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**Cost Behavior, Operating Leverage, and Profitability Analysis**

Chapter Fifteen Cost Behavior, Operating Leverage, and Profitability Analysis In Chapter Fifteen, we will focus on cost behavior. We will classify all costs as either fixed or variable relative to activity. After we have an insight into basic cost behavior relationships, we will examine the impact of a company’s cost structure on profitability at different activity levels.

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Learning Objective 1 Distinguish between fixed and variable cost behavior. Learning Objective One: Distinguish between fixed and variable cost behavior.

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**Fixed Cost Behavior When activity . . . .**

Consider the following concert example where the band will be paid $48,000 regardless of the number of tickets sold. Total fixed cost does not change as activity increases or decreases. For example, your monthly car payment remains the same regardless of the number of miles that you drive in a month. However, when expressed on a per unit basis, a fixed cost is inversely related to activity—the per unit cost decreases when activity increases and increases when activity decreases. For example, if you divide your monthly car payment by the number of miles driven in a month, you will find that the cost per mile decreases as the number of miles increases. Consider the following concert example where the band will be paid forty-eight thousand dollars regardless of the number of tickets sold.

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**Fixed Cost Behavior $48,000 ÷ 3,000 Tickets = $16.00 per Ticket**

The band cost is fixed as they will be paid forty-eight thousand dollars regardless of the number of tickets sold. Notice that the per ticket cost of the band decreases as the number of tickets sold increases, from a high of seventeen dollars and seventy-eight cents at two thousand seven hundred tickets, to a low of fourteen dollars fifty-five cents at three thousand three hundred tickets.

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Learning Objective 2 Demonstrate the effects of operating leverage on profitability. Learning Objective Two: Demonstrate the effects of operating leverage on profitability.

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**Consider the following concert example where all costs are fixed.**

Operating Leverage A measure of the extent to which fixed costs are being used in an organization. Operating leverage is greatest in companies that have a high proportion of fixed costs in relation to variable costs. Fixed Costs Small percentage change in revenue Large percentage change in profits Consider the following concert example where all costs are fixed. Operating leverage is a measure of the extent to which fixed costs are being used in an organization. Operating leverage is greatest in companies that have a high proportion of fixed costs relative to variable costs. Generally, companies with a high fixed cost structure will show higher net income in good years than companies with lower fixed cost structures because a small percentage change in revenue produces a large percentage change in profits. Just the opposite is true in bad years.

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**90% Gross Profit Increase**

Operating Leverage 10% Revenue Increase The illustration on your screen is a continuation of the example where the band is paid a fixed amount of forty-eight thousand dollars regardless of the number of tickets sold. The ten percent increase in revenue results in a ninety percent increase in gross profit. The operating leverage is high because costs are fixed. When all costs are fixed, every additional sales dollar contributes an additional dollar to gross profit. When all costs are fixed, every additional sales dollar contributes one dollar to gross profit. 90% Gross Profit Increase

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**Risk and Reward Assessment**

Risk refers to the possibility that sacrifices may exceed benefits. Risk may be reduced by converting fixed costs into variable costs. The rewards may be greater at high activity levels when costs are fixed, but the risks are greater at low activity levels. Risk may be reduced by converting fixed costs into variable costs. Let’s see what happens to the concert example if the band receives a variable fee of sixteen dollars per ticket sold instead of the forty-eight thousand dollar fixed amount. Let’s see what happens to the concert example if the band receives $16 per ticket instead of $48,000.

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**Risk and Reward Assessment**

The total variable cost increases in direct proportion to the number of tickets sold. The total variable cost for the band increases as the number of tickets sold increases. The variable cost per ticket sold remains at sixteen dollars regardless of the number of tickets sold. Notice that the total cost for the band is less than forty-eight thousand dollars when the number of tickets sold activity is low, but higher than forty-eight thousand dollars when the number of tickets sold is high. Variable unit cost per ticket remains at $16 regardless of the number of tickets sold.

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**Variable Cost Behavior**

When activity . . . Total variable cost is directly related to activity as the amount increases when activity increases and decreases when activity decreases. For example, your total gasoline expenditures increase as you drive more miles. However, when expressed on a per unit basis, a variable cost remains constant as activity changes. For example, regardless of the number of miles that you drive, your cost per gallon of gasoline is unchanged.

