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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.

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

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

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

Gross margin

- Cost of goods sold Direct materials
- Direct labor
- Applied overhead
- Applied overhead units produced x

predetermined O/H - Gross Margin Revenue - COGS.

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.

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.

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

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

Breakeven revenue

Breakeven units (BEunits) SP, or SP BEunits

SP(FC/CM) Breakeven revenue FC/(CM/SP)

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

Profit-Volume Graph

I (P - V)X - F

Profit

Slope P - V

Units

Loss

Break-Even Point In Units

- F

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 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.

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

- 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

(No Transcript)

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

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

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.

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.

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.

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

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

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