Prof. Baick 1. Cost-Volume Profit Analysis A technique that examines changes in profits in response to changes in sales volumes, costs, and prices 2. Components of Graphing CVP Analysis Relationships
D C B A
where: F = Total fixed costs P = Price per unit of product (goods or services) Profit = Targeted profit level Q = Quantity of product sold (goods or services) TR = Total revenue TVC = Total variable costs V = Variable cost per unit
Assumptions Made in CVP Analysis Number of output units only revenue driver and only cost driver Total costs can be separated into the primary categories of variable costs and fixed costs Total revenues and total costs are linear within the relevant range (and time period) Unit selling price, unit variable costs, and fixed costs known and constant Single product or constant sales mix Time value of money effects ignored
Basic Formula and Terminology Assume that: U = Number of Units Produced and SOLD SP = Selling Price per Unit VC = Variable Cost per Unit FC = Total Fixed Costs
Fixed Costs =
Breakeven The level of sales whereby total profits are equal to zero. Contribution margin Sales Revenue – Variable Costs Contribution margin per unit Selling price per unit – Variable cost per unit Contribution margin ratio = Total Sales Revenue – Total Variable Costs Total Sales Revenue OR: Selling price per Unit – Variable costs per Unit Selling price per Unit
Breakeven Analysis Breakeven sales Breakeven units
Target Profit Target sales Target units
Margin of Safety
Margin of Safety Ratio
Product Mix Decisions
Leverage and Cost Structure Definition Increasing sales by a given percent and increasing profits by an increasingly larger proportion.
Primacy of Contribution Margin
CVP Graphical Analysis
IMPORTANT FORMULAS: SP VC FC U = = = = Selling price per unit Variable cost per unit Total Fixed costs Units sold
Expenses Variable Fixed FC
- VC(U) -
BREAK EVEN MEANS REVENUES = EXPENSES OR NET INCOME IS 0 Contribution Margin Ratio =
Break-even (Units) =
FC __ SP - VC FC____________ Contribution Margin Ratio
Break-even (Sales) =
Target Profit (Units) =FC + TP SP - VC Target Profit (Sales) = FC + TP Contribution Margin Ratio = Actual (Expected) Sales – Break-even Sales
Margin of Safety
Margin of Safety Ratio =
Margin of Safety Actual (Expected) Sales
Higher is better!
Three Ways of Computing Break-Even 1. Mathematical equation SP(U) – VC(U) – FC = NI 2. Contribution Margin Technique (Formulas) 3. Graphs
Example 1. If sales are $80,000, variable costs are $50,000, and fixed costs are $20,000, the contribution margin ratio is: Sales – Variable Costs Sales 80,000 – 50,000 80,000 = .375 or 37.5%
Example 2. A firm with fixed costs of $61,500 per month sells three products with the following characteristics: Sales Mix Contribution Product Percentage Margin P 25% $48 Q 50% 50 R 25% 52 How many total units must be sold to breakeven? First Compute the Weighted-Average Contribution Margin per Unit = ($48 x .25) + ($50 x .50) + ($52 x .25) = $12 + $25 + $13 = $50 This figure will be used to compute the break-even in total units.
Breakeven in Total Units = Total Fixed Costs Weighted-Avg Contribution Margin per Unit $61,500 50
= 1,230 units in total
Example 3. The Pierson Co. has the following unit and mix data: Do Dah Unit sales price $5.00 $4.00 Unit contribution margin 0.75 1.20 Sales mix ($) 80% 20% Fixed costs Target profit How many units of Dah must be sold at the breakeven point? = $ 99,000 ($0.75 x .80) + ($1.20 x .20) = $99,000 $0.84 = 117,857.143 -> 117, 858 Total units at breakeven (round up).