Agenda:
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A little more vocabulary
C-V-P analysis
Thursday’s class
Group problem solving
Vocabulary
• Gross Margin = Revenue - Cost of goods sold.
• Contribution margin = Revenue - Variable costs
• Gross margin percent = Gross margin/Revenue
• Contribution margin percent = Contribution
margin/Revenue
Safety margin:
• The dollar amount by which sales exceed
what is required to break even.
• The number of units by which sales exceed
what is required to break even.
Cost-Volume-Profit Analysis: A Simple
Model for Evaluating Decision Options
A model is always an abstraction.
It is a representation, sometimes
mathematical, of what are believed
to be the relations among the
relevant decision options.
Simple model:
• The fundamental accounting equation
Profit () = Revenues - Costs
Revenue = SP*units sold
SP = selling price
Costs = FC + VC(units manufactured)
FC = fixed cost
VC = unit variable costs.
Within this model:
We are assuming that units
manufactured = units sold.
What if we want to know how much product
we must sell to break even?
The breakeven point is the point where profit is
zero,
so 
=0
= SP*units sold - FC - VC*units sold
= (SP - VC)*units sold - FC
units sold = FC/(SP - VC)
We will call units sold at = 0: BEunits
Formula for breakeven point
Note: (SP - VC) = unit contribution margin (CM)
units sold at breakeven point = FC/CM
or
BEunits = FC/CM
Breakeven revenue
Breakeven units (BEunits) * SP, or
SP * BEunits = SP*(FC/CM)
Breakeven revenue = FC/(CM/SP)
Assumptions underlying CVP analysis
• In manufacturing firms, the inventory levels at
the beginning and end of the period are the
same. This implies that the number of units
produced during the period equals the number of
units sold.
• The behavior of total revenue is linear (straight
line). This implies that the price of the product
or service will not change as sales volume varies
within the relevant range.
Assumptions underlying CVP analysis
• The behavior of costs is linear (straight line) over the
relevant range. This implies the following more
specific assumptions.
a. Costs can be categorized as fixed, variable, or semivariable. Total fixed costs remain constant as
activity changes, and the unit variable cost remains
unchanged as activity varies.
b. The efficiency and productivity of the production
process and workers remain constant.
Assumptions underlying CVP analysis
• In multi-product organizations, the sales mix
remains constant over the relevant range.
• In multi-product organizations, when we do a
single CVP analysis, we assume the products all
are sold in the same market. Substitutes.
• This means that the product mix does not change
in response to changes in production/sales
volume.
Example 1: equation approach
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Movie theater: $48,000 monthly fixed costs
$8 ticket price.
$2 variable cost per ticket.
Give breakeven units and revenue
Example 1
• Suppose practical capacity per month is 12,000
tickets and that the movie theater has operated
at 60% capacity during December. It is now
December 30.
• Has the theater made money in December?
• If they could capture 1,000 customers by
lowering the ticket price to $7 for New Year’s
Eve, should they do it?
Example 2
Data: Air Safety Systems company manufactures a
component used in aircraft radar systems. The
firm's fixed costs are $4,000,000 per year. The
variable cost of each component is $2,000, and the
components are sold for $3,000 each. The
company sold 5,000 components during the prior
year, and budgets 5,000 in sales for the coming
year. (Ignore taxes)
Example 2
FC = $4,000,000; VC = $2,000; SP = $3,000; sold
prior yr./budgeted this yr. = 5,000 units
1. Compute the breakeven point in units.
2. Compute the breakeven point in dollars.
Example 2
FC = $4,000,000; VC = $2,000; SP = $3,000;
sold prior yr./budgeted this yr. = 5,000 units
What will be the new breakeven point if fixed
costs increase by 10%?
Example 2
FC = $4,000,000; VC = $2,000; SP = $3,000;
sold prior yr./budgeted this yr. = 5,000 units
What was the company's operating income for
the prior year?
Example 2
FC = $4,000,000; VC = $2,000; SP = $3,000; sold
prior yr./budgeted this yr. = 5,000 units
The sales manager believes that a reduction in the
sales price to $2,500 will result in orders for 1,200
more components each year. What will the new
breakeven point be if the price is changed?
Example 2
FC = $4,000,000; VC = $2,000; SP = $3,000; sold
prior yr./budgeted this yr. = 5,000 units
The sales manager believes that a reduction in the
sales price to $2,500 will result in orders for 1,200
more components each year.
Should the price change be made?
Example 2
FC = $4,000,000; VC = $2,000; SP = $3,000;
sold prior yr./budgeted this yr. = 5,000 units
What is the company's current safety margin?
How many units will Air Safety Systems need
to sell if they want to achieve a profit of
$2,500,000?
Example 2
FC = $4,000,000; VC = $2,000; SP = $3,000; sold
prior yr./budgeted this yr. = 5,000 units
Suppose that due to a new labor contract
variable costs increase by 10%. What is the
new breakeven point?
What will operating income be if sales remain
at the same level as last year?
Multiple products
Parry Sound Diskettes:
Economy
Selling price
$10
Less variable costs:
Direct materials
2
Direct labor
2
Mfg. Overhead
1
Selling
2
Contribution margin
$3
Product % of total sales 10%
Standard
$15
Premium
$25
3
4
2
2
$4
5
6
3
2
$9
50%
40%
Weighted average contrib. margin (WACM) = ?
What is expected profit?
Fixed costs:
Manufacturing costs
Advertising
Admin. costs
Total predicted sales
Capacity
$200,000
$100,000
$100,000
80,000 units
100,000 units
Expected Profit = E() = ?
Suppose an advertising budget increase of $100,000 is
expected to increase sales by 20,000. Should the firm
spend $100,000 on additional advertising?
Compute the new expected profit:
= ?
Compare this to profit before the change.
An advertising budget increase of $150,000 is
expected to change the sales mix to (.05, .30, .65).
Should the advertising budget be increased?
New weighted average contribution margin:
?
E() = ?
A 2% selling commission increase is expected to
increase overall demand by 10,000. Should they do it?
Selling commissions are variable costs, so unit contribution
margins will decline.
Change in variable costs:
Economy:
Standard:
Premium:
The new contribution margins are
Economy:
Standard:
Premium:
Should Parry Disketts increase selling
commissions?
New weighted average contribution margin:
?
E() = ?
Example 3: Kaplan Co.
(a) What is Kaplan’s breakeven point?
FC = $900,000
VC = $12 + $5 = $17
CM = $23 - $17 = $6
BEunits = $900,000/$6 = 150,000 units
(b) Unit sales at target income
= ($900,000 + $240,000)/$6
= 190,000 units
Example 3: Kaplan Co.
(a) Last year’s income = 185,000 x $6
- $900,000 = $210,000
= target income
(b) Contribution to date = 30,000 x $6
= $180,000
(c) Target contribution margin = $6.50
Target contribution margin:
Let CM* = target contribution margin
($900,000  $85,000)  ($210,000  $180,000)
CM *
130,000 units = (($900,000-$85,000)
+($210,000-$180,000))/CM*
CM* = $6.50
Prestige
• Using CVP analysis.
• A spreadsheet is a good way to tackle the problem.
• In addition to the financial analysis, you are asked to
consider factors such as mission, marketing, strategy,
and financial flexibility.
Prestige
• I have made a worksheet available to you on the
homepage to help structure your computations.
• Just use it as a guideline for your spreadsheet
analysis.