1. COST-VOLUME-PROFIT RELATIONSHIPS 23  Cost behavior  CVP Analysis  Break-even analysis

2. Cost Behavior Costs that vary in direct proportion to the level of activity. Total cost - increases with activity Per-unit cost -remains nearly constant = $1.21 / ticket y = 1.21x R 2 = 0.98 Variable Cost

3. y = 1604 R 2 = 0.00 Total cost –remains nearly constant = $1604 / month Per-unit cost - decreases with increase in activity (Note: Per-unit fixed cost can be misleading.) Fixed Cost Costs that are unrelated to the level of activity.

4. y = 0.59x + 3,625 R 2 = 0.92 Variable or Fixed Cost? Some expenses have both fixed and variable components.

5. An algebraic expression representing a cost as a function of fixed and variable components. Y=F+VX Y=total cost F=fixed component V=variable cost per unit X=number of units Vehicle Maintenance=$3,625+$0.59 X Cost Functions

6. ( 17,700, $13,100 ) ( 3,300, $5,620 ) High-Low Method

7. ( 17,700, $13,100 ) ( 3,300, $5,620 ) $7,480 14,400 (1) Find the variable cost (slope). Variable cost: $7,480 14,400 = $0.52/unit

8. ( 17,700, $13,100 ) ( 3,300, $5,620 ) Slope = $0.52 (2) Find the fixed cost (y-intercept). ~ $4,000 Fixed cost: $13,100 - $0.52 x 17,700 = $3,896 ( 17,700,$13,100 )

9. y = 0.59x + 3,625 R 2 = 0.92 A more precise way to estimate cost functions. Use trendline function in Excel. Takes all points into account. Least-Squares Regression

10. Don’t use a trendline to estimate. $8,450 $4,100 Some expenses are fixed within a certain range. Relevant Range

11. Costs cannot be negative! Consider this a fixed cost equal to the average amount. Plausible Cost Functions

12. Cost-Volume-Profit Analysis v Volume of output v Sales price v Variable costs v Fixed costs v Product mix An investigation of the interrelationships among:

13. Per Unit $ 350 185 $ 165 Total Sales$ 42,000 Less Variable Expenses 22,200 Contribution Margin$ 19,800 Less Fixed Expenses 13,860 Net Income$ 5,940 Contribution Income Statement CM: covers fixed expenses & provides profit

14. The level of sales at which the contribution margin is just enough to cover fixed expenses Total fixed expenses Per unit contribution margin = 84 units $13,860 165 Break-even point = = Break-Even Point

15. Per Unit $ 350 185 $ 165 Total Sales Less Variable Expenses Contribution Margin Less Fixed Expenses Net Income At 84 units… Total $ 29,400 15,540 $ 13,860 13,860 $ 0

16. Per Unit Sales$ 350 Less Variable Expenses 185 Contribution Margin$ 165 = 47.1% $165 $350 CM Ratio = Contribution Margin Ratio

17. Total fixed expenses Contribution margin ratio = $29,400 $13,860.471 Break-even point = = Break-Even Point In sales dollars

18. How many units must be sold to earn a net income of $8,000? x = number of units Sales-Variable-Fixed=Income 350x-185x-13,860=8,000 165x=21,860 x=133 Target Net Profit