Cost-Volume-Profit Analysis: Key Concepts and Calculations

Posted on Jan 4, 2025 in Mathematics

Cost-Volume-Profit Analysis

Cost-volume-profit (CVP) analysis is used to determine how changes in costs and volume affect operating income and net income.

Assumptions of CVP Analysis

  • Sales price per unit is constant.
  • Variable costs per unit are constant.
  • Total fixed costs are constant.
  • Everything produced is sold.
  • Costs are only affected because activity changes.
  • If a company sells more than one product, they are sold in the same mix.
  • CVP analysis requires costs (manufacturing, selling, and admin) be identified as variable or fixed.

Contribution Margin and Ratio

Contribution margin represents the amount of income or profit the company made before deducting its fixed costs. (the amount of sales dollars available to cover fixed costs)

  • CM: Sales revenue minus all variable costs (calculated using dollars or on a per unit basis).
  • CM $: Example: Sales of $750,000 and total VC of $450,000 = CM is $300,000.
  • CM / Unit: Example: Units sold 250,000 during the year & the per unit sales price is $3 & total VC per unit is $1.80. CM / unit is $1.20.
  • CM Ratio: The percent of sales dollars available to cover fixed costs. Once fixed costs are covered, the next dollar of sales results in the company having income. Calculated using either CM $ or CM / unit. Calculated contribution margin is divided by the sales or revenues amount. Example: 40%.

Income Statements

Contribution Margin Income Statement (Internal Use)

  • Organized by cost behavior.
  • Variable expenses are above the CM line.
  • Variable product costs are used when calculating variable COGS.
  • All fixed costs (including fixed MOH) are expensed below the CM line.
  • Step 1: Separate fixed costs and variable costs (Sales less Variable Expenses).
  • Step 2: Equals CM less Fixed Expenses.
  • Step 3: Fixed MOH & Fixed Operating Expenses.
  • Step 4: Equals Operating Income.

Traditional Income Statement

  • Based on Absorption & Contribution Margin I/S used VC.
  • Both statements produce the same operating income.
  • Manufacturer – equality only occurs when all units produced are sold in the same period (no change in inventory).
  • Service & Merchandising – Operating Income will ALWAYS be the same (no MOH V & absorption costs do not apply).
  • Service Companies have no COGS so ALL costs are Operating Expenses either VC or FC (if MC do it first and estimate the VC & FC portions using regression).
  • Merchandising Companies – have COGS but all inventory purchased is COGS so they are considered VC.

CM = Sales Revenue – Variable Expenses (tells how much profit has been made BEFORE considering FC)

The $1.80 / unit or $450,000 of VC (represent all VC including costs classified as manufacturing costs, selling expenses, and administrative expenses).

Similarly, the FC (represent total manufacturing, selling, and administrative fixed costs).

Break-Even Point

Break-even point is the level of sales where net income = zero (where sales revenue = TVC + TFC & CM = fixed costs).

  • BE $: Break‐even point in dollars. BE $ of $750,000 calculated by FC / CM Ratio (FC $300,000 / CM ratio of 40%).
  • BE $ Equation: VC stated as a % of Sales (VC / Sales $ per unit) VC % of sales $1.80 / $3.00 = 60%.
  • BE Equation: Using FC of $300,000 the BE equation shown below. The break‐even point in units may also be calculated using the mathematical equation where “X” equals break‐even units.
  • BE Units: Break‐even point in units. The break‐even point in units of 250,000 is calculated by dividing fixed costs of $300,000 by contribution margin per unit of $1.20.
  • *Again calculation using the mathematical equation is the same as the first calculation of BE units that used the CM / unit. *
  • Once the BE point in units has been calculated, the BE point in sales dollars is calculated by multiplying the number of break‐even units by the selling price per unit.
  • This also works in reverse. If the break‐even point in sales dollars is known, it can be divided by the selling price per unit to determine the break‐even point in units.

Shortcut Approaches

  • BE using Unit CM: To find BE in Units (FC/CM per Unit).
  • BE using CM Ratio: To Find BE in Revenue (FC/CM Ratio).
  • **Since BE occurs when Operating Income is zero.
  • *FC changes BE point but not CM per Unit.

