10 estimate a Variable and Fixed expense Equation and also Predict Future Costs

Sometimes, a service will should use cost estimation techniques, specifically in the situation of blended costs, so that they can separate the fixed and also variable components, because only the variable components change in the brief run. Estimate is also useful because that using present data to predict the effects of future changes in manufacturing on full costs. Three estimation approaches that deserve to be used incorporate the scatter graph, the high-low method, and also regression analysis. Below we will show the scatter graph and the high-low approaches (you will discover the regression analysis an approach in advanced managerial accountancy courses.

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Functions of price Equations

The expense equation is a direct equation the takes right into consideration full fixed costs, the addressed component of blended costs, and also variable price per unit. Cost equations have the right to use past data to determine patterns that past costs that have the right to then job future costs, or they have the right to use approximated or meant future data to calculation future costs. Remind the mixed cost equation:

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When utilizing this approach, Eagle electronic devices must be specific that that is only predicting costs for its relevant range. Because that example, if they have to hire a 2nd supervisor in order to produce 12,000 units, they must go back and adjust the full fixed prices used in the equation. Likewise, if variable expenses per unit change, these must also be adjusted.

This same method can be supplied to predict costs for service and merchandising firms, as shown by analyzing the prices incurred by J&L bookkeeping to prepare a corporate income tax return, displayed in (Figure).

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

J&L desires to suspect their complete costs if they finish 25 corporate taxes returns in the month that February.

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

Using this equation, J&L deserve to now suspect its full costs (Y) because that the month of February as soon as they anticipate preparing 25 corporate taxes returns:


\(\beginarraycY=\text?3,000+\left(\text?350\phantom\rule0.2em0ex×\phantom\rule0.2em0ex25\right)\hfill \\ Y=\text?3,000+\text?8,750\hfill \\ Y=\text?11,750\hfill \endarray\)

J&L can now use this predicted complete cost figure of ?11,750 to make decisions concerning how lot to charge clients or exactly how much cash they have to cover expenses. Again, J&L have to be careful to try not to predict expenses outside that the relevant selection without adjusting the corresponding full cost components.

J&L deserve to make predictions for their costs due to the fact that they have actually the data castle need, but what happens when a organization wants come estimate total costs yet has not gathered data concerning per-unit costs? This is the situation for the supervisors at the beach Inn, a tiny hotel ~ above the coastline of southern Carolina. They know what their expenses were for June, however now they desire to guess their prices for July. They have gathered the information in (Figure).


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Demonstration the the Scatter Graph method to calculation Future costs at Varying task Levels

One that the presumptions that managers must do in order to usage the price equation is that the connection between task and expenses is linear. In other words, expenses rise in straight proportion to activity. A diagnostic device that is provided to verify this presumption is a scatter graph.

A scatter graph reflects plots of point out that stand for actual prices incurred for assorted levels the activity. Once the scatter graph is constructed, we attract a line (often referred to as a trend line) that appears to finest fit the pattern of dots. Due to the fact that the trend line is rather subjective, the scatter graph is frequently used as a preliminary device to explore the possibility that the relationship between cost and task is typically a direct relationship. Once interpreting a scatter graph, the is necessary to remember the different human being would likely draw various lines, which would lead to various estimations of fixed and variable costs. No one person’s line and cost estimates would necessarily be right or wrong contrasted to another; lock would just be different. After using a scatter graph to recognize whether price and task have a linear relationship, managers frequently move top top to more precise procedures for cost estimation, such as the high-low method or least-squares regression analysis.

To show how a company would usage a scatter graph, let’s revolve to the data because that Regent Airlines, i m sorry operates a fleet of local jets serving the northeast joined States. The federal Aviation management establishes indict for program aircraft maintain based ~ above the variety of flight hours. As a result, Regent finds that its maintenance prices vary from month come month v the number of flight hours, as depicted in (Figure).


