Total costs, respectively are: 5,000, Y=$125,000 + ($70 x 5,000), $475,000; 8,000, Y=$125,000 + ($70 x 8,000), $685,000; 12,000, Y=$125,000 + ($70 x 12,000), $965,000.
Figure 2.27 Total Cost Estimation for Various Production Levels. (attribution: Copyright Rice University, OpenStax, under CC BY-NC-SA 4.0 license)

When using this approach, Eagle Electronics must be certain that it is only predicting costs for its relevant range. For example, if they must hire a second supervisor in order to produce 12,000 units, they must go back and adjust the total fixed costs used in the equation. Likewise, if variable costs per unit change, these must also be adjusted.

This same approach can be used to predict costs for service and merchandising firms, as shown by examining the costs incurred by J&L Accounting to prepare a corporate income tax return, shown in Table 2.10.

Cost Information for J&L Accounting
Cost Incurred Fixed or Variable Cost
Building rent Fixed $1,000 per month
Direct labor (for CPAs) Variable $250 per tax return
Secretarial staff Fixed $2,000 per month
Accounting clerks Variable $100 per return
Table 2.10

J&L wants to predict their total costs if they complete 25 corporate tax returns in the month of February.

  1. Determine total fixed costs: $1,000 + $2,000 = $3,000
  2. Determine variable costs per tax return: $250 + $100 = $350
  3. Complete the cost equation: Y = $3,000 + $350x

Using this equation, J&L can now predict its total costs (Y) for the month of February when they anticipate preparing 25 corporate tax returns:

Y=$3,000+($350×25)Y=$3,000+$8,750Y=$11,750Y=$3,000+($350×25)Y=$3,000+$8,750Y=$11,750

J&L can now use this predicted total cost figure of $11,750 to make decisions regarding how much to charge clients or how much cash they need to cover expenses. Again, J&L must be careful to try not to predict costs outside of the relevant range without adjusting the corresponding total cost components.

J&L can make predictions for their costs because they have the data they need, but what happens when a business wants to estimate total costs but has not collected data regarding per-unit costs? This is the case for the managers at the Beach Inn, a small hotel on the coast of South Carolina. They know what their costs were for June, but now they want to predict their costs for July. They have gathered the information in Figure 2.28.

Cost Incurred, Fixed or Variable, June Costs, respectively: Insurance, Fixed, $700; Loan payment, Fixed, 2,500; Front desk staff, Variable, 3,800; Cleaning staff, Variable, 2,500; Laundry service, Variable, 1,200.
Figure 2.28 Monthly Total Cost Detail for Beach Inn. (attribution: Copyright Rice University, OpenStax, under CC BY-NC-SA 4.0 license)

In June, they had an occupancy of 75 nights. For the Beach Inn, occupancy (rooms rented) is the cost driver. Since they know what is driving their costs, they can determine their per-unit variable costs in order to forecast future costs:

Front Desk Staff75 nights=$3,80075=$50.67variable front desk staff costs per nightCleaning Staff75 nights=$2,50075=$33.33variable cleaning staff costs per nightLaundry Service75 nights=$1,20075=$16.00variable laundry service costs per nightFront Desk Staff75 nights=$3,80075=$50.67variable front desk staff costs per nightCleaning Staff75 nights=$2,50075=$33.33variable cleaning staff costs per nightLaundry Service75 nights=$1,20075=$16.00variable laundry service costs per night

Now, the Beach Inn can apply the cost equation in order to forecast total costs for any number of nights, within the relevant range.

  1. Determine total fixed costs: $700 + $2,500 = $3,200
  2. Determine variable costs per night of occupancy: $50.67 + $33.33 + $16.00 = $100
  3. Complete the cost equation: Y = $3,200 + $100x

Using this equation, the Beach Inn can now predict its total costs (Y) for the month of July, when they anticipate an occupancy of 93 nights.

