Preview of Chapter 3
Cost-Volume-Profit (CVP) Analysis
Purpose
 To
model how revenues and costs (and
profit!) will behave during a given period
of time, depending upon the level of
activity.
3-1
CVP Model

Assumes a contribution margin income statement:
Contribution Mgn Approach vs Absorption Costing
Sales
- Variable Costs:
100%
- VC%
(Var. CGS, Selling, Admin.)
= Cont. Margin
- Fixed Costs:
= CM%
Sales
- CGS
= Gross Margin
- Period Costs
(Selling, Admin.)
(Mfg., Selling, Admin.)
Operating Income
Operating Income
 Same only if inventories are constant (production = sales).
3-2
Questions
Besides “Where’s the breakeven point,” other questions
are of more interest:
 How will the BEP increase if FC or VC increases?
 How much higher could VC/unit rise before we’d
have a loss for the period?
 How far could sales drop below the forecast before
Operating Income would fall below last year’s?
3-3
Equations For CVP Analysis
Graphs are for exposition only.
We must solve using equations.
 A “definitional” equation, defining income:

Sales – Var Cost – Fixed Cost = Operating Income
–
Good starting point to attack unusual CVP
questions
3-4
Example of Relationships
For a particular item,
Unit Price
$2.50
100%
Unit VC
1.75
70% (VC%)
Unit CM
$ .75
30% (CM%)
3-5
Equations For CVP Analysis
 Recognizing that VC and CM are % of sales:
Sales – (VariableCost%)Sales – FixedCost = Operating Income
Contribution Margin
{OR}
Sales x (CM%) – FC = Operating Income
CM
If FC = $10,000, how many must we sell to BE?
S - .7S – 10,000 = 0
.3S = 10,000
S = $33,333 [÷ $2.50 = 13,333 units]
3-6
Other Handy Equation Forms

Sales Dollars = (FC + Oper. Inc.) / CM%

Units Sold = (FC + Oper. Inc.) / (CM per unit)
3-7
Wide Applicability of CVP

CVP applies to any question about proposed
changes in cost structures and related volume
effects.
» Widely applicable.
» Assigned problems are representative.
3-8
Product-Mix Problem
PRODUCT
A
B
C
Price $10
VC
8
CM $ 2
$15
7
$ 8
CM% 20% 53.33%
$25
10
$15
The Weighted
Average CM%
will depend on
actual mix sold
60%
3-9
Product-Mix Problem
Weighted Average based on previous year’s results
(assumed numbers):
A
B
C
Tot. Wtd Avg
Units Sold 5000 10000 15000 30000
Sales
VC
CM
$50,000 150,000
375,000
575,000 1.000
40,000
70,000
150,000
260,000
.452
10,000
80,000
225,000
315,000
.548
3 - 10
Product-Mix Problem

What’s wrong with the following approach?
Product mix is 5/30 “A”, 10/30 “B” and 15/30 “C”
So 5/30 x .20 + 10/30 x .533 + 15/30 x .60 = .511 ≠ .548

Error: Done in terms of units, but the CM% is
contribution/$, not contribution/unit!
Correct:
(50/575)(.20) + (150/575)(.533) + (375/575)(.60) = .548
3 - 11
Considering Income Tax

Recall the “definitional” equation, defining
income:
Sales – Var Cost – Fixed Cost = Operating Income
(1-r)*(Sales – Var Cost – Fixed Cost) = Income after tax
Sales – Var Cost – Fixed Cost = (Income after tax)/ (1-r)
So, divide desired after-tax income by (1-r) to
get the desired before-tax income and use
the formulas as usual.
3 - 12
Effect of Income Taxes
 Any
amount “after tax” or net of taxes =
(1-r) (The amount before taxes)
[Applies to an expense, revenue, or Operating Income]

$1,000 expense is tax deductible
So at 40% rate:

(1-.4) 1,000 = $600 net expense
$1,000 revenue is taxable
So at 40% rate:
(1-.4) 1,000 = $600 net
3 - 13
Effect of Income Taxes

All numbers in the CVP equations are before tax.
Therefore questions involving “after tax” effects require
you to convert to “before tax” before using the equation.

Ex. How many units sold to earn $900,000 after tax at a 45% tax
rate?
AT amt. = (1-r) BT amt.
900,000 = (1-.45) BT amt.
BT amt. = 900,000/.55 = $1,636,364
Thus, using my Eq. 4: Units = FC + 1,636,364
CM/unit

3 - 14