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**Risk and Reward Assessment**

10% Revenue Increase Shifting the cost structure from fixed to variable not only reduces risk but also the potential for profits. The ten percent increase in revenue results in only a ten percent increase in gross profit when costs are variable. Shifting the cost structure from fixed to variable not only reduces risk but also the potential for profits. 10% Gross Profit Increase

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**Relationship Between Cost Behavior & Revenue**

Fixed Cost Structure Revenue $ Profit Fixed Cost Loss The graph on your screen illustrates the relationship of profits and losses to activity when all costs are fixed. Operating leverage is high when costs are fixed, resulting in rapid increases in profits as activity increases. On the down side, risk is higher. As activity decreases, profits decline rapidly. Units 1

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**Relationship Between Cost Behavior & Revenue**

Variable Cost Structure Revenue $ Variable Cost Profit This graph illustrates the relationship of profits to activity when costs are variable. Profit increases are much less dramatic as activity increases, because variable costs also increase. When compared to the previous graph with fixed costs, operating leverage is lower, risk is lower, but the rate of change in profits is also lower when activity increases. Units 1

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**Learning Objective 3 Show how cost behavior affects profitability.**

Learning Objective Three: Show how cost behavior affects profitability.

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**The Effect of Cost Structure on Profit Stability**

Do companies with higher levels of fixed costs experience more earnings volatility? Fixed Costs Variable Costs The preceding examples might cause us to reason that companies with higher levels of fixed costs experience more earnings volatility. Let’s look at an example to confirm this.

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**The Effect of Cost Structure on Profit Stability**

All three companies sell ten units at ten dollars each, and all three companies have incomes of forty dollars at this sales level. The All Fixed Company has sixty dollars of fixed costs and zero dollars of variable costs. The All Variable Company has variable costs of six dollars per unit for a total of sixty dollars, but zero fixed costs. The Combination Company has thirty dollars of fixed costs and variable costs of three dollars per unit for a total cost of sixty dollars. First, let’s see what happens to income when we increase the number of units sold from ten to eleven. Now let’s see what happens when the number of units sold increases.

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**The Effect of Cost Structure on Profit Stability**

The income is greater for all three companies. The All Fixed Company has the highest income and the All Variable Company has the lowest income. The income increase is greater in the All Fixed Company.

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**The Effect of Cost Structure on Profit Stability**

If sales decrease, will the income decrease be greater in the All Fixed Company? Fixed Costs Now, let’s see what happens to income when we decrease the number of units sold to nine. Variable Costs

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**The Effect of Cost Structure on Profit Stability**

The income is lower for all three companies. The All Fixed Company has the lowest income and the All Variable Company has the highest income. Yes, the income decrease is greater in the All Fixed Company.

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**The Effect of Cost Structure on Profit Stability**

Fixed Costs Our conclusion from these examples is that a high level of fixed costs results in higher earnings volatility, while a low level of fixed costs results in lower earnings volatility. Variable Costs

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Learning Objective 4 Prepare an income statement using the contribution margin approach. Learning Objective Four: Prepare an income statement using the contribution margin approach.

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**Income Statement - Contribution Margin Approach**

The contribution margin format emphasizes cost behavior. Contribution margin covers fixed costs and provides for income. The contribution approach provides an income statement format geared directly to cost behavior. This approach to income statement preparation separates costs into those that are fixed and those that are variable. Subtracting variable costs from sales results in contribution margin. The contribution margin covers fixed costs and provides for income.

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**Learning Objective 5 Calculate the magnitude of operating leverage.**

Learning Objective Five: Calculate the magnitude of operating leverage.

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**Measuring Operating Leverage Using Contribution Margin**

Contribution margin Net income Operating Leverage = Show me an example. The degree of operating leverage is a measure, at any given level of sales, of how a percentage change in sales volume will affect profits. It is computed by dividing contribution margin by net operating income. Let’s look at an example.