CVP Analysis Components

Cost-Volume-Profit Analysis – Expresses the relationship between costs, volume & profit used to determine BE & find volume needed to earn a target profit (prepare/respond to economic changes).

  • Sales Price: Sales Price will remain constant throughout relevant range.
  • Volume: Manager classifies each cost (or component of MC) as VC or FC (resulting costs are linear).
  • VC: Inventory levels will not change.
  • FC: Mix of products offered remains constant.
  • Profit/Loss: Unit CM the CM I/S dividing line all VC above & FC below.
  • All VC must be included whether Product or Period Costs.

Key Formulas

  • CM/Unit: Sales $ – VC. CM is the excess of Sales Revenue OVER Variable Expenses (tells how much revenue is left after paying VC to contribute toward FC & Operating Income).
  • Shortcut CM: CM (# of Units x CM/Unit). CM is stated as a Total Amount on the CM I/S.
  • Operating Income: CM less FC. Can be expressed as CM/Unit or Unit CM (is the excess of selling price over VC/unit).
  • **Whether operating at profit or loss every time another unit is sold the company will improve by the amount of the Unit CM.
  • CM Ratio (using CM/unit): CM per Unit/Sales $ per Unit =%.
  • CM Ratio (using volume of sales): CM/Sales Revenue = %. *Both CM Ratios give % of each sales $ available for paying FC & generating a profit.
  • ** CM Ratio of 40% means for each $1.00 of Sales Revenue 0.60₵ is VC / 0.40₵ is CM.
  • BE (1) I/S Approach: BE is Total Revenue = Total Expenses. ***CM Ratio is used to forecast operating income within a relevant range, motivate sales staff.
  • BE (2) Using CM / Unit: Sales below BE = LOSS. ****CVP Analysis can be used to determine BE – the sales level at which Operating Income is Zero.
  • BE (3) Using CM Ratio: Sales above BE = Profit.
  • BE / Unit: FC / CM per Unit.
  • BE / Sales Rev: FC / CM Ratio.

Breakeven Approaches

  • Breakeven – Income Statement Approach
  • Breakeven Using Unit CM (shortcut)
  • Breakeven Using CM Ratio (shortcut)

Cost-Volume-Profit Relationships

Calculate CVP

CVP Graph

Graphing CVP Relationships – how level of sales affect profit

  • Step 1: Choose Sales Volume Plot the Point for Total Sale Revenue at that Volume.
  • Step 2: Draw the sales revenue line from the origin 0 through that point.
  • Step 3: Draw FC Line horizontal intersects y-axis.
  • Step 4: Draw Total expense line sum of VC + FC = Total MC.
  • Step 5: ID BE Point.
  • Step 6: Mark Operating Income & Loss.
  • *Right of BE is Profit.
  • Breakeven is TOTAL SALES = TOTAL COST.
  • Profit is the shaded area to the upper right of the BE point.
  • Net Loss is the shaded area to the lower left.
  • Total VC are a diagonal line (the higher the production, the greater the VC).
  • Total FC is the horizontal line (regardless of production – relevant range- FC stay the same).
  • Total Cost = the SUM of TVC & TFC.

Targeted Income

CVP analysis is used to determine what level of sales is necessary to reach a specific level of income.

  • Required Sales Dollars: FC + Target Income / CM per Unit. **There are additional VC incurred every time an additional unit is sold; these costs reduce the extra revenues when calculating income.
  • Required Sales Level: FC + Target Income / CM Ratio. ***A summarized contribution margin income statement can be used to prove these calculations.

Sensitivity Analysis

“What if” technique that asks what results will be if actual prices or costs change or if we change the sales mix.

  • Calculate New CM / Unit.
  • Calculate New BE / Unit.
  • Calculate New Profit Goal.

Changing VC

Sales in Units = Fixed Expense + Operating Income / CM per Unit

  • Based on Unit
  • Based on Price

Choosing a Cost Structure

Margin of Safety (MOS)

Cushion (budgeted Sales – BE Sales) Higher MOS greater cushion

Operating Leverage

text here!