The McGraw-Hill Companies, Inc. 2006McGraw-Hill/Irwin 12 Financial and Cost- Volume-Profit Models.

The McGraw-Hill Companies, Inc. 2006McGraw-Hill/Irwin

12Financial and Cost-

Volume-Profit Models

12-2


Definition of Financial Models

Accurate, reliable Accurate, reliable simulations of simulations of

relations among relations among relevant costs, relevant costs,

benefits, value and benefits, value and risk that is useful for risk that is useful for supporting business supporting business

decisions.decisions.

Accurate, reliable Accurate, reliable simulations of simulations of

relations among relations among relevant costs, relevant costs,

benefits, value and benefits, value and risk that is useful for risk that is useful for supporting business supporting business

decisions.decisions.

Relationships between costs,

revenues, & income.

Relationships between costs,

revenues, & income.

Relationships between current

investments and value.

Relationships between current

investments and value.

Pro forma financial

statements.

Pro forma financial

statements.

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Objectives of Financial Modeling

Useful fordecisionmaking

Useful fordecisionmaking

Accurate and reliablesimulation of relevant

factors and relationships

Accurate and reliablesimulation of relevant

factors and relationships

Flexible andresponsiveanalyses

Flexible andresponsiveanalyses

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Basic Cost-Volume-Profit (CVP) Model

Revenue Revenue == Variable Costs + Fixed Costs + Income Variable Costs + Fixed Costs + Income

Assumptions:Assumptions:Revenue can be estimated as:Revenue can be estimated as:

sales price (P) × units sold (Q)sales price (P) × units sold (Q)

Total variable costs can be estimated as:Total variable costs can be estimated as:variable cost per unit (V) × units sold (Q)variable cost per unit (V) × units sold (Q)

Total fixed costs (F) will remain constantTotal fixed costs (F) will remain constant over the relevant range. over the relevant range.


Assumptions:Assumptions:Revenue can be estimated as:Revenue can be estimated as:

sales price (P) × units sold (Q)sales price (P) × units sold (Q)

Total variable costs can be estimated as:Total variable costs can be estimated as:variable cost per unit (V) × units sold (Q)variable cost per unit (V) × units sold (Q)

Total fixed costs (F) will remain constantTotal fixed costs (F) will remain constant over the relevant range. over the relevant range.

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PQ = PQ = VQ + F + IVQ + F + I

At the break-even point income = 0At the break-even point income = 0

PQ = VQ + FPQ = VQ + F

Combining terms and solving for Q, the number of Combining terms and solving for Q, the number of units that must be sold to break even:units that must be sold to break even:

Q = F Q = F ÷ (P – V)÷ (P – V)


PQ = PQ = VQ + F + IVQ + F + I

At the break-even point income = 0At the break-even point income = 0

PQ = VQ + FPQ = VQ + F

Combining terms and solving for Q, the number of Combining terms and solving for Q, the number of units that must be sold to break even:units that must be sold to break even:

Q = F Q = F ÷ (P – V)÷ (P – V) (P – V) is the unit

contribution margin

Let’s see some

numbers!

Basic CVP Model andthe Break-Even Point

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The break-even point is the point in the volume of activity where the organization’s revenues and

expenses are equal.

Sales 200,000$ Less: variable expenses 120,000 Contribution margin 80,000 Less: fixed expenses 80,000 Net income -$

Sales 200,000$ Less: variable expenses 120,000 Contribution margin 80,000 Less: fixed expenses 80,000 Net income -$


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Consider the following informationdeveloped by the accountant at Curl, Inc.:

Total Per Unit PercentSales (500 surf boards) 250,000$ 500$ 100%Less: variable expenses 150,000 300 60%Contribution margin 100,000$ 200$ 40%

Less: fixed expenses 80,000 Net income 20,000$




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For each additional surf board sold, Curl generates $200 in contribution margin.


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Fixed expenses Unit contribution margin

=Break-even point

(in units)

$80,000 $200

= 400 surf boards






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Here is the proof!


Less: fixed expenses 80,000 Net income -$



400 × $500 = $200,000 400 × $300 = $120,000


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Calculate the break-even point in sales dollars rather than units by using the contribution margin ratio.

Contribution margin Sales

= CM Ratio

Fixed expense CM Ratio

Break-even point(in sales dollars)

=


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$80,000 40%

$200,000 sales=


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Viewing CVP relationships in a graph gives managers a perspective that can be obtained

in no other way.

