Chapter 5
Cost-Volume-Profit Relationships
Uses for CVP Analysis
• Income and profitability
– Costs, revenues and income
• Investment profitability
– Current expenditure v. long term profit
• Pro-forma financial statements
• Other specialized modeling
– Complex sales or demand forecasting
Cost Volume Profit Inputs
• Basic Cost Volume Profit (CVP) Analysis
uses:
– Sales levels
– Unit sales price
– Unit variable cost
– Total fixed cost
• All of these might be: historical, budgeted,
projected, hypothetical, etc.
Cost-Volume-Profit Models
• Relate income and Sales volume
• Breakeven Analysis
– Special instance of cost volume profit
– Income is exactly zero
– Cautions
• Can be discussed in units or dollars
• Multiple products must assume a sales mix
Breakeven based on contribution
margin
• Contribution margin is Sales – Var. Costs
• Amount that the sale “contributes” to profit
– How much higher income is due to this sale
• For a profit, total contribution margin must
exceed fixed costs
• Breakeven is the # of units where total
contribution margin = fixed costs.
Breakeven by Equations
• Income = Sales revenue – costs
• Income = Sales revenue – var. costs – fixed costs
• Income = Price x vol. – var. costs – fixed costs
• Income = Price x vol. – (Var/unit x volume) – fixed costs
• Income = (Price – var.) x volume – fixed costs
• Income = (CM/unit) x volume – fixed costs
Thus, if income is zero:
• 0 = (CM/unit) x volume – fixed costs
• (CM/unit) x volume = fixed costs or: fixed costs = Vol
CM/unit
Breakeven
• Fixed costs = Breakeven volume
CM/unit
Example:
• Fixed costs: $40,000
• Sales price: $12/unit
• Var. costs: $10/unit
• $40,000 = 20,000 units breakeven point
$2/unit
Target Income
• Breakeven is target income of zero
• Adding target income to fixed costs will
lead to volume to achieve target income
• From prior slide, for income of $25,000:
$25,000 + 40,000
= 32,500 units
$2/unit
Contribution Margin Percentage
• What percent of each sales dollar is
contribution margin?
• From Text Example:
• Sales price = $250
• Contribution Margin = $100
• $100/$250 = 40%
Contribution Margin in Dollars
$Sales to breakeven = Fixed Expenses
CM Percentage
=$35,000 = $87,500
40%
Breakeven by Dollars
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•
•
•
•
Use for companies with many products
The dollar is the “unit”
Thus, CM per “unit” = CM per dollar
CM %age = CM per dollar
Then, as before Fixed costs = BE
CM/ unit
• Remember “unit” is sales dollar
Contribution Margin on Dollars
•
•
•
•
•
•
Sales
2,000,000
VC
700,000
FC
600,000
CM = 2,000,000-700,000 = 1,300,000
1,300,000/2,000,000= CM ratio=.65
CM per sales $ = $.65, thus for B/E:
$600,000 = $923,076
.65
Operating Leverage
• Relates contribution margin to income
• Can measure “downside risk” of not meeting
expected income levels
• Companies with high fixed costs
– High operating leverage
– Low var. costshigh Cm/unit
– Changes in CM = change in income
• Investing in fixed assets often increase upside
income potential, but higher operating leverage
Operating Leverage
• Degree of op. lev. + Contribution Margin
Net operating income
High operating leverage comes from
relatively high fixed costs
Multiple Products/Sales Mix
• Multiple products complicates
breakeven/profitability analysis
• Must assume a mix or alternate mix
• Different real-world ability to alter the sales
mix.
• 2 Approaches:
– weighted-average contribution margin
– Compute contribution margin ratio (text)
Weighted average contribution
margin
• CM per unit for each product, times that
product’s percentage of sales
• Leads to Breakeven volume in Units
• Must then apply the percentages to get
number and dollars of each product
Multiple Product Contribution
Margin Example
• Sell two models of skis:
– Expert:
CM = $200
– Intermediate: CM =$150
• Sales Mix: 30% expert/70% intermed.
• Weighted Ave. Contrib. Margin:
$200*(.3) + $150 *(.7)= 60 + 105 = $165
• If FC = 500,000
500,000/165 = 3030 pairs of skis
Multiple Product Contribution
Margin Example (cont.)
• Sell 3030 skis to break even
• Sales mix: 30% expert, 70% intermed.
• Mix:
– 3030 x 30% = 909 expert
– 3030 x 70% = 2121 intermediate
3030 total
• 3030 is B/E only at this sales mix
• How would change in mix affect B/E?