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**Measuring Operating Leverage Using Contribution Margin**

At a sales level of five thousand hammers, the net income is five thousand dollars and the contribution margin is twenty thousand dollars. Operating leverage is four. We determine this by dividing the twenty thousand dollars of contribution margin by the net income of five thousand dollars. If sales increase ten percent, the operating leverage of four tells us that net income will increase by forty percent. We multiply the percentage increase in sales by the degree of operating leverage to find the percentage increase in net income. Let’s look at an example to verify the forty percent increase in profit. $20,000 $5,000 Operating Leverage = = 4 A measure of how a percentage change in sales will affect profits.

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**Measuring Operating Leverage Using Contribution Margin**

A ten percent increase in sales would increase hammer sales from the current level of five thousand to five thousand five hundred. Look at the contribution margin income statement and notice that income increased from five thousand dollars to seven thousand dollars. That two thousand dollar increase in net income is a forty percent increase. So it is true that a ten percent increase in sales results in a forty percent increase in net income. This is very important information for a manager to have. A 10 percent increase in sales results in a 40 percent increase in net income. (10% × 4 = 40 %)

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Learning Objective 6 Use cost behavior to create a competitive operating advantage. Learning Objective Six: Use cost behavior to create a competitive operating advantage.

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**Using Fixed Cost to Provide a Competitive Operating Advantage**

Consider the following two companies: Consider two companies, MaHall that pays employees fixed salaries totaling sixteen thousand dollars, and Strike that pays employees a rate of eight dollars per hour. At a service level of two thousand hours both companies earn six thousand dollars. What happens if each company cuts the service revenue rate from eleven dollars per hour to seven dollars per hour in order to double the amount of business? What happens if each company cuts the service revenue to $7 per hour in order to double the amount of business?

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**Using Fixed Cost to Provide a Competitive Operating Advantage**

Revenue for both companies increased from twenty-two thousand dollars to twenty-eight thousand dollars. The service revenue rate of seven dollars per hour is one dollar per hour less than Strike pays its employees. At four thousand hours, Strike is losing four thousand dollars. MaHall has the advantage because its fixed costs did not increase as the volume of business increased. Advantage to MaHall, the all fixed company.

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**Using Fixed Cost to Provide a Competitive Operating Advantage**

What happens if the price is cut to $7 per hour and the demand remains at 2,000 hours for each company? Now, let’s see what happens if the service revenue rate is cut to seven dollars per hour and the demand remains at two thousand hours for each company.

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**Using Fixed Cost to Provide a Competitive Operating Advantage**

In this case both companies lose two thousand dollars because total service revenue of fourteen thousand dollars is less than total cost of sixteen thousand dollars. Neither company has an advantage in this situation. Both companies incur losses.

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**Using Fixed Cost to Provide a Competitive Operating Advantage**

One suppose fixed costs are better if volume is increasing, but variable costs may be better if business is declining. We have seen several examples that indicate that a company with a higher proportion of fixed costs will earn more profits as business volume increases. However, as business volume decreases, the leverage works against a company with a high level of fixed costs. A variable cost structure may be better in periods of declining business volume.

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**Cost Behavior Summarized**

Your monthly basic telephone bill is probably fixed and does not change when you make more local calls. Total Fixed Cost Monthly Basic Telephone Bill Total fixed cost is constant over a wide range of activity, referred to as the relevant range of activity. In other words, fixed costs do not change with changes in activity that fall within the relevant range. For example, your monthly basic telephone bill probably is a fixed amount and does not change based on the number of calls you make. Number of Local Calls

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**Cost Behavior Summarized**

The fixed cost per local call decreases as more local calls are made. Fixed Cost Per Unit Monthly Basic Telephone Bill per Local Call However, when expressed on a per unit basis, a fixed cost is inversely related to activity—the per unit cost decreases when activity rises and increases when activity falls. For example, the average fixed cost per local call decreases as more local calls are made. Number of Local Calls

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**Cost Behavior Summarized**

Your total long distance telephone bill is based on how many minutes you talk. Total Long Distance Telephone Bill Total Variable Cost Total variable cost varies in direct proportion to changes in the level of activity. For example, your long distance telephone bill may be based on how many minutes you talk—the total bill varies with the number of minutes that you talk. Minutes Talked

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**Cost Behavior Summarized**

The cost per minute talked is constant. For example, 10 cents per minute. Variable Cost Per Unit Per Minute Telephone Charge Although variable costs change in total as the activity level rises and falls, variable cost per unit is constant. For example, the cost per long distance minute may be ten cents a minute, regardless of the number of minutes that you talk. Minutes Talked

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**Cost Behavior Summarized**

When activity level changes . . . It is helpful to think about variable and fixed cost behavior in a two by two matrix, as illustrated here. Take a few minutes and review this summary of cost behavior for variable and fixed costs.

