1-1 Cost Behavior and Cost Volume Profit Analysis Dr. Hisham Madi.

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Cost Behavior and Cost Volume Profit Analysis

Dr. Hisham Madi

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Cost Behavior Analysis

Cost behavior analysisis the study of how specific costs respond to changes in the level of business activity.Example: for an airline company such as Egypt or Etihad , the longer the flight the higher the fuel costs.Hospital: Costs to staff the emergency room on any given night are relatively constant regardless of the number of patients treated.

Cost driver is a variable, such as the level of activity or volume that causally affects costs over a given time span.

The level of activity or volume is a cost driver if there is a cause-and-effect relationship between a change in the level of activity or volume and a change in the level of total costs

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Cost Behavior Analysis

A manufacturer, for example, may use direct labor hours or units of output for manufacturing costs and sales revenue or units sold for selling expenses.

The number of vehicles assembled is the cost driver of the total cost of steering wheels.

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Variable costs are costs that vary in proportion to changes in the level of activity.

Variable costs remain the same per unit at every level of activity.

Example,

Assume that Jason Sound Inc. produces stereo systems. The parts for the stereo systems are purchased from suppliers for $10 per unit and are assembled by Jason Sound Inc. For Model JS-12, the direct materials costs for the relevant range of 5,000 to 30,000 units of production are shown below

Variable Costs

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Variable Costs

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Fixed Costs

Fixed costs are costs that remain the same in total dollar amount as the activity base changes.

Fixed cost per unit cost varies inversely with activity: As volume increases, unit cost declines, and vice versa.

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Fixed Costs

ExampleAssume that Minton Inc. manufactures, bottles, and distributes perfume. The production supervisor is Jane Sovissi, who is paid a salary of $75,000 per year. For the relevant range of 50,000 to 300,000 bottles of perfume, the total fixed cost of $75,000 does not vary as production increases. However, the fixed cost per bottle decreases as the units produced increase; thus, the fixed cost is spread over a larger number of bottles, as shown below

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Fixed Costs

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Mixed Costs

Mixed costs (sometimes called semivariable or semifixed costs) have characteristics of both a variable and a fixed cost. Over one range of activity, the total mixed cost may remain the same. Over another range of activity, the mixed cost may change in proportion to changes in level of activity.

Example Assume that Simpson Inc. manufactures sails, using rented machinery.The rental charges are as follows:

Rental Charge = $15,000 per year + $1 times each machine hour over 10,000 hours

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The high-low method is a cost estimation method that may be used for separating mixed costs into their fixed and variable components

The high-low method uses the highest and lowest activity levels and their related costs to estimate the variable cost per unit and the fixed cost.

Example

Assume that the Equipment Maintenance Department of Kason Inc. incurred the following costs during the past five months:

High-Low Method

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High-Low Method

The number of units produced is the activity base, and the relevant range is the units produced between June and October. For Kason Inc., the difference between the units produced and total costs at the highest and lowest levels of production are as follows:

The total fixed cost does not change with changes in production. Thus, the $20,250difference in the total cost is the change in the total variable cost

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High-Low Method

The fixed cost is estimated by subtracting the total variable costs from the total costs for the units produced as shown below.

Fixed Cost = Total Costs - (Variable Cost per Unit * Units Produced)

The fixed cost is the same at the highest and the lowest levels of production asshown below for Kason Inc

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High-Low Method

Using the variable cost per unit and the fixed cost, the total equipment maintenance product.

To illustrate, the estimated total cost of 2,000 units of production is $60,000, as computed below:

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Cost-Volume-Profit Relationships

CVP is the examination of the relationships among selling prices, sales and production volume, costs, expenses, and profits.

Analyzing the effects of changes in selling prices on profits Analyzing the effects of changes in costs on profits Analyzing the effects of changes in volume on profits Setting selling prices

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Contribution Margin

The contribution margin is the excess of sales revenues over variable costs.

Contribution margin is especially useful because it provides insight into the profit potential of a company.

Contribution Margin = Sales - Variable Costs

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The contribution margin ratio, sometimes called the profit-volume ratio, indicates the percentage of each sales dollar available to cover fixed costs and to provide income from operations

Contribution Margin Ratio

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The contribution margin ratio is most useful when the increase or decrease in sales.

