Cost-Volume-Profit (CVP) Analysis
The Cost-Volume-Profit model examines the relationship between firm cost structure (i.e.,
relative proportion of fixed and variable costs) and sales volume and the effects of this
relationship on the profitability of a firm. The model can be used by managers for the purposes of
planningand decision making.
This basic model combines four important variables — volume of sales, costs, revenue, and
profits. The basic model can be extended to assess the impact of price, cost, and volume changes,
along with changes in product mix and income taxes.
Following are some applications of CVP analysis.
▯ What are the total sales (either in units or dollars) that the company needs to generate in
order to break-even or to attain a desired level of profit?
▯ What effects will changes in operating activities (such as changes in selling price or
operating costs) have on the company’s profit? For example:
o What effect will an increase in fixed costs such as rent or advertising will have
on our BEP and our profits?
o What effect will increase or decrease in sale price have on the company’s profit?
o Should the company buy or lease a new machine?
o What effect will adopting a new technology that leads to increase in fixed costs by
a certain percentage but at the same time leads a reduction of variable costs by a
certain percentage will have on BEP or the company’s profit?
▯ Should we produce more of product A and less of product B or vice versa?
Single Product Case Multiple Products Case
▯ Mathematical Solution
Mathematical Solution Graphical Solution
▯ Effect of Income Tax
▯ Sensitivity Analysis
▯ Operating Leverage
▯ Margin of Safety
It is important to note that the CVP analysis is performed at the firm wide level. The Basics of CVP Analysis
The Basic Assumptions of CVP Model:
The CVP model is simplified by the following assumptions:
1. Both the revenue function and the cost function are linear.
2. The selling prices, total fixed costs, and unit variable costs are known with certainty in
advance and will remain unchanged during the period.
3. The number of units produced equals the number of units sold. This suggests that there
no changes in the level of inventory during the period.
4. The productivity of workers is constant.
5. For multiple-product analysis, the sales mix is assumed to be known in advance and
remains constant during the period.
The Concept of Contribution Margin (CM):
▯ Contribution margin is the amount remaining from sales revenue after variable expenses
have been deducted. This amount contributes towards covering fixed costs and then
towards making profit.
▯ Contribution margin is the net summary of the changes in that operating income. As the
quantity of units sold increases, both total variable costs and total revenues increase at the
same rate. If revenues increase due to volume increases, the contribution margin increases.
▯ Understanding contribution margin enables the manager to quickly note that an increase
in selling price without a corresponding change in variable cost will increase the
“contribution” to cover fixed cost and make income. Or a decrease in variable cost
without a corresponding decrease in selling price will “contribute” more to income and/or
the coverage of fixed costs.
▯ Using revenues and variable costs as per unit measures, the “contribution” per unit of
product sold can provide a shortcut to breakeven calculations or “what-if” questions.
Each unit of product sold contributes that amount as it “walks out the door.”
How to Calculation of Contribution margin:
There several ways to calculate and express the CM
a. Unit CM = Unit SP – Unit VC
b. Total CM = Total Sales Revenues – Total Variable costs
c. Total CM = Unit CM x Q
d. CM% = Total CM/ Total Sales Revenues
e. CM% = Unit CM/Unit SP
f. CM% + VC% = 100% I. S INGLE PRODUCT CASE
A. M ATHEMATICAL S OLUTION
X (units) = the number of units that should be produced and sold to achieve the desired level of profit
X ($) = the total sales revenues that should be generated to achieve the desired level of profit
NI = the desired (target) level of profit
SP = selling price per unit
VC = variable cost per unit
TR = total revenues
TVC = total Variable Costs =
FC = total fixed costs
NI = TR – TVC – FC
= X(SP) – X(VC) – FC
NI = X(SP-VC) – FC
X (SP-VC) = FC +NI
X (units) = FC + NI = FC + NI
Unit sales to attain target profits =expenses + Target profi(1)
Unit contributi on margin
Similarly, the basic equation can also be expressed in terms of sales dollars using the variable expense
ratio to drive the formula for the dollar Sales needed to achieve target income as follows:
Net Income = Sales - (Variable expense ratio ▯ Sales) - Fixed expenses
(1 ▯ Variable expense ratio) ▯ Sales = Fixed expenses + Net Income
Contribution margin ratio* ▯ Sales = Fixed expenses + Net Income
Sales =FC + NI
* 1 ▯ Variable expense ratio = 1▯ Sales
= Sales - Variableexpenses
Contributi on margin
= = CM%
Sales $ to achieve target profits = (2)
CM% Example 1:
The following information is extracted from ABC Co.
Sales price per unit $ 36.00
Per unit variable costs
Production costs 18.60
Sales commissions 5.40
Total per unit variable costs $ 24.00
Total fixed costs per period
Advertising $ 24,000
Total fixed costs $180,000
1. How many units to break even?
2. How many units to achieve net income of $200,000?
3. Repeat 1 and 2 above for the amounts rather than number of units.
Steve Bendo owns car service station in Hamilton. Steve is considering leasing a machine that will allow
him to offer customers the mandatory Ontario emissions test. Every car in Ontario must be tested every
two years. The machine costs $6,000 per month to lease. The variable cost per test (i.e., per car inspected)
is $10. The amount that Steve can charge each customer is set by the Province law, and is currently $40.
1. How many inspections would Steve have to perform monthly to break even from this part of his
2. How many inspections would Steve have to perform monthly to generate a profit of $3,000 from
this part of his business? Example 3:
Alice Waters (age 9) runs a lemonade stand in the summer in Dundas, Ontario. Her daily fixed costs are
$20. Her variable costs are $2 per glass of ice-cold, refreshing, lemonade. Alice sells an average of 100
glasses per day.