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Learning Objective 7 Demonstrate how the relevant range and the decision-making context affect cost behavior. Learning Objective Seven: Demonstrate how the relevant range and the decision-making context affect cost behavior.

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The Relevant Range Example: Office space is available at a fixed rental rate of $30,000 per year in increments of 1,000 square feet. As the business grows more space is rented, increasing the total cost. Rent for office space is an example of changes in total fixed costs that occur in different ranges of activity. A company can rent one thousand square feet of office space for thirty thousand dollars per year. If the company fills its current space and needs additional office space, the next one thousand square feet will cost an additional thirty thousand dollars per year. Continue

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**Rent Cost in Thousands of Dollars**

The Relevant Range 90 Total fixed cost doesn’t change for a range of activity, and then jumps to a new higher cost for the next higher range of activity. Relevant Range 60 Rent Cost in Thousands of Dollars 30 So when a company needs one thousand square feet of office space, the fixed office rent is thirty thousand dollars. If another one thousand square feet are needed, the fixed office rent will be sixty thousand dollars. Fixed costs only stay constant in total within the relevant range of activity. As we adjust the relevant range of activity upward or downward we see changes in total fixed costs. These upward or downward adjustments are generally very wide. , , , Rented Area (Square Feet)

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**Possible Variable Cost Behavior Our Variable Cost Assumption**

The Relevant Range Our variable cost assumption (constant unit variable cost) applies within the relevant range. Total Cost Relevant Range Possible Variable Cost Behavior Not all variable costs are linear as shown in our previous examples. Over a range of activity from zero to extremely high levels, most variable costs are curvilinear. However, in the range of activity that a company is likely to operate (the relevant range), costs are either linear, or very close to linear. The relevant range is the range of activity within which the assumptions made about cost behavior are valid. Our Variable Cost Assumption Activity

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**Context Sensitive Definitions of Fixed and Variable**

Recall the earlier concert example, where the band was paid $48,000 regardless of the number of tickets sold. The cost of the band is fixed relative to the number of tickets sold for a specific concert. Costs that are fixed relative to one activity base may be variable relative to another activity base. Recall the band examples earlier in the chapter where the band was paid a fixed fee of forty-eight thousand dollars for a performance, regardless of the number of tickets sold. Now let’s assume that we want to hire the band for a number of performances at different locations, all at forty-eight thousand dollars per performance. The band’s cost which is fixed relative to the number of tickets sold for one performance, is variable relative to the number of performances. As the number of performances increases, the total amount paid to the band increases, although the amount paid per performance is constant. The cost of the band is variable relative to the number of concerts produced.

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Learning Objective 8 Select an appropriate time period for calculating the average cost per unit. Learning Objective Eight: Select an appropriate time period for calculating the average cost per unit.

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Cost Averaging Lake Resorts provides water-skiing lessons for its guests with the following costs: Equipment rental $80 per day Instructor pay $15 per hour Fuel $ 2 per hour What is the average cost per one-hour lesson for two lessons per day? Five lessons per day? Ten lessons per day? Average cost per unit declines as activity increases when fixed costs are involved. Consider the example where Lake Resorts provides water skiing lessons. The equipment rental is a fixed amount per day. The instructor pay and fuel for the boat is variable based on hours of instruction. What is the average cost per one-hour lesson if there are two lessons per day? Five lessons per day? Ten lessons per day?

