Financial and Cost VolumeProfit Models

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• Financial and Cost-Volume-Profit Models

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Definition of Financial Models
Relationships between costs, revenues, income.
Accurate, reliable simulations of relations among
relevant costs, benefits, value and risk that is
useful for supporting business decisions.
Pro forma financial statements.
Relationships between current investments and
value.
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Objectives of Financial Modeling
Accurate and reliablesimulation of
relevantfactors and relationships
Useful fordecisionmaking
Flexible andresponsiveanalyses
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Basic Cost-Volume-Profit (CVP) Model

• Revenue Variable Costs Fixed Costs Income
• Assumptions
• Revenue can be estimated as
• sales price (P) units sold (Q)
• Total variable costs can be estimated as
• variable cost per unit (V) units sold (Q)
• Total fixed costs (F) will remain constant
  over the relevant range.

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Basic CVP Model andthe Break-Even Point
Revenue Variable Costs Fixed Costs Income
PQ VQ F I At the break-even point income
0 PQ VQ F Combining terms and solving for
Q, the number of units that must be sold to break
even Q F (P V)
Lets see some numbers!
(P V) is the unitcontribution margin
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Basic CVP Model andthe Break-Even Point

• The break-even point is the point in the volume
  of activity where the organizations revenues and
  expenses are equal.

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Basic CVP Model andthe Break-Even Point

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

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Basic CVP Model andthe Break-Even Point

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

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Basic CVP Model andthe Break-Even Point
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Basic CVP Model andthe Break-Even Point

• Here is the proof!

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Basic CVP Model andthe Break-Even Point

• 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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Basic CVP Model andthe Break-Even Point
80,000 40
200,000 sales

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Basic CVP Model in Graphical Format

• Viewing CVP relationships in a graph gives
  managers a perspective that can be obtainedin no
  other way.
• Consider the following information for
  Curl, Inc.

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Basic CVP Model in Graphical Format
Total sales
Break-even point
Profit area
Total expenses
Sales in Dollars
Fixed expenses
Loss area
Units Sold
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Profit-Volume Graph
Some managers like the profit-volume graph
because it focuses on profits and volume.
Profit area
Loss area
Break-even point
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CVP and Target Income

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

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CVP and Target Income
We can also use the equation approachto get
the same result.
Revenue Variable costs Fixed costs Income
Q 900 surf boards
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Operating Leverage
Reflects the risk of missing sales
targets. Measured as the ratio of
contributionmargin to operating income.
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Operating Leverage
Contribution margin Net income
Operating leverage factor

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Operating Leverage

• 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?

Heres the proof!
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Operating Leverage
10 increase in sales from 250,000 to 275,000 .
. .
. . . 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.
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.
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Modeling Taxes
We can adjust the basic CVPmodel to incorporate
income 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)
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Modeling Multiple Products
When a company sells multiple products, modeling
requires 1. An estimate of the relative
proportion of each product in the sales mix.
2. A computation of the Weighted Average Unit
Contribution Margin.
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Modeling Multiple Products

• For a company with more than one product,sales
  mix is the relative combination in which a
  companys products are sold.
• Different products have different selling prices,
  cost structures, and contribution margins.
• Lets assume Curl sells surf boards and sail
  boards and see how we deal with break-even
  analysis.

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Modeling Multiple Products

• Curl provides us with the following information

Sales mix computation
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Modeling Multiple Products

• Weighted-average unit contribution margin

200 62.5
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Modeling Multiple Products

• 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

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Modeling Multiple Products
Break even is 514 combined units. We can use
thesales mix to find the number of units of
eachproduct 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 activity-based
costing, that costs may be a function of multiple
activities, not merely 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)
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Sensitivity Analysis
An examination of the changes in outcomes
causedby changes in each of a models parameters.
For example, we can examine the impact on
Curlsprofit (outcome) if the parameters of
selling price, quantitysold, 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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Sensitivity Analysis
?Estimate the likelyrange of eachparameter.
?Change one parameterto upper and lower endof
range, keeping otherparameters at the
mostlikely values.
?Estimatethe most likely valueof
eachparameter.
?Record profitfor each change and
repeatprocess forall parameters.
Because of the number of computations involved,
computerized models are used for sensitivity
analysis.
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Sensitivity Analysis
Model elasticityThe ratio of percentage
changein 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.
Because of the number of computations involved,
computerized models are used for sensitivity
analysis.
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Scenario Analysis
Realistic 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).
• Lets look at the Rose Company example.

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Modeling Scarce Resources

• Rose Company produces three productsand
  selected data is shown below

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Modeling Scarce Resources

• 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 next week?

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Modeling Scarce Resources

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

Product 2 should be emphasized because it has the
highest contribution per minute on machine A1,
the scarce resource.
If there are no other considerations, the best
plan would be to produce to meet current demand
for Product 2 and then use remaining capacity to
make Product 3.
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Modeling Scarce Resources

• Lets see how this plan would work.

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Modeling Scarce Resources

• Lets see how this plan would work.

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Modeling Scarce Resources

• Lets see how this plan would work.

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Modeling Scarce Resources
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?
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Modeling Scarce Resources
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Modeling Scarce Resources
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 demandfor Product 1 is 2,000 units. Rose
needs an additional 1,900minutes to produce
enough Product 1 to satisfy demand.
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Modeling Scarce Resources
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.
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Modeling Scarce Resources
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 capacityas long as Product 2 could be
sold.
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End of Chapter 12