Y=$3,200+($100×93)Y=$3,200+$9,300Y=$12,500Y=$3,200+($100×93)Y=$3,200+$9,300Y=$12,500

In all three examples, managers used cost data they have collected to forecast future costs at various activity levels.

Your Turn

Waymaker Furniture

Waymaker Furniture has collected cost information from its production process and now wants to predict costs for various levels of activity. They plan to use the cost equation to formulate these predictions. Information gathered from March is presented in Table 2.11.

March Cost Information for Waymaker Furniture
Cost Incurred Fixed or Variable March Cost
Plant supervisor salary Fixed $12,000 per month
Lumber (direct materials) Variable $75,000 total
Production worker wages Variable $11.00 per hour
Machine maintenance Variable $5.00 per unit produced
Lease on factory Fixed $15,000 per month
Table 2.11

In March, Waymaker produced 1,000 units and used 2,000 hours of production labor.

Using this information and the cost equation, predict Waymaker’s total costs for the levels of production in Table 2.12.

Waymaker’s Levels of Production
Month Activity Level
April 1,500 units
May 2,000 units
June 2,500 units
Table 2.12

Solution

Total Fixed Cost = $12,000 + $15,000 = $27,000. Direct Materials per Unit = $75,000 / 1,000 Units = $75 per unit. Direct Labor per Hour = $11.00. Machine Maintenance = $5.00 per unit. Total Variable Cost per Unit = $75 + $11 + $5 = $91 per unit.

Month, Activity Level, VC per Unit, Total VC, Fixed Cost, Total Cost, respectively: April, 1,500 units, $91, $136,500, $27,000, $163,500; May, 2,000 units, $91, $182,000, $27,000, $209,000; April, 12,500 units, $91, $227,500, $27,000, $254,500.

Demonstration of the Scatter Graph Method to Calculate Future Costs at Varying Activity Levels

One of the assumptions that managers must make in order to use the cost equation is that the relationship between activity and costs is linear. In other words, costs rise in direct proportion to activity. A diagnostic tool that is used to verify this assumption is a scatter graph.

A scatter graph shows plots of points that represent actual costs incurred for various levels of activity. Once the scatter graph is constructed, we draw a line (often referred to as a trend line) that appears to best fit the pattern of dots. Because the trend line is somewhat subjective, the scatter graph is often used as a preliminary tool to explore the possibility that the relationship between cost and activity is generally a linear relationship. When interpreting a scatter graph, it is important to remember that different people would likely draw different lines, which would lead to different estimations of fixed and variable costs. No one person’s line and cost estimates would necessarily be right or wrong compared to another; they would just be different. After using a scatter graph to determine whether cost and activity have a linear relationship, managers often move on to more precise processes for cost estimation, such as the high-low method or least-squares regression analysis.

To demonstrate how a company would use a scatter graph, let’s turn to the data for Regent Airlines, which operates a fleet of regional jets serving the northeast United States. The Federal Aviation Administration establishes guidelines for routine aircraft maintenance based upon the number of flight hours. As a result, Regent finds that its maintenance costs vary from month to month with the number of flight hours, as depicted in Figure 2.29.

Month, Activity Level: Flight Hours, Maintenance Costs, respectively: January, 21,000, $84,000; February 23,000, 90,000; March 14,000, 70,500; April 17,000, 75,000; May 10,000, 64,500; June 19,000, 78,000.
Figure 2.29 Monthly Maintenance Cost and Activity Detail for Regent Airlines. (attribution: Copyright Rice University, OpenStax, under CC BY-NC-SA 4.0 license)

When creating the scatter graph, each point will represent a pair of activity and cost values. Maintenance costs are plotted on the vertical axis (Y), while flight hours are plotted on the horizontal axis (X). For instance, one point will represent 21,000 hours and $84,000 in costs. The next point on the graph will represent 23,000 hours and $90,000 in costs, and so forth, until all of the pairs of data have been plotted. Finally, a trend line is added to the chart in order to assist managers in seeing if there is a positive, negative, or zero relationship between the activity level and cost. Figure 2.30 shows a scatter graph for Regent Airlines.

