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23 COST-VOLUME-PROFIT RELATIONSHIPS • Cost behavior • CVP Analysis • Break-even analysis
Variable Cost Cost Behavior Costs that vary in direct proportion to the level of activity. y = 1.21x R2 = 0.98 Total cost - increases with activity Per-unit cost - remains nearly constant = $1.21 / ticket
Fixed Cost Costs that are unrelated to the level of activity. y = 1604 R2 = 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.)
Variable or Fixed Cost? Some expenses have both fixed and variable components. y = 0.59x + 3,625 R2 = 0.92
Cost Functions 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
High-Low Method ( 17,700, $13,100 ) ( 3,300, $5,620 )
( 17,700, $13,100 ) ( 3,300, $5,620 ) $7,480 14,400 (1) Find the variable cost (slope). $7,480 14,400 Variable cost: = $0.52/unit
( 17,700, $13,100 ) ( 3,300, $5,620 ) (2) Find the fixed cost (y-intercept). ( 17,700, $13,100 ) Slope = $0.52 Slope = $0.52 Fixed cost: $13,100 - $0.52 x 17,700 = $3,896 ~ $4,000
Least-Squares Regression A more precise way to estimate cost functions. Use trendline function in Excel. Takes all points into account. y = 0.59x + 3,625 R2 = 0.92
Relevant Range Don’t use a trendline to estimate. $8,450 $4,100 Some expenses are fixed within a certain range.
Plausible Cost Functions Costs cannot be negative! Consider this a fixed cost equal to the average amount.
Cost-Volume-Profit Analysis An investigation of the interrelationships among: • Volume of output • Sales price • Variable costs • Fixed costs • Product mix
Contribution Income Statement Total Sales $ 42,000 Less Variable Expenses 22,200 Contribution Margin $ 19,800 Less Fixed Expenses 13,860 Net Income $ 5,940 Per Unit $ 350 185 $ 165 CM: covers fixed expenses & provides profit
Break-Even Point Total fixed expenses Per unit contribution margin $13,860 165 The level of sales at which the contribution margin is just enough to cover fixed expenses Break-even point = = = 84 units
At 84 units… Total Sales Less Variable Expenses Contribution Margin Less Fixed Expenses Net Income Total $ 29,400 15,540 $ 13,860 13,860 $ 0 Per Unit $ 350 185 $ 165
Contribution Margin Ratio $165 $350 Per Unit Sales $ 350 Less Variable Expenses 185 Contribution Margin $ 165 CM Ratio = = 47.1%
Break-Even Point Total fixed expenses Contribution margin ratio $13,860 .471 In sales dollars Break-even point = = = $29,400
Target Net Profit 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