Consider the following information for Curl, Inc.:

Basic CVP Model in Graphical Format

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The McGraw-Hill Companies, Inc. 2006McGraw-Hill/IrwinUnits Sold

Sal

es i

n D

oll

ars

Profit area

Loss area

Break-evenBreak-evenpointpoint

Break-evenBreak-evenpointpoint

Fixed expensesFixed expenses

Total expensesTotal expenses

Total salesTotal sales

Basic CVP Model in Graphical Format

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1 3 4 52 6 7 8

Pro

fit

Units sold (00s)

Some managers like the profit-volumeSome managers like the profit-volumegraph because it focuses on profits and volume.graph because it focuses on profits and volume.

Some managers like the profit-volumeSome managers like the profit-volumegraph because it focuses on profits and volume.graph because it focuses on profits and volume.

Profit

area

Loss area

Break-evenpoint

Break-evenpoint

Profit-Volume Graph

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We can determine the number of surfboards that Curl must sell to earn a profit of $100,000 using the contribution

margin approach.

We can determine the number of surfboards that Curl must sell to earn a profit of $100,000 using the contribution

margin approach.

Fixed expenses + Target income Unit contribution margin

=Units sold to earnthe target income

$80,000 + $100,000 $200 per surf board

= 900 surf boards

CVP and Target Income

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Revenue = Variable costs + Fixed costs + Income

($500 × Q) ($300 × Q)= + $80,000 + $100,000

$200Q = $180,000

Q = 900 surf boards

We can also use the equation approachto get the same result.

We can also use the equation approachto get the same result.

CVP and Target Income

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Operating Leverage

Reflects the risk of missing sales targets.Reflects the risk of missing sales targets.

Measured as the ratio of contributionMeasured as the ratio of contributionmargin to operating income.margin to operating income.

Reflects the risk of missing sales targets.Reflects the risk of missing sales targets.

Measured as the ratio of contributionMeasured as the ratio of contributionmargin to operating income.margin to operating income.

A high operating leverage is indicative

of high committed costs (e.g. interest).

A relatively small change in sales can

lead to a loss.

A high operating leverage is indicative

of high committed costs (e.g. interest).

A relatively small change in sales can

lead to a loss.

A low operating leverage is indicative

of low committed costs (e.g. interest). More of the costs are

variable in nature.

A low operating leverage is indicative

of low committed costs (e.g. interest). More of the costs are

variable in nature.

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Contribution margin Net income

Operating leveragefactor

=

$100,000 $20,000

= 5

Operating Leverage

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

its sales by 10%, what will be the percentage increase in net income?

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

its sales by 10%, what will be the percentage increase in net income?

Percent increase in sales 10%Operating leverage factor × 5Percent increase in profits 50%

Percent increase in sales 10%Operating leverage factor × 5Percent increase in profits 50%

Operating Leverage

Here’s the proof!

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Operating Leverage

10% increase in sales from$250,000 to $275,000 . . .

10% increase in sales from$250,000 to $275,000 . . .

. . . results in a 50% increase inincome from $20,000 to $30,000.. . . results in a 50% increase in

income from $20,000 to $30,000.

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Computer Spreadsheet Models

1. Gather all the facts,

assumptions, and estimates

for your model; i.e., parameters.

1. Gather all the facts,

assumptions, and estimates

for your model; i.e., parameters. 2. Describe the relations

between the parameters. This usually results in an

algebraic equation.

2. Describe the relations between the parameters. This usually results in an

algebraic equation.

3. Separate parameters and formulas. Use cell

addresses, instead of actual numbers.

3. Separate parameters and formulas. Use cell

addresses, instead of actual numbers.

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Modeling Taxes

Using the following notation:

A = Income after tax

B = Income before tax

T = Tax rate

A = B – BT

A = B (1 – T) or solving for B:

B = A ÷ (1 – T)

Using the following notation:

A = Income after tax

B = Income before tax

T = Tax rate

A = B – BT

A = B (1 – T) or solving for B:

B = A ÷ (1 – T)

We can adjust the basic CVPmodel to incorporate income taxes.

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Modeling Multiple Products

When a company sells When a company sells multiple products, multiple products, modeling requires:modeling requires:

1. An estimate of the 1. An estimate of the relative proportion of relative proportion of

each product in the “each product in the “sales sales mixmix”. ”.

2. A computation of the 2. A computation of the Weighted Average Unit Weighted Average Unit Contribution Margin.Contribution Margin.

When a company sells When a company sells multiple products, multiple products, modeling requires:modeling requires:

1. An estimate of the 1. An estimate of the relative proportion of relative proportion of

each product in the “each product in the “sales sales mixmix”. ”.