A scatter graph showing Maintenance Costs on the y axis and Activity: Flight Hours on the x axis. Points graphed are 10,000 hours and $64,500 in costs, 14,000 hours and $70,500 in costs, 17,000 hours and $75,000 in costs, 19 hours and $78,000 in costs, 21,000 hours and $84,000 in costs, and 23,000 hours and $90,000 in costs. The line shows a definite relationship since it comes very close to all the points.
Figure 2.30 Scatter Graph of Maintenance Costs for Regent Airline. (attribution: Copyright Rice University, OpenStax, under CC BY-NC-SA 4.0 license)

In scatter graphs, cost is considered the dependent variable because cost depends upon the level of activity. The activity is considered the independent variable since it is the cause of the variation in costs. Regent’s scatter graph shows a positive relationship between flight hours and maintenance costs because, as flight hours increase, maintenance costs also increase. This is referred to as a positive linear relationship or a linear cost behavior.

Will all cost and activity relationships be linear? Only when there is a relationship between the activity and that particular cost. What if, instead, the cost of snow removal for the runways is plotted against flight hours? Suppose the snow removal costs are as listed in Table 2.13.

Snow Removal Costs
Month Activity Level: Flight Hours Snow Removal Costs
January 21,000 $40,000
February 23,000 50,000
March 14,000 8,000
April 17,000 0
May 10,000 0
June 19,000 0
Table 2.13
A scatter graph showing Snow Removal Costs on the y axis and Flight Hours by Month on the x axis. The points shown are 10,000 hours and $0 in costs, 14,000 hours and $8,000 in costs, 17,000 hours and $0 in costs, 19 hours and $0 in costs, 21,000 hours and $40,000 in costs, and 23,000 hours and $50,000 in costs.
Figure 2.31 Scatter Graph of Snow Removal Costs for Regent Airlines. (attribution: Copyright Rice University, OpenStax, under CC BY-NC-SA 4.0 license)

As you can see from the scatter graph, there is really not a linear relationship between how many flight hours are flown and the costs of snow removal. This makes sense as snow removal costs are linked to the amount of snow and the number of flights taking off and landing but not to how many hours the planes fly.

Using a scatter graph to determine if this linear relationship exists is an essential first step in cost behavior analysis. If the scatter graph reveals a linear cost behavior, then managers can proceed with a more sophisticated analyses to separate mixed costs into their fixed and variable components. However, if this linear relationship is not present, then other methods of analysis are not appropriate. Let’s examine the cost data from Regent Airline using the high-low method.

Demonstration of the High-Low Method to Calculate Future Costs at Varying Activity Levels

As you’ve learned, the purpose of identifying costs is to control them, and managers regularly use past costs to predict future costs. Since we know that variable costs change with the level of activity, we can conclude that there is usually a positive relationship between cost and activity: As one rises, so does the other. Ideally, this can be confirmed on a scatter graph. One of the simplest ways to analyze costs is to use the high-low method, a technique for separating the fixed and variable cost components of mixed costs. Using the highest and lowest levels of activity and their associated costs, we are able to estimate the variable cost components of mixed costs.

Once we have established that there is linear cost behavior, we can equate variable costs with the slope of the line, expressed as the rise of the line over the run. The steeper the slope of the line, the faster costs rise in response to a change in activity. Recall from the scatter graph that costs are the dependent Y variable and activity is the independent X variable. By examining the change in Y relative to the change in X, we can predict cost:

Variable cost equals rise of the line divided by run of the line, equals Y subscript 2 minus Y subscript 1 divided by X subscript 2 minus X subscript 1.

where Y2 is the total cost at the highest level of activity; Y1 is the total cost at the lowest level of activity; X2 is the number of units, labor hours, etc., at the highest level of activity; and X1 is the number of units, labor hours, etc., at the lowest level of activity.

Using the maintenance cost data from Regent Airlines shown in Figure 2.32, we will examine how this method works in practice.

