Cost-Volume-Profit Analysis

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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.

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Sample Questions Raised and Answered by CVP
Analysis

• 1. How many units must be sold (or how much sales
  revenue must be generated) in order to break
  even?
• 2. How many units must be sold to earn a
  before-tax profit equal to 60,000? A before-tax
  profit equal to 15 percent of revenues? An
  after-tax profit of 48,750?
• 3. Will total profits increase if the unit price
  is increased by 2 and units sold decrease 15
  percent?
• 4. What is the effect on total profit if
  advertising expenditures increase by 8,000 and
  sales increase from 1,600 to 1,750 units?

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Sample Questions Raised and Answered by CVP
Analysis (contd)

• 5. What is the effect on total profit if the
  selling price is decreased from 400 to 375 per
  unit and sales increase from 1,600 units to 1,900
  units?
• 6. What is the effect on total profit if the
  selling price is decreased from 400 to 375 per
  unit, advertising expenditures are increased by
  8,000, and sales increased from 1,600 units to
  2,300 units?
• 7. What is the effect on total profit if the
  sales mix is changed?

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Vocabulary

• Gross Margin Revenue - Cost of goods sold.All
  costs are manufacturing costs. Some of them are
  fixed costs.
• Contribution margin Revenue - Variable
  costsSome variable costs are manufacturing
  costs, but some may be non-manufacturing costs.
  None are fixed costs.
• Gross margin percent Gross margin/Revenue
• Contribution margin percent Contribution
  margin/Revenue

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Gross margin

• Cost of goods sold Direct materials
• Direct labor
• Applied overhead
• Applied overhead units produced x
  predetermined O/H
• Gross Margin Revenue - COGS.

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Contribution margin

• Variable costs manufacturing variable costs
• non-manufacturing variable costs.
• Gross margin fixed mfg. overhead
  non-manufacturing variable costs Contribution
  margin.
• Contribution margin non-manufacturing variable
  costs - fixed mfg. costs Gross margin.

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Safety margin

• The dollar amount by which sales revenue exceeds
  what is required to break even.
• The number of units by which sales exceed what is
  required to break even.

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The Model

• The fundamental accounting equation
• Profit (?) Revenues - Costs
• Revenue SPunits sold
• SP selling price
• Costs FC VC(units manufactured)
• FC fixed cost
• VC unit variable costs.
• We are assuming that units manufactured equal
  units sold

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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 Revenue - Cost
SPunits sold - FC - VCunits sold
(SP - VC)units sold - FC units sold
FC/(SP - VC) We will call units sold at ?? 0
BEunits
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Breakeven revenue
Breakeven units (BEunits) SP, or SP BEunits
SP(FC/CM) Breakeven revenue FC/(CM/SP)
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Cost-Volume-Profit Graph
Total Revenue
Revenue
Profit
Total Cost
Y
Loss
X
Unit sold
X Break-even point in units Y Break-even
point in revenue
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Profit-Volume Graph
I (P - V)X - F
Profit
Slope P - V
Units
Loss
Break-Even Point In Units
- F
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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.

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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 semi-variable. 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.

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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.

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Example 1 equation approach

• Movie theater 48,000 monthly fixed costs
• 8 ticket price.
• 2 variable cost per ticket.
• Give breakeven units and revenue
• BEunits 48,000/(8 - 2)
• BEunits 8,000 tickets.
• BErevenue 64,000

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Example 1 Contd

• 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 Years Eve, should
  they do it?

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Example 2

• Data The Doral Company manufactures and sells
  pens. Present sales output is 5,000,000 per year
  at a selling price of .50 per unit. Fixed costs
  are 900,000 per year. Variable costs are .30
  per unit.
• What is the current yearly operating income?
• What is the current breakeven point in sales
  dollars?

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Example 2 Contd

• Compute the new operating income if . . .
• 1. A .04 per-unit increase in variable costs.
• 2. A 20 decrease in fixed costs, a 20 decrease
  in selling price, a 10 decrease in variable
  costs, and a 40 increase in units sold.

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Example 2 Contd

• Compute the new breakeven point in units for
• each of the following changes.
• A 10 increase in fixed costs
• A 10 increase in selling price and a 20,000
  increase in fixed costs.

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Example 3
The Rapid Meal has two restaurants that are open
24 hours per day. Fixed costs for the two
restaurants together total 450,000 per year.
Service varies from a cup of coffee to full
meals. The average sales check for each customer
is 8.00. The average cost of food and other
variable costs for each customer is 3.20. The
income tax rate is 30. Target net income is
105,000.
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Example 3 Contd

• Compute the total dollar sales needed to obtain
  the
• target net income.
• How many sales checks are needed to break even?
• Compute net income if the number of sales checks
• is 150,000

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Multiple-Product Example
Assume the following
Regular Deluxe Total Percent Units sold
400 200 600 ----
Sales price per unit
500 750 ---- ---- Sales
200,000 150,000 350,000 100.0 Less Variable
expenses 120,000 60,000 180,000 51.4
Contribution margin 80,000
90,000 170,000 48.6 Less Fixed expenses

130,000 Net income

40,000
1. What is the break even point?
2. How much sales revenue of each product must
be generated to earn a before tax profit 50,000?