22 - 1©2002 prentice hall, inc. business publishing accounting, 5/e horngren/harrison/bamber...

22 - 1©2002 Prentice Hall, Inc. Business Publishing Accounting, 5/E Horngren/Harrison/Bamber

Chapter 22

Cost-Volume-Profit Analysis


Identify differentcost behavior

patterns.

Objective 1


Variable

Fixed

Mixed

Types of Costs


Variable Costs Example

Consider Grand Canyon Railway. Assume that breakfast costs Grand Canyon

Railway $3 per person. If the railroad carries 2,000 passengers, it

will spend $6,000 for breakfast services.


Variable Costs Example

0 1 2 3 4 5

$24 –

$18 –

$12 –

$6 –

– – ––

Volume(Thousands of passengers)

Tot

al V

aria

ble

Cos

ts(t

hous

ands

)


Fixed Costs Example

0 1 2 3 4 5

$400 –

$300 –

$200 –

$100 –

– – ––Volume

(Thousands of passengers)

Tot

al F

ixed

C

osts

(tho

usan

ds)


Mixed Costs Example

A mixed cost is part variable and part fixed. Assume a department of a company has fixed

costs of $50 per month ($600 per year). There are also variable costs of $3 per hour.


Mixed Costs Example

0 125 250 375 500 625

$2,850 –

$2,100 –

$1,350 –

$600 –

– – ––Volume (hours)

Tot

al

Cos

ts VariableCost

FixedCost


Relevant Range...

– is a band of volume in which a specific relationship exists between cost and volume.

Outside the relevant range, the cost either increases or decreases.

A fixed cost is fixed only within a given relevant range and a given time span.


Relevant Range

Fix

ed

Cos

ts

Volume in Units

$160,000 –

$120,000 –

$80,000 –

$40,000

0 5,000 10,000 15,000 20,000 25,000

– – –

Relevant Range


Use a contribution margin

income statement to makebusiness decisions.

Objective 2


Conventional income statementConventional income statement

Contribution margin income statementContribution margin income statement

Two Approaches to Compute Profits


Conventional Income Statement

Sales –Cost of

Goods Sold =

GrossMargin

–OperatingExpenses

=Net

Income

GrossMargin


Contribution Margin

Income Statement

Sales –VariableExpenses =

ContributionMargin

–Fixed

Expenses=

NetIncome

ContributionMargin


Contribution Margin Example

Luis and Tom manufacture a device that allows users to take a closer look at icebergs from a ship.

The usual price for the device is $100. Variable costs are $70. They receive a proposal from a company in

Newfoundland to sell 20,000 units at a price of $85.


Contribution Margin Example

There is sufficient capacity to produce the order.

How do we analyze this situation? $85 – $70 = $15 contribution margin. $15 × 20,000 units = $300,000 (total

increase in contribution margin)


Objective 3

Compute breakeven sales and

perform sensitivity analyses.


0

100

200

300

400

500

600

0 1 2 3 4 5

Units (000)

$ (0

00)


— Sales

— Fixed

— Fixed + Variable


Sx – Vx – F = 0


Accountants use two methods to perform CVP analysis.

Both methods use an equation or formula derived from the contribution margin income statement.


Equation Approach

With the equation approach, breakevensales in units is calculated as follows:

Unit sales price × Units soldUnit sales price × Units sold

Variable unit cost × Units soldVariable unit cost × Units sold

Fixed expenses Fixed expenses Operating incomeOperating income=

–

–


Breakeven Point Example

Assume that fixed expenses amount to $90,000.

How many devices must be sold at the regular price of $100 to break even?

($100 × Units sold) – ($70 × Units sold) – $90,000 = 0

Units sold = $90,000 ÷ $30 = 3,000


Per Unit Percent RatioSales price $100 100 1.00Variable expenses 70 70 .70Contribution margin $ 30 30 .30

Contribution Margin


(Fixed expenses + Operating income)÷ Contribution margin per unit = Units

($90,000 + 0) ÷ $30 = 3,000 Units

Contribution Margin Formula


(Fixed expenses + Operating income)÷ Contribution margin ratio = $ Sales

($90,000 + 0) ÷ .30 = $300,000

Contribution Margin Ratio Formula


Change in Sales Price Example

Suppose that the sales price per device is $106 rather than $100.

What is the revised breakeven sales in units? New contribution margin: $106 – $70 = $36 $90,000 ÷ $36 = 2,500 units


Change in Variable Costs Example

Suppose that variable expenses per device are $75 instead of $70.