2. A computation of the 2. A computation of the Weighted Average Unit Weighted Average Unit Contribution Margin.Contribution Margin.

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For a company with more than one product,sales mix is the relative combination in which a company’s products are sold.

Different products have different selling prices, cost structures, and contribution margins.

Let’s assume Curl sells surf boards and sail boards and see how we deal with break-even analysis.

For a company with more than one product,sales mix is the relative combination in which a company’s products are sold.

Different products have different selling prices, cost structures, and contribution margins.

Let’s assume Curl sells surf boards and sail boards and see how we deal with break-even analysis.


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Curl provides us with the following information:


Sales mix computation

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Weighted-average unit contribution margin

$200 × 62.5%$200 × 62.5%$200 × 62.5%$200 × 62.5%


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Break-even point

Break-even point

= Fixed expenses

Weighted-average unit contribution margin

Break-even point

= $170,000

$331.25

Break-even point

= 514 combined units


Fixed costs increased from $80,000 due to expansion needed to

sell multiple products.

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Break even is 514 combined units. We can use thesales mix to find the number of units of each

product that must be sold to breakeven.


The break-even point of 514 units is validonly for the sales mix of 62.5% and 37.5%.

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Modeling Multiple Cost Drivers

Recall from our discussion of Recall from our discussion of activity-based costing, that activity-based costing, that costs may be a function of costs may be a function of

multiple activities, not merely multiple activities, not merely sales volume.sales volume.

Total Cost = (Unit variable cost × Sales units)+ (Batch cost × Batch activity)+ (Product cost × Product activity)+ (Customer cost × Customer activity)+ (Facility cost × Facility activity)

Some costs viewed as fixed

using sales volume as the only activity may now

be considered variable.

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Sensitivity Analysis

An examination of the changes in outcomes causedby changes in each of a model’s parameters.

For example, we can examine the impact on Curl’sprofit (outcome) if the parameters of selling price, quantity

sold, unit variable cost, and or fixed costs change.

For example, we can examine the impact on Curl’sprofit (outcome) if the parameters of selling price, quantity

sold, unit variable cost, and or fixed costs change.

Because of the number of computations involved, computerized models are used for sensitivity analysis.

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Estimatethe most

likely valueof each

parameter.

Estimate the likely

range of eachparameter.

Change one parameterto upper and lower endof range, keeping otherparameters at the most

likely values.


Record profitfor each change

and repeatprocess for

all parameters.

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Model elasticityThe ratio of percentage change

in outcome (profit) to percentagechange in a parameter.

If greater than 1.0,change in parameter

has a large effect on profit.

If less than 1.0,change in parameter has a small effect

on profit.

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Scenario Analysis

Realistic combinations of changed parametersRealistic combinations of changed parameters

Best case scenarioRealistic combination of highest prices and quantities, along with

the lowest costs.

Worst case scenarioRealistic combination of lowest prices and quantities, along with

the highest costs.

Most likely case scenarioRealistic combination of most likely prices and

quantities, along with the most likely costs.

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Modeling Scarce Resources

Firms often face the problem of deciding how to best utilize a scarce resource.

Usually fixed costs are not affected by this particular decision, so management can focus on maximizing total throughput (usually equal to contribution margin).

Let’s look at the Rose Company example.

Firms often face the problem of deciding how to best utilize a scarce resource.

Usually fixed costs are not affected by this particular decision, so management can focus on maximizing total throughput (usually equal to contribution margin).

Let’s look at the Rose Company example.

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Rose Company produces three productsand selected data is shown below:


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Operating time on machine A1 is the scarce resource as it is being used at 100% of its capacity.

There is excess capacity on all other machines. Machine A1 has a capacity of 2,400 minutes per

week.

Which product should Rose emphasize Which product should Rose emphasize next week?next week?

Operating time on machine A1 is the scarce resource as it is being used at 100% of its capacity.

There is excess capacity on all other machines. Machine A1 has a capacity of 2,400 minutes per

week.

Which product should Rose emphasize Which product should Rose emphasize next week?next week?


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The key is the contribution marginper unit of the scarce resource.

Product 2 should be emphasizedProduct 2 should be emphasized because it has the highest because it has the highest contribution per minute on machine A1, the scarce resource. contribution per minute on machine A1, the scarce resource. Product 2 should be emphasizedProduct 2 should be emphasized because it has the highest because it has the highest

contribution per minute on machine A1, the scarce resource. contribution per minute on machine A1, the scarce resource.