1. What price would Alice have to charge per glass, in order to break-even per day?
2. What price would Alice have to charge per glass, in order to generate profit of $20 per day?
3. Refer to the information about Alice, but now assume that Alice wants to charge $3 per glass of
lemonade, and at this price, Alice can sell 110 glasses of lemonade daily. What would the variable
cost per glass have to be, in order to generate profits of $200 per day?
Sunshine Co. sells a single product. The company's most recent income statement is given below.
Sales (4,000 units) $120,000
Less variable expenses (68,000)
Contribution margin 52,000
Less fixed expenses (40,000)
Net income $ 12,000
a. Contribution margin per unit is $ _______ per unit
b. If sales are doubled to $240,000,
total variable costs will equal $ _______________
c. If sales are doubled to $240,000,
total fixed costs will equal $ _______________
d. If Sunshine is past the breakeven point and
10 more units are sold, profits will increase by $ _______________
e. Compute how many units must be sold to break even. # ______________
f. Compute how many units must be sold
to achieve a profit of $20,000. # _______________
1.. Nantucket Company has the following cost-volume-profit (CVP) relationships: Breakeven point in units sold 2,000
Sales price per unit $ 625
Total fixed costs $125,000
What is the variable cost per unit?
2. AAA Company produced a product which had a selling price of $20 and a variable cost which
amounted to 60% of sales. Given a fixed cost of $60,000, the breakeven sales will be
a. 5,000 units
b. 5,500 units
c. 6,000 units
d. 7,000 units
e. 7,500 units
3. AAA Company produced a product which had a selling price of $20 and a variable cost which
amounted to 40% of sales. The company wants a profit before tax of $15,000. The tax rate is 20%
and fixed costs amount to $60,000. AAA must sell
a. 6,250 units
b. 7,396 units
c. 9,375 units
d. 9,844 units
e. None of the above
4. AAA currently has a profit of $15,000 at a sales volume of 9375 units and a fixed cost which amounts
to $65,625 and a selling price of $20 per unit. Variable cost per unit should be
e. None of the above
Q 1 2 3 4
A b e a c THE EFFECT OF INCME TAX
▯ Organizations making profit must pay income taxes. A business only gets to keep income after
taxes (net income). Thus, the CVP analysis is more informative if it shows what it will take to
generate a target amount of net income.
▯ In order to calculate the sales volume needed to achieve a specified amount of net income, a tax
rate as a percentage of operating income is assumed. Target profit must be adjusted by
incorporating income tax.
▯ Mathematically, the amount of net income can be expressed as a percentage of operating income.
Therefore, the target after-tax profit must be converted to its before-tax equivalent using
the following formula:
Target after - tax profit
Target before - tax profit ▯
1 - Tax rate
X (units) = Fixedcost ▯[(After tax profit)/(1– Tax rate)] (1')
▯ Note that the BEP unaffected by income taxes because no tax is no operating income
Use the following data to answer the next two questions:
Kelvin Co. produces and sells socks. Variable costs are $4 per pair, and fixed costs for the year total $90,000. The
selling price is $6 per pair.
1. The sales units required to make an after-tax profit of $15,000, given an income tax rate of forty percent, are
calculated to be:
A) 56,000 units.
B) 56,500 units.
C) 57,000 units.
D) 60,000 units.
E) 57,500 units.
2. The sales dollars required to make an after-tax profit of $15,000, given an income tax rate of forty percent,
are calculated to be:
Q 1 2
A e e Sensitivity analysis
▯ Sensitivity analysis: “what-if” technique managers use to examine how a result will change if
original predicted data not achieved or if an underlying assumption changes
▯ Uncertainty: possibility that an actual amount will deviate from an expected amount
▯ Used before committing costs: Perform analysis of changes in operating income for changes
Selling price per unit $500
Variable cost per unit $300
Total monthly fixed cost $200,000
Units sold per month 1,600
1. How many units do we need to sell to break even?
2. What effect will a 10% discount on sales price have on BEP in units?
3. New equipment will increase FC by 30%, but decrease VC per unit by 30%. What effect will it
have on BEP in units?
4. Purchase of higher quality raw materials will increase VC by $25 per unit, but decrease FC by
$17,500. How many units do we need to sell to maintain operating income of $120,000?
1. AAA currently has a profit of $15,000 at a sales volume of 6250 and a variable cost of $8 and a
selling price of $20. If variable costs increase to $9, by how much can the fixed costs change to still
maintain the same profit?
a. $6,000 decrease
b. $6,250 decrease
c. $6,000 increase
d. $6,250 increase
2. AAA Company produced a product which had a selling price of $20 and a variable cost which
amounted to 60% of sales. The company wants a profit after tax of $15,000. The tax rate is 20% and
fixed costs amount to $60,000. AAA must sell
3. The Beta Mu Omega Chi (BMOC) fraternity is looking to contract with a local band to perform at its
annual mixer. If BMOC expects to sell 250 tickets to the mixer at $10 each, which of the following
arrangements with the band will be in the best interest of the fraternity?
a. $2500 fixed fee
b. $1000 fixed fee plus $5 per person attending
c. $10 per person attending
d. $25 per couple attending
Q 1 2 3
A b d b CVP RELATIONSHIPS IN GRAPHIC FORM.
▯ Graphs of CVP relationships can be used to gain insight into the behavior of expenses and profits.
The basic CVP graph is drawn with dollars on the vertical axis and volume in units on the horizontal
axis. Total fixed expense is drawn first, then variable expense is added to the fixed expense in order
to draw the total expense line. Finally, the total revenue line is drawn. The total profit (or loss) is the
vertical difference between the total revenue and total expense lines.
▯ The cost-volume-profit graph depicts the relationships among cost, volume, and profits.
▯ The point where the total revenue line and the total cost line intersec