lecture 4b cost volume profit edited

8/8/2019 Lecture 4b Cost Volume Profit Edited

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Cost-Volume-Profit Analysis: A SimpleModel for Evaluating Decision Options

A model is always an abstraction. It is a

representation, sometimes mathematical,

of what are believed to be the relationsamong the relevant decision options.



Sample Questions Raised and

Answered by CVP Analysis1. How many units must be sold (or how much sales

revenue must be generated) in order to breakeven?

2. How many units must be sold to earn a before-taxprofit equal to $60,000? A before-tax profit equalto 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 15percent?

4. What is the effect on total profit if advertisingexpenditures increase by $8,000 and salesincrease from 1,600 to 1,750 units?



Sample Questions Raised and Answered

by CVP Analysis (cont¶d)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 expendituresare increased by $8,000, and sales

increased from 1,600 units to 2,300units?

7.What is the effect on total profit if thesales 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 = Contributionmargin/Revenue



Gross margin:

Cost of goods sold = Direct materials

Direct labor

Applied overhead

Applied overhead = units producedx 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 revenueexceeds 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 (T) = Revenues - Costs

Revenue = SP*units sold

SP = selling price

Costs = FC + VC(units manufactured)

FC = fixed costVC = 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 T = 0 = Revenue - Cost

= SP*units sold - FC - VC*units sold

= (SP - VC)*units sold - FC

units sold = FC/(SP - VC)

We will call units sold at T= 0: BEunits



Breakeven revenue

Breakeven units (BEunits

) * SP, or

SP * BEunits = SP*(FC/CM)

Breakeven revenue = FC/(CM/SP)



Cost-Volume-ProfitGraph

RevenueTotal Revenue

Total Cost

Unit soldX

Y

Loss

Profit

X = Break-even point in units

Y = Break-even point in revenue



Profit-Volume Graph

Profit

- F

Loss Break-Even Point

In Units

Units

Slope = P - V

I = (P - V)X - 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.




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.



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 inresponse 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



Profit

Loss

-50

2,000 4,000 6,000 8,000 10,000

0

10

20

30

40

$000(per month)

-10

-20

-30

-40

Fixed expenses = $48,000

Loss area

Profitarea

Break-even point: 8,000 tickets

Volume of tickets sold

in onemonth



Example 1 Cont¶d Suppose practical capacity per month is 12,000

tickets and that the movie theater has operated

at 60% capacity during December. It is nowDecember 30.

Has the theater made money in December?

If they could capture 1,000 customers bylowering the ticket price to $7 for New Year¶s

Eve, should they do it?



Example 2

Data: The Doral Company manufactures andsells pens. Present sales output is5,000,000 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 insales dollars?



Example 2 Cont¶dCompute the new operating income if . . .

1. A $.04 per-unit increase in variablecosts.

2. A 20% decrease in fixed costs, a 20%decrease in selling price, a 10% decrease

in variable costs, and a 40% increase inunits sold.



Example 2 Cont¶d

Compute the new breakeven point in unitsfor

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 Cont¶d

Compute the total dollar sales needed toobtain the

target net income.

How many sales checks are needed to breakeven?

Compute net income if the number of saleschecks

is 150,000



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=======

Multiple-Product Example

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?

lecture 4b cost volume profit edited

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