1. Fundamentals of Cost-Volume-Profit Analysis
Accounting Chapter 3
Fundamentals of Cost-Volume-Profit Analysis

2. Cost-Volume-Profit Analysis
Procedure that examines changes in costs -- variable and fixed-- and volume levels and the resulting effects on net income.
Used for planning -- to determine effects of anticipated changes in revenues, variable costs, fixed costs and volume
Used for controlling -- what happens to net income when changes occur

3. Contribution Margin Sales - Variable Costs Per unit Ratio
Sales Price per unit - var. costs per unit
Tells us how much in $ is contributed to firm
Ratio
CM per unit/Sales price per unit
Tells us what % of each dollar is contributed to the firm

4. Example of Contribution Margin
Billy Bob’s Bicycles (Sales of 200 bikes)
Sales Revenues $100,000
Var. Costs ,000
Contr. Margin ,000
Less Fixed costs ,000
Net Income $30,000

5. Contribution Margin CM in total = $60,000 CM per unit = CM Ratio =
$100,000/200 bikes = $500 sales price per bike
$ 40,000/200 bikes = $200 var.costs per bike
$ 60,000/200 bikes = $300 CM per bike
CM Ratio =
$300/$500 = 60% OR
$60,000/$100,000 = 60%

6. CM = Net income if 1 more bike sold
Sale of 201 bikes
Sales Revenues $100,500 (201 x $500)
Var. Costs ,200 (201 x $200)
Contribution Margin 60,300
Less fixed costs ,000
Net income $30,300
Sales of one more unit = $300 increase in Net Income (due to contribution margin)

7. Break-Even Analysis Break-even (Point where Net Income = 0)
Sales = Variable costs + Fixed costs
How many bikes do we need to sell in order to break-even?
2 methods
Algebraic equation method
Contribution margin method

8. Break-even Analysis Algebraic equation method:
Sales = Var. Costs + Fixed Costs
$500x = $200x + $30,000
$300x = $30,000
x = 100 bikes
Check
Sales $50,000 (100 x $500)
Var. Costs 20, (100 x $200)
CM $30,000
- Fixed ,000
Net Income

9. Equation Method Break-even in sales dollars
Sales = 100% x
Variable costs = VC/SP = 200/500 = 40%x
Fixed costs are the same for all sales levels
Therefore, equation :
1X = .40X + $30,000
.60X = $30,000
x = $50,000 Break-even in sales dollars

10. Break-even Analysis Contribution Margin Method
1) Determine the CM per unit
$500 - $200 = $300
2) Calculate how many units must be sold to break even by the following formula:
Fixed costs $30, = 100 bikes
CM per unit $300

11. Break-even Analysis In Sales Dollars
B.E. in units x Sales price per unit OR
Fixed Costs
CM ratio
= $30,000/.60 = $50,000

12. Who wants to break even? Target Profit Analysis
Add Profit to previous equations
Profit is treated just like a fixed cost

13. Target Profit Analysis Add desired profit to fixed costs Before-Tax
Equation Method
$500x = $200x + $30,000 fixed + $60,000 Desired profit
$300x = $90,000
x = 300 bikes
Contribution Margin Approach
$30,000 + $60,000
$300
= $90,000/300 =
300 bikes

14. Target Net Profit Analysis (After-tax)
Desired After-Tax Profit = Before-tax
100% - Tax rate profit
Example for after-tax profit of $36,000:
$36,000/1-.40
=$36,000/.60
=$60,000 Before tax profit

15. Cost Structure- what portions of costs are fixed or variable
Company 1 - Pizza Pizza
Sales $200,000
-Var. costs 150,000
CM ,000
-Fixed costs 20,000
Net income 30,000
Company 2 - Pizza oven manufacturers
Sales $200,000
-Var. costs 50,000
CM ,000
-Fix. costs 120,000
Net income 30,000

16. Cost Structure What is CM ratio for each company?
Which company is riskier?
Operating Leverage = Contribution Margin Net Income
Higher operating leverage, more risky company

17. Margin of Safety Current sales - Break-even sales = Margin of safety
Tells you how far sales can drop before you have no net income. Indicates a safety cushion.
You can calculate margin of safety in dollars, units, or a percentage.
Margins of safety will change any time you have a different sales level.

18. Sensitivity Analysis - CM
Changes in sales price
Increase, CM increases
Decrease, CM decreases
Changes in variable costs
Increase, CM decreases
Decrease, CM increases
Changes in fixed costs
Increase or decrease, no change in CM

19. How Changes Affect Break-even Point
Changes in sales price
Increase, BEP decreases
Decrease, BEP increases
Changes in variable costs
Increase, BEP increases
Decrease, BEP decreases
Changes in fixed costs
Increase , BEP increases

20. C-V-P in a Multiproduct Environment
Sales Mix - more than one product sold
Ratio of each product sold to total
Example: Pizza Hut sells pizza, breadsticks, etc.
How many pizzas sold per breadsticks?
Assume four pizzas to one breadstick
Sales mix = 4P + 1B
This equation is called a “basket” of goods

21. C-V-P in a Multiproduct Environment
Breakeven/Target Profit analysis for multiproducts - use the CM per basket of goods
Example: Assume the CM for pizzas is $4 and the CM for breadsticks is $2, equation would be:
4P ($4) + 1B ($2) = $18 CM per basket of goods
Proceed as usual with break-even analysis

22. C-V-P for Multiproducts Basket of Goods Approach
Example: Fixed costs = $90,000
Break-even point = $90,000/18 CM
= 5,000 baskets of goods
1 basket = 4 P + 1B, therefore
Break-even is 4 x 5000 = 20,000 pizzas and 1 x 5000 = 5,000 breadsticks
All analysis is based on baskets of goods!!!

23. C-V-P for Multiproducts Weighted Average Approach
Can weight the basket of goods to get a weighted average CM per unit
(4/5 x $4) + (1/5 x $2) = $3.60
$90,000/ $3.60 = 25,000 total items
25,000 x 4/5 = 20,000 pizzas
25,000 x 1/5 = 5,000 breadsticks
If actual sales mix is different than predicted, break-even analysis and profit calculations will be different than predicted.

24. Multiple Cost Drivers
Often times, there are many mixed costs, each with a different cost driver
What-if Analysis on Excel allows you to determine net income of various scenarios.