Slides identify sensitive variables

Sensitive Variables• $5 decrease in ticket price 17% causes: • 25% decrease in unit Contribution Margin • 33% increase in the breakeven point in units • The 20% increase in unit Variabl

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Identify Sensitive Variables

Principles of Cost Analysis and

Management

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We assume cross traffic will stop What if our

assumption is incorrect?

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Terminal Learning Objective

• Action: Identify Sensitive Variables Through What-if

Scenarios

• Condition: You are a cost advisor technician with access

to all regulations/course handouts, and awareness of

Operational Environment (OE)/Contemporary

Operational Environment (COE) variables and actors.

• Standard: With 80% accuracy:

1 Define “sensitive variable”

2 Calculate new breakeven point given changes in assumptions

3 Calculate breakeven selling price for a given sales quantity

4 Solve for missing variables in the breakeven equation given

changed assumptions

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Review: Key Variables and Assumptions:

• The Breakeven Equation:

Revenue - Variable Cost - Fixed Cost = Profit

• What are the key variables?

Revenue = #Units Sold * Selling Price $/Unit Variable Cost = #Units Sold * Variable Cost $/Unit

• Assumes… ONLY ONE product or service is sold

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• Assumes ONLY ONE product or service is sold

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What is Sensitivity Analysis?

• Recognizes that the validity of the decision

depends on the validity of the underlying

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What if?

• How does my decision point or breakeven

point change if I change an assumption or an estimate?

• How does that change affect the overall

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Check on Learning

• How do we test our assumptions?

• What is a sensitive variable?

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• Breakeven point = 100 Tickets

• How does breakeven point in units change if:

• Price decreases by $5/Ticket? Increases by $10?

• Unit variable cost increases 20%? Decreases 10%?

• Fixed cost increases by 10%? Decreases by 20%?

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Sensitive Variables

• $5 decrease in ticket price (17%) causes:

• 25% decrease in unit Contribution Margin

• 33% increase in the breakeven point in units

• The 20% increase in unit Variable Cost causes:

• 10% decrease in unit Contribution Margin

• 11% increase in breakeven point in units

• Which variable would you define as sensitive?

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Check on Learning

• How will breakeven point in units change if

fixed cost increases?

• How will breakeven point in units change if

Contribution Margin increases?

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Sensitivity and Breakeven

• The breakeven equation includes five variables:

• Number of Units, Selling Price per Unit, Variable Cost per Unit, Fixed Cost, and Target Profit

Revenue – VC – FC = Profit

(Price$/Unit*#Units) – (VC$/Unit*#Units) – FC = Profit

-or-• So far, we have assumed all variables are known

except Number of Units

• What if one of the other variables is the unknown?

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• What if one of the other variables is the unknown?

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What Ifs Involving Other Variables

• What if quantity of tickets is limited to 80 due

to building capacity?

• Task: Calculate the breakeven price per ticket

• How would you set up the equation?

• What is the unknown variable?

• How would you express Revenue? Variable

Cost?

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Solving for Breakeven $Price

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Graphic Solution – 80 Tickets

VC

$10/tkt Fixed Cost

$

X Axis = Unknown Price per Ticket

Revenue increases as ticket price increases$35

VC = 80 tickets * $10/ticket

FC = $2000 Total Cost = $2800

VC = 80 tickets * $10/ticket

FC = $2000 Total Cost = $2800

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Interpreting the Result

• In order to breakeven at a volume of 80

tickets, we must charge $35 per ticket

• Questions to ask:

• Is the new price reasonable?

• Can we sell all 80 tickets for $35/ticket?

• What other factors might be considered?

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Check on Learning

• When number of units is known, how will

variable cost be expressed in the breakeven equation?

• What does the horizontal (x) axis represent on the graph?

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• What if the market will not bear an increase in

ticket price above $30?

• AND Fixed Cost increases by 10%?

• Task: Calculate the target variable cost per ticket

that will maintain a breakeven of 100 tickets

• How would you set up the equation?

• How would you express Revenue? Variable Cost?