Month, Activity Level: Flight Hours, Maintenance Costs, respectively: January, 21,000, $84,000; February 23,000, 90,000; March 14,000, 70,500; April 17,000, 75,000; May 10,000, 64,500; June 19,000, 78,000.
Figure 2.32 Monthly Maintenance Cost and Activity Detail for Regent Airlines. (attribution: Copyright Rice University, OpenStax, under CC BY-NC-SA 4.0 license)

The first step in analyzing mixed costs with the high-low method is to identify the periods with the highest and lowest levels of activity. In this case, it would be February and May, as shown in Figure 2.33. We always choose the highest and lowest activity and the costs that correspond with those levels of activity, even if they are not the highest and lowest costs.

Activity Level (Flight Hours), Cost (Maintenance Costs), respectively are: Highest level (February), 23,000, $90,000; Lowest level (May), 10,000, 64,500.
Figure 2.33 High–Low Data Points for Regent Airlines Maintenance Costs. (attribution: Copyright Rice University, OpenStax, under CC BY-NC-SA 4.0 license)

We are now able to estimate the variable costs by dividing the difference between the costs of the high and the low periods by the change in activity using this formula:

Variable cost equals change in cost divided by change in activity, equals cost at the high activity level minus cost at the low activity level divided by highest activity level minus lowest activity level.

For Regent Airlines, this is:

Variable Cost=$90,000$64,50023,00010,000=$1.96per flight hourVariable Cost=$90,000$64,50023,00010,000=$1.96per flight hour

Having determined that the variable cost per flight-hour is $1.96, we can now determine the amount of fixed costs. We can determine these fixed costs by taking the total costs at either the high or the low level of activity and subtracting this variable component. You will recall that total cost = fixed costs + variable costs, so the fixed cost component for Regent Airlines can be isolated as shown:

Fixed cost=total costvariable costFixed cost=$90,000(23,000×$1.96)Fixed cost=$44,920Fixed cost=total costvariable costFixed cost=$90,000(23,000×$1.96)Fixed cost=$44,920

Notice that if we had chosen the other data point, the low cost and activity, we would still get the same fixed cost of $44,920 = [$64,500 – (10,000 × $1.96)].

Now that we have isolated both the fixed and the variable components, we can express Regent Airlines’ cost of maintenance using the total cost equation:

Y=$44,920+$1.96xY=$44,920+$1.96x

where Y is total cost and x is flight hours.

Because we confirmed that the relationship between cost and activity at Regent exhibits linear cost behavior on the scatter graph, this equation allows managers at Regent Airlines to conclude that for every one unit increase in activity, there will be a corresponding rise in variable cost of $1.96. When put into practice, the managers at Regent Airlines can now predict their total costs at any level of activity, as shown in Figure 2.34.

Activity Level (Flight Hours), Fixed Costs, Variable Cost at $1.96 per hour, Total Costs, respectively: 10,000, $44,920, $19,600, $64,520; 20,000, $44,920, $39,200, $84,120; 30,000, $44,920, $58,800, $103,720; 40,000, $44,920, $78,400, $123,320.
Figure 2.34 Predictions of Total Cost and Cost Components at Different Levels of Activity for Regent Airlines. (attribution: Copyright Rice University, OpenStax, under CC BY-NC-SA 4.0 license)

Although managers frequently use this method, it is not the most accurate approach to predicting future costs because it is based on only two pieces of cost data: the highest and the lowest levels of activity. Actual costs can vary significantly from these estimates, especially when the high or low activity levels are not representative of the usual level of activity within the business. For a more accurate model, the least-squares regression method would be used to separate mixed costs into their fixed and variable components. The least-squares regression method is a statistical technique that may be used to estimate the total cost at the given level of activity based on past cost data. Least-squares regression minimizes the errors of trying to fit a line between the data points and thus fits the line more closely to all the data points.

Understanding the various labels used for costs is the first step toward using costs to evaluate business decisions. You will learn more about these various labels and how they are applied in decision-making processes as you continue your study of managerial accounting in this course.

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