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Cost Averaging Each lesson is one hour in length. The variable portion of the cost increases with activity as we multiply the number of hours of instruction times fifteen dollars per hour for instruction and two dollars per hour for fuel. However, the fixed portion of the total cost remains constant at eighty dollars per day regardless of the number of hours of instruction. Dividing the total cost by the number of hours of instruction to get an average cost per lesson shows that the average cost declines from fifty-seven dollars per lesson to twenty-five dollars per lesson as the activity increases. Average costs decline as activity increases when fixed costs such as equipment rental are involved. Managers must use these average costs with caution as they differ at every level of activity.

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**Learning Objective 9 Define the term mixed costs.**

Learning Objective Nine: Define the term mixed costs.

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**A mixed cost has both fixed and variable components.**

Mixed Costs A mixed cost has both fixed and variable components. A mixed cost has both a fixed and variable element. We will illustrate mixed costs by looking at a monthly utility bill for electricity. Consider the following electric utility example.

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**Variable Utility Charge Fixed Monthly Utility Charge**

Mixed Costs Total mixed cost Variable Utility Charge Total Utility Cost If you pay your utility bill, you know that a portion of your total bill is fixed and a portion is variable. The fixed portion is referred to as a connection fee that is the same regardless of the amount of electricity that you use. The variable portion of your utility costs depends on the number of kilowatt hours you consume. The graph on your screen demonstrates the nature of a normal utility bill. Fixed Monthly Utility Charge Activity (Kilowatt Hours)

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Learning Objective 10 Use the high-low method and scattergraphs to estimate fixed and variable costs. Learning Objective Ten: Use the high-low method and scattergraphs to estimate fixed and variable costs.

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**Estimating Fixed and Variable Costs**

High-Low Method Scattergraph Method We will focus on two methods to analyze mixed costs: the high-low method and the scattergraph method.

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The High-Low Method Iris Company recorded the following production activity and maintenance costs for two months: Using these two levels of activity, compute: the variable cost per unit the fixed cost the total cost In our high-low example, we’re going to look at a company’s relationship between maintenance cost and units of production. During the year, the company reports production and maintenance costs on a monthly basis. The month with the high level of production shows ten thousand units and a corresponding maintenance cost of nine thousand seven hundred dollars. The month with the low level of production shows five thousand units with a corresponding maintenance cost of five thousand seven hundred dollars. We will use this information to compute the variable maintenance cost per unit of production and the total fixed cost. Then we will write a linear equation to describe the cost behavior. Let’s see how the high-low method works.

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The High-Low Method Unit variable cost = $4,000 ÷ 5,000 units = $.80 per unit Fixed cost = Total cost – Total variable cost Fixed cost = $9,700 – ($.80 per unit × 10,000 units) Fixed cost = $9,700 – $8,000 = $1,700 Total cost = Fixed cost + Variable cost Total cost = $1,700 + $0.80X Part One First we determine the change in activity and the change in cost. Part Two To determine the variable costs per unit of activity, we divide the change in cost by the change in production activity. In our case, the change in maintenance cost is four thousand dollars and the change in units produced is five thousand. The result is a variable cost rate of eighty cents per unit produced. Part Three Next, we calculate the fixed cost by subtracting the total variable cost from the total cost. Since total cost and total variable cost are different amounts at different activity levels, we must choose either the high level or the low level for our computations. Let’s choose the high level of activity, ten thousand units. Our first step is to calculate the total variable cost. At ten thousand units, the total variable cost is eighty cents per unit times ten thousand units resulting in a total variable cost of eight thousand dollars. Next, we subtract eight thousand dollars from the total cost at the high activity, to get the fixed cost, one thousand seven hundred dollars. We will obtain the same result if using the low level of activity to compute fixed cost. Part Four Now, we can write a linear equation using our variable cost of eighty cents per unit and our fixed cost of one thousand seven hundred dollars. Total cost equals one thousand seven hundred dollars plus eighty cents per unit for any number of units within the relevant range.

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The High-Low Method If sales salaries and commissions are $10,000 when 80,000 units are sold and $14,000 when 120,000 units are sold, what is the variable portion of sales salaries and commissions? a. $.08 per unit b. $.10 per unit c. $.12 per unit d. $.125 per unit See if you can apply what we have just discussed to determine the variable portion of sales salaries and commissions for this company.

