10 Estimate a Variable and Fixed Cost Equation and also Predict Future Costs

Sometimes, a company will certainly should use cost estimation approaches, especially in the instance of mixed prices, so that they have the right to separate the addressed and also variable components, given that only the variable components adjust in the brief run. Estimation is also helpful for making use of current information to predict the impacts of future alters in production on complete prices. Three estimation methods that can be supplied encompass the scatter graph, the high-low method, and regression evaluation. Here we will certainly show the scatter graph and the high-low methods (you will learn the regression analysis approach in advanced managerial accounting courses.

You are watching: The graph of a variable cost when plotted against its related activity base appears as a


Functions of Cost Equations

The price equation is a straight equation that takes right into consideration full addressed expenses, the resolved component of blended expenses, and also variable cost per unit. Cost equations have the right to usage past information to recognize patterns of previous costs that can then task future prices, or they deserve to use estimated or expected future data to estimate future costs. Respeak to the mixed price equation:

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When utilizing this technique, Eagle Electronics should be particular that it is just predicting expenses for its appropriate selection. For instance, if they must hire a 2nd supervisor in order to produce 12,000 units, they should go back and change the total addressed costs used in the equation. Likewise, if variable prices per unit readjust, these need to also be changed.

This same approach deserve to be used to predict expenses for service and merchandising firms, as displayed by studying the costs incurred by J&L Accounting to prepare a corpoprice revenue taxation rerotate, displayed in (Figure).

Cost Information for J&L AccountingCost IncurredFixed or VariableCost
Building rentFixed?1,000 per month
Direct labor (for CPAs)Variable?250 per tax return
Secretarial staffFixed?2,000 per month
Accounting clerksVariable?100 per return

J&L desires to predict their total expenses if they complete 25 corporate taxation returns in the month of February.

Determine total resolved costs: ?1,000 + ?2,000 = ?3,000Determine variable costs per taxation return: ?250 + ?100 = ?350Complete the expense equation: Y = ?3,000 + ?350x

Using this equation, J&L deserve to now predict its full costs (Y) for the month of February once they anticipate preparing 25 corpoprice taxation returns:


(eginarraycY= ext?3,000+left( ext?350phantom ule0.2em0ex×phantom ule0.2em0ex25 ight)hfill \ Y= ext?3,000+ ext?8,750hfill \ Y= ext?11,750hfill endarray)

J&L have the right to currently use this predicted complete price number of ?11,750 to make decisions concerning how a lot to charge clients or how much cash they have to cover expenses. Aget, J&L should be careful to attempt not to predict costs outside of the relevant variety without adjusting the corresponding full price components.

J&L can make predictions for their prices because they have actually the information they require, but what happens when a service wants to estimate total expenses however has actually not accumulated information regarding per-unit costs? This is the instance for the supervisors at the Beach Inn, a small hotel on the shore of South Carolina. They recognize what their costs were for June, but now they want to predict their prices for July. They have gathered the indevelopment in (Figure).


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

One of the assumptions that supervisors need to make in order to use the cost equation is that the relationship between task and costs is straight. In various other words, expenses rise in direct proportion to task. A diagnostic tool that is offered to verify this assumption is a scatter graph.

A scatter graph mirrors pseveral points that reexisting actual prices incurred for miscellaneous levels of activity. Once the scatter graph is created, we draw a line (frequently described as a trend line) that shows up to best fit the pattern of dots. Due to the fact that the trend line is somewhat subjective, the scatter graph is regularly provided as a preliminary tool to discover the opportunity that the connection between expense and also task is generally a straight connection. When interpreting a scatter graph, it is necessary to remember that different civilization would certainly likely attract different lines, which would certainly bring about various estimations of resolved and also variable expenses. No one person’s line and cost approximates would certainly necessarily be ideal or wrong compared to another; they would certainly simply be various. After utilizing a scatter graph to recognize whether expense and also task have a linear relationship, managers often move on to more exact processes for price estimation, such as the high-low technique or least-squares regression analysis.

To demonstrate exactly how a firm would certainly usage a scatter graph, let’s rotate to the data for Regent Airlines, which operates a fleet of neighborhood jets serving the northeast United States. The Federal Aviation Administration creates guidelines for routine aircraft maintenance based upon the number of trip hours. As a result, Regent finds that its maintenance expenses vary from month to month with the variety of flight hours, as portrayed in (Figure).