Other factors remain unchanged. $90,000 ÷ $25 = 3,600 $90,000 ÷ 0.25 = $360,000


Change in Fixed Costs Example

Suppose that rental costs increased by $30,000. What are the new fixed costs? $90,000 + $30,000 = $120,000 What is the new breakeven point? $120,000 ÷ $30 = 4,000 units $120,000 ÷ 0.30 = $400,000


Compute the sales level needed to

earn a target operating income.

Objective 4


Target Operating Income Example

Suppose that a business would be content with operating income of $45,000.

Assuming $100 per unit selling price, variable expenses of $70 per unit, and fixed expenses of $90,000, how many units must be sold?

($90,000 + $45,000) ÷ $30 = 4,500


Graph a set of cost-volume-profit

relationships.

Objective 5


Various Sales Levels Example

Assume selling price is $35 per unit. Variable expense is $21 per unit. Fixed cost is $7,000. What is the breakeven point? 500 units or $17,500


Cost-Volume-Profit Graph

$0

$5,000

$10,000

$15,000

$20,000

$25,000

$30,000

$35,000

$40,000

0 300 500 1000

Units

Dol

lars

Breakeven sales point500 units or $17,500 Sales revenue lin

e

Total expense line

Fixed expense line



What operating income is expected when sales are 300 units?

$14 × 300 = $4,200

$4,200 – $7,000 = ($2,800)



What operating income is expected when sales are 1,000 units?

$14 × 1,000 = $14,000

$14,000 – $7,000 = $7,000


Compute a margin of safety.

Objective 6


Margin of Safety Example

Margin of safety is the excess of expected sales over breakeven sales.

Assume Luis and Tom’s breakeven point is 3,000 devices.

Suppose they expect to sell 4,000 during the period.

What is the margin of safety?


4,000 – 3,000 = 1,000 units

1,000 × $100 = $100,000

Margin of Safety Example

1,000 × 4,000 = 25%

$100,000 × $400,000 = 25%


Assumptions of CVP Analysis

1 Expenses can be classified as either variable or fixed.

2 CVP relationships are linear over a wide range of production and sales.

3 Sales prices, unit variable cost, and total fixed expenses will not vary within the relevant range.


Assumptions of CVP Analysis

4 Volume is the only cost driver.5 The relevant range of volume is specified.6 Inventory levels will be unchanged.7 The sales mix remains unchanged during

the period.


Use the sales mix in CVP analysis.

Objective 7


Sales Mix Example

Suppose that Luis and Tom plan to sell two types of devices instead of one.

They estimate that sales will be 3,000 regular devices and 1,000 large devices.

This is a 3:1 sales mix. They expect 3/4 of the devices sold to be

regular devices and 1/4 to be large devices.


Regular LargeSales price $100 $154Variable expenses 70 100Contribution margin 30 54Sales mix (units) 3 1

$ 90 $ 54

The total is $144.

Sales Mix Example


Sales Mix Example

Weighted-averagecontribution margin$144 ÷ (3 + 1) = $36

Breakeven sales$90,000 ÷ $36 = 2,500

2,500 × 3/4 = 1,875regular devices

2,500 × 1/4 = 625large devices


Sales Mix Example

1,875 regular × $100 = $187,500 625 large × $154 = 96,250Breakeven $283,750

$90,000 ÷ $144 = 625packages in the mix


Compute income using variable

costing and absorption costing.

Objective 8


Absorption costing assigns allmanufacturing costs to products.

Financial statements prepared underGAAP use absorption costing.

Absorption costing assigns allmanufacturing costs to products.

Financial statements prepared underGAAP use absorption costing.

Variable costing assigns only variable manufacturing costs to products.

Variable costing is for internal use only.

Variable costing assigns only variable manufacturing costs to products.

Variable costing is for internal use only.

Product Costing


Assume the following costs:Direct material unit cost $6.00Direct labor unit cost $3.00Variable manufacturing overhead $2.00Variable marketing $2.50Fixed manufacturing overhead per unit $5.00

What is the product cost/unit?

Product Costing Example


Absorption CostingAbsorption Costing

Direct materials $ 6.00 Direct labor 3.00 Variable manufacturing overhead 2.00 Fixed manufacturing overhead 5.00 Total $16.00



Variable CostingVariable Costing

Direct materials $ 6.00 Direct labor 3.00 Variable manufacturing overhead 2.00 Fixed manufacturing overhead -0- Total $11.00



End of Chapter 22

22 - 1©2002 prentice hall, inc. business publishing accounting, 5/e horngren/harrison/bamber...

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