Cost-Volume-Profit Analysis

Identify how changes in volume affect costs.

Variable

Fixed

Mixed

Minutes Talked

To

tal L

on

g D

ista

nce

Tel

eph

on

e B

illTotal variable costs change

when activity changes.

Your total long distancetelephone bill is basedon how many minutes

you talk.

Minutes Talked

Per

Min

ute

Tel

eph

on

e C

har

ge

Variable costs per unit do not changeas activity increases.

The cost per long distance

minute talked is constant.

For example, 10cents per minute.

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.

0 1 2 3 4 5

$24 –

$18 –

$12 –

$6 –

– – ––

Volume(Thousands of passengers)

Tot

al V

aria

ble

C

osts

(th

ousa

nd

s)

Number of Local Calls

Mo

nth

ly B

asic

T

elep

ho

ne

Bill

Total fixed costs remain unchangedwhen activity changes.

Your monthly basic

telephone bill probably

does not change when

you make more local calls.

Contain fixed portion that is incurred even when facility is unused & variable portion that increases with usage.

Example: monthly electric utility charge◦ Fixed service fee◦ Variable charge per kilowatt hour used

Total mixed cost

Variable

Utility Charge

Activity (Kilowatt Hours)

To

tal

Uti

lity

Co

st

Fixed Monthly

Utility Charge

…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.

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 CVP analysis to compute breakeven point.

Expenses can be classified as either variable or fixed.

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

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

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

the period.

Sales- Variable Costs

Contribution Margin- Fixed Costs

Operating Income

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 per unit. They receive a proposal from a company in

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

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)

Sales (20,000 x $85)

$1,700,000Variable costs (20,000 x $70)

(1,400,000)Contribution margin

$300,000

The unique sales level at which a company earns neither a profit nor incurs a loss.

Sales – Variable Costs – Fixed Costs = 0

Let’s look back at Luis and Tom’s manufacturing, assuming that the fixed

cost are $90,000.

Use CVP analysis for profit planning and graph the cost-volume-profit relations

Volume in Units

Co

sts

and

Rev

enu

ein

Do

llar

s Total fixed costs

Plot total fixed costs on the vertical axis.

Total costs

Draw the total cost line with a slopeequal to the unit variable cost.

Volume in Units

Co

sts

and

Rev

enu

ein

Do

llar

s Total fixed costsTotal costs

SalesStarting at the origin, draw the sales line with a slope equal to the unit sales price.

Break-even Point

What operating income is expected when sales are _____ units?

Suppose that our business would be content with operating income of _________________.

How many units must be sold?

Use CVP method to perform sensitivity analysis.

Suppose that the sales price per device is _____ rather than ____

What is the revised breakeven sales in units?

Suppose that variable expenses per device are ____ instead of ____

Other factors remain unchanged.

Suppose that fixed costs increased by $30,000.

What are the new fixed costs? What is the new breakeven point?

Excess of expected sales over breakeven sales.

Atlanta Braves

$-$1,000$2,000$3,000$4,000$5,000$6,000$7,000

- 50 100 150 200 250

(in thousands)

(in

th

ou

sa

nd

s)

Revenues

Total Expense

Fixed expenseBreak even point

Profit

Loss

Break even in units = 1,200,000Break even in $ = 1,200,000 x 24 = $28,800,000

Unit contribution margin is replaced with contribution margin for a composite unit.

A composite unit is composed of specific numbers of each product in proportion to the product sales mix.

Sales mix is the ratio of the volumes of the various products.

The resulting break-even formulafor composite unit sales is:

Break-even pointin composite units

Fixed costsContribution marginper composite unit

=

Windows Doors

Selling Price $200 $500 Variable Cost 125 350 Unit Contribution 75$ 150$ Sales Mix Ratio 4 1

A company sells windows and doors. They sell 4 windows for every door.

Step 1: Compute contribution margin per composite unit.

Windows Doors Selling Price $200 $500 Variable Cost 125 350 Unit Contribution 75$ 150$ Sales Mix Ratio Composite C/M

Break-even pointin composite units

Fixed costsContribution marginper composite unit

=

Step 2: Compute break-even point in composite units.

Break-even pointin composite units

Fixed costsContribution marginper composite unit

=

Break-even pointin composite units

$900,000

$450 per composite unit

=

Step 2: Compute break-even point in composite units.

Break-even pointin composite units

= 2,000 composite units

Sales CompositeProduct Mix Units UnitsWindow 4 × 2,000 = 8,000

Door 1 × 2,000 = 2,000

Step 3: Determine the number of windows and doors that must be sold to break even.

Windows Doors Combined

Selling Price $200 $500 Variable Cost 125.00 350.00 Unit Contribution 75.00$ 150.00$ Sales Volume × 8,000 × 2,000 Total Contribution 600,000$ 300,000$ 900,000$

Fixed Costs 900,000 Income $ 0

Step 4: Verify the results.