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In scatter graphs, cost is taken into consideration the dependent variable bereason price depends upon the level of task. The activity is considered the independent variable since it is the reason of the variation in costs. Regent’s scatter graph shows a positive connection in between flight hours and also maintenance costs because, as flight hours boost, maintenance costs also boost. This is referred to as a positive linear connection or a direct expense behavior.

Will all expense and also task relationships be linear? Only as soon as tright here is a relationship between the activity and also that particular expense. What if, instead, the cost of scurrently removal for the runways is plotted against flight hours? Suppose the snow removal costs are as provided in (Figure).

Snow Removal CostsMonthActivity Level: Flight HoursScurrently Removal Costs
January21,000?40,000
February23,00050,000
March14,0008,000
April17,0000
May10,0000
June19,0000

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wbelow Y2 is the full cost at the highest possible level of activity; Y1 is the total expense at the lowest level of activity; X2 is the number of systems, labor hrs, and so on, at the highest possible level of activity; and X1 is the variety of units, labor hours, and so on, at the lowest level of task.

Using the maintenance price data from Regent Airlines shown in (Figure), we will certainly study how this method functions in exercise.


The first step in analyzing combined costs with the high-low technique is to identify the durations through the greatest and also lowest levels of activity. In this case, it would be February and also May, as presented in (Figure). We constantly choose the highest and also lowest activity and the costs that correspond with those levels of activity, even if they are not the greatest and lowest prices.


We are currently able to estimate the variable costs by separating the distinction between the costs of the high and the low durations by the adjust in activity making use of this formula:

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Using the high-low method, express the company’s maintenance expenses as an equation wright here x represents the gallons of paint created. Then estimate the addressed and also variable expenses.Predict the maintenance costs if 90,000 gallons of paint are developed.Predict the maintenance expenses if 81,000 gallons of paint are developed.Using Excel, develop a scatter graph of the cost data and also explain the connection between gallons of paint produced and also devices maintenance costs.

(Figure)This cost information from Hickory Furniture is for the year 2017.

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Using the high-low technique, expush the company’s overtime wages as an equation wright here x represents number of invoices processed. Assume BC has actually monthly addressed prices of ?3,800.Predict the overtime wperiods if 9,000 invoices are processed.Predict the overtime wperiods if 6,500 invoices are processed.Using Excel, develop a scatter graph of the price data and also define the relationship between the variety of invoices processed and overtime wage expense.

(Figure)This expense information from Hickory Furniture is for the year 2017.

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Prepare a scatter graph of the shipping information. Plot expense on the vertical axis and yachts shipped on the horizontal axis. Is the partnership between shipping costs and unit shipped approximately linear? Draw a straight line via the scatter graph.Using the high-low method, create the price formula for Carolina Yachts’ shipping expenses.The least-squares regression strategy was provided and also the evaluation led to this expense equation: Y = 4,000 + 1,275x. Comment on the accuracy of your high-low technique estimation.What would certainly you estimate shipping expenses to be if Carolina Yachts shipped 10 yachts in a solitary month? Use the price formula you derived in part B. Comment on how accurately this is reflected by the scatter graph you built.What components other than variety of yachts shipped execute you think might affect Carolina Yachts’ shipping expense? Exordinary.

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(Figure)Gadell Farms produces veniboy saintake that is distributed to grocery stores throughout the Southeastern. They have gathered this shipping cost data:

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Prepare a scatter graph of the shipping information. Plot expense on the vertical axis and also tons created on the horizontal axis. Is the relationship between packaging costs and lots produced about linear? Draw a straight line with the scatter graph.Using the high-low method, estimate the expense formula for Gadell Farms’ packaging prices.The least-squares regression technique was provided and the evaluation caused this price equation: Y = 1650 + 78.57x. Comment on the accuracy of your high-low approach estimation.What would you estimate packaging prices to be if Gadell Farms shipped 10 loads in a single month? Use the expense formula you derived in component B. Comment on exactly how accurately this is reflected by the scatter graph you constructed.What components other than number of lots produced carry out you think could influence Gadell Farm’s packaging expense? Exordinary.

Glossary

high-low methodstrategy for separating the fixed and also variable expense components of blended costsscatter graphplot of pairs of numerical information that represents actual prices incurred for various levels of activity, via one variable on each axis, offered to identify whether there is a connection in between them