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CHAPTER 18

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CHAPTER 18

Cost Behavior & Cost-Volume-Profit Analysis

- In planning, we must understand how costs behave.
- For example, do costs change as production activity changes or do they stay the same?

- __________– costs that increase as production activity increases (direct materials, direct labor)
- __________– costs that stay the same over a range of activity levels (depreciation, rent) within a given time period.

Variable Costs

Total Variable Cost Graph

Unit Variable Cost Graph

$300,000

$250,000

$200,000

$150,000

$100,000

$50,000

$20

$15

$10

$5

Cost per Unit

Total Costs

0

102030

Units Produced (000)

0

102030

Units Produced (000)

Units Total Cost

Produced Cost per Unit

5,000 $ 50,000 $10

10,000 100,000 10

15,000 150,000 10

20,000 200,000 10

25,000 250,000 10

30,000 300,000 10

Fixed Costs

Total Fixed Cost Graph

Unit Fixed Cost Graph

$150,000

$125,000

$100,000

$75,000

$50,000

$25,000

$1.50

$1.25

$1.00

$.75

$.50

$.25

Total Costs

Cost per Unit

0

0

100200300

100200300

Units Produced (000)

Units Produced (000)

Units Total Cost

Produced Cost per Unit

50,000 $75,000 $1.500

100,000 75,000 .750

150,000 75,000 .500

200,000 75,000 .375

250,000 75,000 .300

300,000 75,000 .250

- Cost relationships remain stable only over some range of production activity.
- Outside that range the relationships may change.
- __________is the expected range of activity we are interested in.
- We estimate the cost relationships within that range.
- We cannot extrapolate outside the range.

- __________Costs
- include both fixed and variable costs; we separate fixed from variable costs when perform cost-volume profit analysis.

- __________Costs
- fixed within a relevant range, but if total production increases significantly, total costs increase by a lump sum amount

- __________Costs
- increase at a non-constant rate as volume increases.

- Some costs have a _______component and a __________component.
- We can separate mixed costs into the two components using the ________________.

$

Total costs

Equation of line : y = a + bx

Slope = VC/unit

FC

activity

Mixed Costs

Total Mixed Cost Graph

$40,000

$35,000

$30,000

$25,000

$20,000

$15,000

$10,000

$5,000

Mixed costs are sometimes called semivariable or semifixed costs.

Total Costs

Mixed costs are usually separated into their fixed and variable components for management analysis.

0

10203040

Total Machine Hours (000)

The objective is to classifyall costs as either fixed or variable.

20

*

*

*

*

*

*

*

*

Total Cost in1,000’s of Dollars

*

*

10

0

0 1 2 3 4

Activity, 1,000s of Units Produced

- A __________of past cost behavior may be helpful in analyzing mixed costs.

Draw a line through the plotted data points so that about equal numbers of points fall above and below the line.

Estimated fixed cost = 10,000

Δin costΔin units

20

*

*

*

*

*

*

*

*

Total Cost in1,000’s of Dollars

*

*

10

0

0 1 2 3 4

Activity, 1,000s of Units Produced

Variable Cost unit= Slope =

Vertical distance is the change in cost.

Horizontal distance is the change in activity.

- Determine the __________by finding the slope
- change in ____÷ change in _____
- (see prev. slide)

- Determine the __________component
- Using the high (or the low) point, plug in the cost (y), the activity (x), and the slope (VC/unit).
- Solve for the y- intercept.

- Given the equation of the cost line, we can now use it to predict cost over some range of activity.