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In scatter graphs, cost is considered the dependent variable because cost depends ~ above the level of activity. The task is taken into consideration the elevation variable because it is the cause of the sport in costs. Regent’s scatter graph shows a optimistic relationship in between flight hours and maintenance costs because, as trip hours increase, maintenance costs additionally increase. This is described as a positive straight relationship or a linear price behavior.

Will all price and task relationships be linear? Only when there is a relationship in between the activity and that certain cost. What if, instead, the expense of snow removal because that the runways is plotted against flight hours? expect the snow removal prices are as listed in (Figure).

Snow remove CostsMonthActivity Level: flight HoursSnow removed Costs
January21,000?40,000
February23,00050,000
March14,0008,000
April17,0000
May10,0000
June19,0000

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where Y2 is the full cost in ~ the highest possible level the activity; Y1 is the complete cost at the lowest level of activity; X2 is the variety of units, job hours, etc., at the highest possible level the activity; and X1 is the number of units, labor hours, etc., at the shortest level that activity.

Using the maintenance price data indigenous Regent Airlines shown in (Figure), we will certainly examine exactly how this an approach works in practice.


The very first step in examining mixed expenses with the high-low technique is to identify the periods with the highest and also lowest levels of activity. In this case, it would be February and also May, as displayed in (Figure). We always choose the highest and lowest activity and the prices that correspond through those levels of activity, even if they space not the highest and lowest costs.


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

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Using the high-low method, refer the this firm maintenance prices as an equation wherein x to represent the gallons of paint produced. Then calculation the fixed and variable costs.Predict the maintenance costs if 90,000 gallons of paint are produced.Predict the maintenance costs if 81,000 gallons of repaint are produced.Using Excel, develop a scatter graph that the expense data and explain the relationship between gallons of paint produced and equipment maintain expenses.

(Figure)This cost data from Hickory Furniture is because that the year 2017.

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Using the high-low method, refer the this firm overtime incomes as one equation where x represents number of invoices processed. I think BC has monthly fixed expenses of ?3,800.Predict the overtime salaries if 9,000 invoices are processed.Predict the overtime incomes if 6,500 invoices room processed.Using Excel, develop a scatter graph of the cost data and also explain the relationship between the number of invoices processed and also overtime wage expense.

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

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Prepare a scatter graph that the shipping data. Plot cost on the vertical axis and yachts transport on the horizontal axis. Is the relationship between shipping costs and unit shipped roughly linear? attract a directly line with the scatter graph.Using the high-low method, develop the price formula because that Carolina Yachts’ shipping costs.The least-squares regression method was used and also the evaluation resulted in this price equation: Y = 4,000 + 1,275x. Talk about the accuracy of your high-low technique estimation.What would certainly you calculation shipping expenses to it is in if Carolina Yachts transport 10 yachts in a solitary month? usage the price formula you acquired in part B. Talk about how accurately this is reflected by the scatter graph friend constructed.What determinants other than variety of yachts shipped do you think could impact Carolina Yachts’ shipping expense? Explain.

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(Figure)Gadell ranches produces wild sausage the is dispersed to grocery stores throughout the Southeast. Castle have built up this shipping expense data:

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Prepare a scatter graph that the shipping data. Plot expense on the upright axis and tons created on the horizontal axis. Is the relationship in between packaging costs and also tons produced about linear? draw a directly line with the scatter graph.Using the high-low method, estimate the expense formula because that Gadell Farms’ packaging costs.The least-squares regression method was used and the evaluation resulted in this price equation: Y = 1650 + 78.57x. Comment on the accuracy of your high-low an approach estimation.What would you estimate packaging prices to it is in if Gadell farms shipped 10 tons in a single month? use the cost formula you derived in component B. Comment on how correctly this is reflect by the scatter graph girlfriend constructed.What factors other than variety of tons produced do you think could influence Gadell Farm’s packaging expense? Explain.

Glossary

high-low methodtechnique for separating the fixed and variable cost components of blended costsscatter graphplot of bag of numerical data the represents actual prices incurred for miscellaneous levels of activity, through one change on every axis, supplied to identify whether there is a relationship between them