Product1 2 3

Contribution margin per unit 24$ 15$ 20$ Minutes required to produce one unit 1.00 0.50 0.80 Contribution margin per minute 24.00$ 30.00$ 25.00$

If there are no other considerations, the best plan would be to If there are no other considerations, the best plan would be to produce to meet current demand for Product 2 and then use produce to meet current demand for Product 2 and then use

remaining capacity to make Product 3.remaining capacity to make Product 3.

If there are no other considerations, the best plan would be to If there are no other considerations, the best plan would be to produce to meet current demand for Product 2 and then use produce to meet current demand for Product 2 and then use

remaining capacity to make Product 3.remaining capacity to make Product 3.

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Let’s see how this plan would work.Let’s see how this plan would work.

Alloting Our Constrained Recource (Machine A1)

Weekly demand for Product 2 2,200 unitsTime required per unit × 0.50 min.Total time required to make Product 2 1,100 min.




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Total time available 2,400 min.Time used to make Product 2 1,100 min.Time available for Product 3 1,300 min.



Total time available 2,400 min.Time used to make Product 2 1,100 min.Time available for Product 3 1,300 min.

Let’s see how this plan would work.Let’s see how this plan would work.


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Let’s see how this plan would work.Let’s see how this plan would work.Alloting Our Scarce Recource (Machine A1)


Total time available 2,400 min.Time used to make Product 2 1,100 min.Time available for Product 3 1,300 min.Time required per unit ÷ 0.80 min.Production of Product 3 1,625 units

Alloting Our Scarce Recource (Machine A1)


Total time available 2,400 min.Time used to make Product 2 1,100 min.Time available for Product 3 1,300 min.Time required per unit ÷ 0.80 min.Production of Product 3 1,625 units


Is this a problem?

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The market for Product 3 is only 1,500 units perweek, so Rose should not produce 1,625 units.

The market for Product 3 is only 1,500 units perweek, so Rose should not produce 1,625 units.

So Rose should produce 1,500 units of Product 3,leaving time to produce how many Product 1?

So Rose should produce 1,500 units of Product 3,leaving time to produce how many Product 1?

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Remaining time available 1,300 min.Time used to make Product 3 1,200 min.Time available for Product 1 100 min.Time required per unit ÷ 1.00 min.Production of Product 1 100 units



Remaining time available 1,300 min.Time used to make Product 3 1,200 min.Time available for Product 1 100 min.Time required per unit ÷ 1.00 min.Production of Product 1 100 units

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Suppose Rose Company could buy additionalminutes of capacity on machine A1.

How many additional minutes does Rose need to satisfy unmet sales demand?

Suppose Rose Company could buy additionalminutes of capacity on machine A1.

How many additional minutes does Rose need to satisfy unmet sales demand?

Rose had only 100 minutes remaining for Product 1which requires 1.00 minutes per unit. The weekly demand

for Product 1 is 2,000 units. Rose needs an additional 1,900minutes to produce enough Product 1 to satisfy demand.

Rose had only 100 minutes remaining for Product 1which requires 1.00 minutes per unit. The weekly demand

for Product 1 is 2,000 units. Rose needs an additional 1,900minutes to produce enough Product 1 to satisfy demand.

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What is the maximum amount Rose would pay per minutefor the additional 1,900 minutes to produce Product 1?

What is the maximum amount Rose would pay per minutefor the additional 1,900 minutes to produce Product 1?


Contribution per minute for Product 1 is $24.00. Rosecould pay up to $24.00 per minute for additional capacity.

Contribution per minute for Product 1 is $24.00. Rosecould pay up to $24.00 per minute for additional capacity.

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Now, assume that the demand for all three products is unlimited and that Rose company

could again buy additionalminutes of capacity on machine A1.

What is the maximum amount Rose would pay per minute for additional capacity?

Now, assume that the demand for all three products is unlimited and that Rose company

could again buy additionalminutes of capacity on machine A1.

What is the maximum amount Rose would pay per minute for additional capacity?

Contribution per minute for Product 2 is $30.00. Rosecould pay up to $30.00 per minute for additional capacity

as long as Product 2 could be sold.

Contribution per minute for Product 2 is $30.00. Rosecould pay up to $30.00 per minute for additional capacity

as long as Product 2 could be sold.

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End of Chapter 12

The McGraw-Hill Companies, Inc. 2006McGraw-Hill/Irwin 12 Financial and Cost- Volume-Profit Models.

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Transcript of The McGraw-Hill Companies, Inc. 2006McGraw-Hill/Irwin 12 Financial and Cost- Volume-Profit Models.