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Solving for Breakeven $VC/Ticket

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Solving for Breakeven $VC/Ticket

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X Axis = Variable Cost per Ticket

Total cost increases as variable cost per ticket increases

$8

Revenue = 100 tickets * $30/ticket

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• In order to maintain the breakeven point of

100 tickets, we need to reduce variable cost per ticket from $10 to $8

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Sensitivity Analysis Spreadsheet

Select the “Solve Breakeven VC” Tab

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Help messages appear when you mouse over the

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Enter problem data into the white cells:

# units = 100

$price/unit = $30 Fixed Cost = $2000 +$200 Profit Target = $0 (default value)

Enter problem data into the white cells:

# units = 100

$price/unit = $30 Fixed Cost = $2000 +$200 Profit Target = $0 (default value)

The spreadsheet automatically calculates the unknown VC$/Unit

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• What if the market will not bear an increase in ticket price above $30?

• Variable cost increases by 30%

• Task: Calculate target fixed cost that will

maintain a breakeven point of 100 tickets

• Which spreadsheet tool will I use?

• How would I set up the equation?

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Solving for Breakeven $Fixed Cost

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Solving for Breakeven $Fixed Cost

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$

X Axis = Unknown Fixed Cost

Total cost increases as Fixed Cost increases$1700

VC = 100 tickets * $13/ticket Revenue = 100 tickets * $30/tkt

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• In order to maintain the breakeven point of

100 tickets, we need to reduce fixed cost from

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Your spreadsheet should look like this

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Your graph should look like

this

Your graph should look like

this

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Check on Learning

• When using the Sensitivity Analysis

Spreadsheet, what is the first question we

should ask?

• Once we have found the solution to the

unknown variable, what questions should we ask?

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Sales Mix Issues

• Remember our key assumptions!

• What if an entity sells more than one product?

• Breakeven analysis is based on the Sales Mix

• What percentage of the Total Sales in units does each product comprise?

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Sales Mix Example

• Sebastian’s Dinner Theater offers a Senior

Discount in addition to regular price

• Senior price is $20 per ticket

• Seniors receive a reduced food portion

• Variable cost = $7 per ticket

• Sales Mix is 30% Senior and 70% Regular

• Regular price is $30 and Variable Cost is $10/ticket

• Fixed costs = $2000

• Task: Calculate the breakeven number of tickets

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Sales Mix

• Calculate Weighted Average $Price/Ticket:

percentage1 * price1 + percentage2 * price2

30%*$20 + 70%*$30 = $6 + $21 = $27

percentage1 and price1 represent Senior ticketspercentage2 and price2 represent Regular tickets

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Sales Mix

• Calculate Weighted Average $VC/Ticket:

percentage1 * VC1 + percentage2 * VC2

30%*$7 + 70%*$10 = $2.10 + $7 = $9.10

percentage1 and VC1 represent Senior tickets

percentage2 and VC2 represent Regular tickets

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Sales Mix

• What is the weighted average Contribution

Margin per unit?

$CM/Ticket = $Price/Ticket - $VC/Ticket

$27/Ticket - $9.10/Ticket = $17.90/Ticket

• For each Ticket sold, profit will increase by an

average of $17.90

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Sales Mix

• Use the Sales Mix tab on the 9.2 Sensitivity

Analysis spreadsheet to calculate:

• Weighted average price

• Weighted average variable cost per unit

• Weighted Average contribution margin

• Breakeven point

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Enter the percentage for each product

The spreadsheet will verify that the

total equals 100%

Enter the percentage for each product

The spreadsheet will verify that the

total equals 100%

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Enter price per unit and variable cost per

unit for each product

Enter price per unit and variable cost per

unit for each product

The spreadsheet calculates CM per unit for each product, and weighted average selling price, variable cost, and contribution margin

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of units that must be sold to breakeven

The spreadsheet calculates the quantity of each type of product and the total number

of units that must be sold to breakeven

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Breakeven Theory

If:

Contribution Margin = Revenue – Variable Cost

And the breakeven equation is:

Revenue – Variable Cost – Fixed Cost = 0

OrContribution Margin – Fixed Cost = 0

Then breakeven occurs when:

Contribution Margin = Fixed Cost

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Graphic Illustration

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What if?

• How would the breakeven point change if the actual sales mix was 40% Senior and 60%

Regular? 50/50?

• What else might Sebastian’s management

consider in this decision?

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Check on Learning

• What is the first step when calculating

breakeven for an entity that sells more than one product?

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Practical Exercises

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