Cost-Volume-Profit Analysis 
What is CVP Analysis?
  • CVP (Cost-Volume-Profit) Analysis breaks down costs into those that are fixed and those that are variable and then uses this information for rational decision making.
Contribution Margin

1. How does a contribution margin-based income statement organize costs, and why?

  • A contribution margin-based income statement organizes costs as variable and fixed to aid in management decision making.  Knowing how costs behave, management can better budget the profitability of various decisions.  This format also provides a better understanding of how volume changes influences revenues, costs, and profit.
2. What is contribution margin per unit (CMU)?  What does it tell management?
  • The product’s CMU is the difference between its sales price and variable costs.  This is an important concept for managers because it tells them the amount of money each additional sale will contribute to covering fixed costs and providing a profit.  It equals the change in profit resulting from one additional sale.
3. What is a contribution margin ratio?  What does it tell management?
  • CM ratio is the difference between selling price and variable costs per unit (or revenues and total variable costs), expressed as a ratio or percentage of the selling price.   Thus, a 40% contribution margin ratio means 40 cents of every sales dollar is contributed to fixed costs and profits.  Or, each additional dollar of revenue creates 40¢ in extra profit
CVP Assumptions and Limitations
  • accurately break down costs into fixed and variable elements
  • fixed costs will remain fixed during the period affected by the decision being made
  • variable costs vary in a linear fashion with sales
  • works best when limited to a specific situation or department
  • economic and other conditions are assumed to remain relatively stable
  • it is only a guide to decision making

The Profit Equation  ==>  the CVP Equation!

We use the profit equation to derive the CVP equations

  • Profit  =  Revenues  -  Expenses
    • now rewrite revenues as Sales price * volume  (i.e., number of units sold)
  • Profit  =  (SP * Vol)  -  Expenses
    • now rewrite expenses as variable costs plus fixed costs
  • Profit  =  (SP * Vol)  -  (VC + FC)
    • now rewrite VC as VC per unit * volume
  • Profit  =  (SP * Vol)  -  [(VC/unit * Vol) + FC]
    • distribute the minus sign and collect terms
  • Profit  =  Vol*(SP - VC/unit) - FC
    • notice that SP - VC/unit is the same thing as contribution margin per unit
  • Profit  =  Vol*(CM/unit) - FC
    • solving the equation for volume we get
         
  •                       FC + Profit
     Vol(units)  =  -----------------    ==>  this is the CVP formula!
                            CM/unit
CVP Formulas
                     FC + Profit
 Vol(units)  =  --------------
                      $CM/unit
                FC + Profit
 Vol($)  =  --------------
                    CM%
Note:  When  profit = 0  this is a break-even analysis
           We can solve for either break-even volume or break-even revenues

Graphical Representation
Graphical representation of the break even point!
What-If Analysis

1. Describe “what-if” analysis.

  • “What-if” analysis changes a CVP equation variable and seeks its effect on volume, revenues, or profit.  For example, a “what-if” scenario might involve determining the extra profit from spending $10,000 on advertising if it increases sales by 10%.

2. What is the margin of safety?  What does it tell management?

  • The difference between the sales forecast and the break-even point is called the margin of safety, which is usually expressed as a percentage of the sales forecast. This is the percentage decline in sales that can occur before the company reaches its break-even point.


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this page is maintained by Reed Fisher
last updated January 15, 2011