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The High-Low Method If sales salaries and commissions are $10,000 when 80,000 units are sold and $14,000 when 120,000 units are sold, what is the variable portion of sales salaries and commissions? a. $.08 per unit b. $.10 per unit c. $.12 per unit d. $.125 per unit $4,000 ÷ 40,000 units = $.10 per unit To determine the variable costs per unit of activity, we divide the change in cost by the change in activity. In our case, the change in cost is four thousand dollars and the change in units is forty thousand. The result is a variable cost rate of ten cents per unit.

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The High-Low Method If sales salaries and commissions are $10,000 when 80,000 units are sold and $14,000 when 120,000 units are sold, what is the fixed portion of sales salaries and commissions? a. $ 2,000 b. $ 4,000 c. $10,000 d. $12,000 Using the same data, calculate the total fixed cost portion of sales salaries and commissions.

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The High-Low Method If sales salaries and commissions are $10,000 when 80,000 units are sold and $14,000 when 120,000 units are sold, what is the fixed portion of sales salaries and commissions? a. $ 2,000 b. $ 4,000 c. $10,000 d. $12,000 We calculate the fixed cost by subtracting the total variable cost from the total cost. Since total cost and total variable cost are different amounts at different activity levels, we must choose either the high level or the low level for our computations. Let’s choose the high level of activity, one hundred twenty thousand units. Our first step is to calculate the total variable cost. At one hundred twenty thousand units, the total variable cost is ten cents per unit times one hundred twenty thousand units resulting in a total variable cost of twelve thousand dollars. Next, we subtract twelve thousand dollars from the total cost at the high activity, to get the fixed cost, two thousand dollars. You should get the same result if you choose the low level of activity to compute fixed cost.

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**Plot the data points on a graph (total cost vs. activity).**

The Scattergraph Method Plot the data points on a graph (total cost vs. activity). * Total Cost in 1,000’s of Dollars 10 20 Activity, 1,000’s of Units Produced X Y A scattergraph is a plot of cost data points on a graph. It is almost always helpful to plot cost data to be able to observe a visual picture of the relationship between cost and activity. Scattergraphs can reveal outlier data points and confirm possible relationships between the variables. A scattergraph plot is a quick and easy way to isolate the fixed and variable components of a mixed cost. The first step is to identify the cost, which is referred to as the dependent variable, and plot it on the Y axis. The activity, referred to as the independent variable, is plotted on the X axis.

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**Total Cost in 1,000’s of Dollars**

The Scattergraph Method Draw a line through the data points with about an equal number of points above and below the line. * Total Cost in 1,000’s of Dollars 10 20 Activity, 1,000’s of Units Produced X Y Next, we draw a straight line through the data points with about an equal number of observations above and below the line. We continue the line past the observed points until it intersects with the vertical axis.

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**The Scattergraph Method**

Variable cost per unit is represented by the slope of the line. Y 20 * * * * * * * * Vertical distance is total cost, approximately $16,000. Total Cost in 1,000’s of Dollars * * 10 The intercept in this case is our fixed cost, which is estimated to be ten thousand dollars. The vertical distance from the horizontal axis to the line that we have drawn through the data points is the total cost for any activity selected on the horizontal axis. Estimated fixed is $10,000 X Activity, 1,000’s of Units Produced

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**The Scattergraph Method**

Total variable cost = Total cost – Total fixed cost Total variable cost = $16,000 – $10,000 = $6,000 Unit variable cost = $6,000 ÷ 3,000 units = $2 Y 20 * * * * * * * * Vertical distance is total cost, approximately $16,000. Total Cost in 1,000’s of Dollars * * 10 Next, subtract the fixed cost from the total cost we have determined. By doing this we have isolated the total variable cost. Then, we divide the total variable cost by the activity selected on the horizontal axis to arrive at the unit variable cost. Estimated fixed is $10,000 X Activity, 1,000’s of Units Produced

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End of Chapter Fifteen In Chapter Fifteen, our emphasis was on cost behavior. We classified all costs as either fixed or variable relative to activity. After studying basic cost behavior relationships, we examined the impact of a company’s cost structure on profitability at different activity levels. Lastly, we looked at two methods of analyzing mixed costs and separating them into their fixed and variable components.

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