Change in Income from Operations = Change in Sales Dollars * Contribution Margin Ratio

To illustrate, if Lambert Inc. adds $80,000 in sales orders, its income from operations will increase by $32,000, as computed below.

Change in Income from Operations = $80,000 * 40% = $32,000

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Unit Contribution Margin

The unit contribution margin is also useful for analyzing the profit potential of proposed projects.

The unit contribution margin is the sales price per unit less the variable cost per unit.

To illustrate, if Lambert Inc.’s unit selling price is $20 and its variable cost per unit is $12, the unit contribution margin is $8 as shown below.

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Cost-Volume-Profit Analysis

Equation MethodThe break-even point is the level of operations at which a company’s revenues and expenses are equal.

At breakeven, a company reports neither an income nor a loss from operations

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Baker Corporation’s fixed costs are estimated to be $90,000. The unit contribution margin is calculated as follows:


Unit selling price $25Unit variable cost 15Unit contribution margin $10

The break-even point (in units) is calculated using the following equation:

Break-Even Sales (units) =

Fixed CostsUnit Contribution

Margin

Break-Even Sales (units) =$90,000

$10

Break-Even Sales (units) = 9,000 units

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The break-even point in sales dollars can be determined directly as follows:

The contribution margin ratio can be computed using the unit contribution margin and unit selling price as follows:

Thus, the break-even sales dollars for Baker Corporation of $225,000 can be computed directly as follows:


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Target ProfitThe sales volume required to earn a target profit is determined by modifying the break-even equation.


Sales (units) = Fixed Costs + Target ProfitUnit Contribution Margin

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Units Required for Target Profit

Fixed costs are estimated at $200,000, and the desired profit is $100,000. Unit contribution margin is $30.

Unit selling price $75Unit variable cost 45Unit contribution margin $30

Sales (units) =

Fixed Costs + Target ProfitUnit Contribution Margin$30

Sales (units) = 10,000 units

$200,000 $100,000

3Cost-Volume-Profit Analysis

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Units Required for Target Profit

The following income statement verifies this computation:

The sales of $750,000 needed to earn the target profit of $100,000 can be computed directly using the contribution margin ratio, as shown below.


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Cost-Volume-Profit Chart

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Cost-Volume-Profit Chart

1. Volume in units of sales is indicated along the horizontal axis.2. A sales line is plotted by beginning at zero on the left corner of the graph. A

second point is determined by multiplying any units of sales on the horizontal axis by the unit sales price of $50. For example, for 10,000 units of sales, the total sales would be $500,000 (10,000 units *$50). The sales line is drawn upward to the right from zero through the $500,000 point.

3. A cost line is plotted by beginning with total fixed costs, $100,000, on the vertical axis. A second point is determined by multiplying any units of sales on the horizontal axis by the unit variable costs and adding the fixed costs. For example, for 10,000 units of sales, the total estimated costs would be $400,000 [(10,000 units*$30) +$100,000]. The cost line is drawn upward to the right from $100,000 on the vertical axis through the $400,000 point.

4. The break-even point is the intersection point of the total sales and total cost lines

A vertical dotted line drawn downward at the intersection point indicates the units of sales at the break-even point. A horizontal dotted line drawn to the left at the intersection point indicates the sales dollars and costs at the break-even point.

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Mathematical Equation

Formula for required sales to meet target net income.

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Operating Leverage

The relationship of a company’s contribution margin to income from operations.

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Both companies have the same contribution margin.

Jones Inc. Wilson Inc.

Sales $400,000 $400,000Variable costs 300,000 300,000Contribution margin $100,000 $100,000Fixed costs 80,000 50,000Income from operations $ 20,000 $ 50,000

Operating leverage ? ?

Operating Leverage Example

5Operating Leverage

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Contribution Margin

Income from Operations

$100,000

$20,000= 5 Jones Inc.:





5

5Operating Leverage

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5 2

Contribution Margin

Income from Operations

$100,000

$50,000= 2 Wilson Inc.:

Operating Leverage

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1-1 Cost Behavior and Cost Volume Profit Analysis Dr. Hisham Madi.

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