Mixed Costs: High-Low Method

Actual costs incurred

Highest and lowest levels

ProductionTotal

UnitsCost

ProductionTotal

UnitsCost

June1,000$45,550

July1,50052,000

August2,10061,500

September1,80057,500

October75041,250

Highest level

Lowest level

Difference

Mixed Costs: High-Low Method

Actual costs incurred

Highest and lowest levels

ProductionTotal

UnitsCost

ProductionTotal

UnitsCost

June1,000$45,550

July1,50052,000

August2,10061,500

September1,80057,500

October75041,250

Highest level2,100$61,500

Lowest level

Difference

Mixed Costs: High-Low Method

Actual costs incurred

Highest and lowest levels

ProductionTotal

UnitsCost

ProductionTotal

UnitsCost

June1,000$45,550

July1,50052,000

August2,10061,500

September1,80057,500

October75041,250

Highest level2,100$61,500

Lowest level75041,250

Difference

Mixed Costs: High-Low Method

Actual costs incurred

Highest and lowest levels

ProductionTotal

UnitsCost

ProductionTotal

UnitsCost

June1,000$45,550

July1,50052,000

August2,10061,500

September1,80057,500

October75041,250

Highest level2,100$61,500

Lowest level75041,250

Difference1,350$20,250

Difference in total cost

Difference in production

Variable cost

per unit

1

=

Mixed Costs: High-Low Method

Actual costs incurred

Highest and lowest levels

ProductionTotal

UnitsCost

ProductionTotal

UnitsCost

June1,000$45,550

July1,50052,000

August2,10061,500

September1,80057,500

October75041,250

Highest level2,100$61,500

Lowest level75041,250

Difference1,350$20,250

Difference in total cost

Difference in production

$20,250

1,350 units

Variable cost

per unit

1

=

=

=

$15

Mixed Costs: High-Low Method

Actual costs incurred

Highest and lowest levels

ProductionTotal

UnitsCost

ProductionTotal

UnitsCost

June1,000$45,550

July1,50052,000

August2,10061,500

September1,80057,500

October75041,250

Highest level2,100$61,500

Lowest level75041,250

Difference1,350$20,250

Difference in total cost

Difference in production

$20,250

1,350 units

Variable cost

per unit

1

=

=

=

$15

Total

cost

Fixed

cost

Variable cost

per unit

Units of

production

2

=

–

x

Mixed Costs: High-Low Method

Actual costs incurred

Highest and lowest levels

ProductionTotal

UnitsCost

ProductionTotal

UnitsCost

June1,000$45,550

July1,50052,000

August2,10061,500

September1,80057,500

October75041,250

Highest level2,100$61,500

Lowest level75041,250

Difference1,350$20,250

Difference in total cost

Difference in production

$20,250

1,350 units

Variable cost

per unit

1

=

=

=

$15

Total

cost

Fixed

cost

Variable cost

per unit

Units of

production

2

=

–

x

=

–

=

Highest level:

$61,500

( $15 x 2,100 )

$30,000

Mixed Costs: High-Low Method

Actual costs incurred

Highest and lowest levels

ProductionTotal

UnitsCost

ProductionTotal

UnitsCost

June1,000$45,550

July1,50052,000

August2,10061,500

September1,80057,500

October75041,250

Highest level2,100$61,500

Lowest level75041,250

Difference1,350$20,250

Difference in total cost

Difference in production

$20,250

1,350 units

Variable cost

per unit

1

=

=

=

$15

Total

cost

Fixed

cost

Variable cost

per unit

Units of

production

2

=

–

x

=

–

=

Highest level:

$61,500

( $15 x 2,100 )

$30,000

=

–

=

Lowest level:

$41,250

( $15 x 750 )

$30,000

Mixed Costs: High-Low Method

Actual costs incurred

Highest and lowest levels

ProductionTotal

UnitsCost

ProductionTotal

UnitsCost

June1,000$45,550

July1,50052,000

August2,10061,500

September1,80057,500

October75041,250

Highest level2,100$61,500

Lowest level75041,250

Difference1,350$20,250

Difference in total cost

Difference in production

$20,250

1,350 units

Variable cost

per unit

1

=

=

=

$15

Total

cost

Fixed

cost

Variable cost

per unit

Units of

production

2

=

–

x

=

–

=

Highest level:

$61,500

( $15 x 2,100 )

$30,000

=

–

=

Lowest level:

$41,250

( $15 x 750 )

$30,000

- Given our fixed and variable costs, we can use CVP techniques to help predict our profit at various activity levels.
- We define
- __________= Sales – VC
- __________= SP/unit – VC/unit
- __________= CM/SP

- We can use this set of techniques to answer the following types of questions.
- How many units do we need to sell to break even?
- How much profit will we generate at a given level of sales?
- If we want to earn a target profit, how many units do we need to sell?
- If we change our sales price, what happens to our profitability?

Contribution margin is amount by which revenue exceeds the variable costsof producing the revenue.

Computing Break-Even Point

P2

How much contribution margin must this company have to cover its fixed costs (break even)?

Answer: $24,000

Computing Break-Even Point

P2

How many units must this company sell to cover its fixed costs (i.e. to break even)?

Answer: $24,000 ÷ $30 per unit = 800 units

- Sales = VC + FC + profit or
- Profit = Sales – VC – FC
- At breakeven, profit = 0
- 0 = (Sales – VC) – FC
- 0 = CM - FC
- CM = FC or
- (CM/unit)(units) = FC
- And Breakeven Units = FC/(CM/unit)
- Or Breakeven in $ = FC/(CM ratio)

- You can use the CVP idea to determine how much we can sell to earn a desired profit.
- Profit = Sales – VC – FC
- Profit + FC = Sales – VC = CM = CM/unit(units)
- Target Salesunits= (FC + Profit) / CM/unit
- Target Sales$ = (FC + Profit) / CM ratio

__________is the amount by which sales can drop before the company incurs a loss.

Margin of safety may be expressed as a percentage of expected sales.

Margin of safety Expected sales - Break-even salespercentage Expected sales

=

C3

Exh.

22-17

- BEunits= FC/(CMcomposite), where
- CMcomposite = [(%A)CMA+ (%B) CMB]
- The number of units that we get will be a combined unit of A and B together.
- You then have to determine the number of A and B each that are actually sold.

- If FC = $100,000 and CM(a) = $40 and CM(b) = $20, and we sell 3 times as many units of B as A, what is the BE point?
- BEunits= 100,000/[(0.25)($40) + (0.75)($20)]
= 4,000 units

- A = (0.25)(4,000) or 1,000 units of A
- B = (0.75)(4,000) or 3,000 units of B

Contribution margin

Net income

Degree of ____________________=

A measure of the extent to which fixed costs are being used in an organization.

A measure of how a percentage change in sales will affect profits.

- We can recast the income statement to highlight the contribution margin.
- Sales
- - VC
- = CM
- - FC
- = operating income

For Internal Reporting purposes only

Now, let’s look at the quick studies!