COST-VOLUME-PROFITRELATIONSHIPS 2323

Cost behavior

CVP Analysis

Break-even analysis

Boston Quack-Tours

$0

$5,000

$10,000

$15,000

$20,000

$25,000

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

Tickets Sold

Tou

r G

uide

Sal

arie

s

Cost Behavior

Costs that vary in direct proportion to the level of

activity.

Total cost - increases with activity

Per-unit cost - remains nearly constant

= $1.21 / ticket

y = 1.21x

R2 = 0.98

Variable Cost

Boston Quack-Tours

$0

$500

$1,000

$1,500

$2,000

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

Tickets Sold

Sup

plie

s

y = 1604

R2 = 0.00Total cost – remains nearly constant

= $1604 / month

Per-unit cost - decreases with increase in activity

(Note: Per-unit fixed cost can be misleading.)

Fixed Cost

Costs that are unrelated to the level of activity.

Boston Quack-Tours

$0

$4,000

$8,000

$12,000

$16,000

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

Tickets Sold

Veh

icle

Mai

nten

ance

y = 0.59x + 3,625

R2 = 0.92

Variable or Fixed Cost?

Some expenses have both fixed and variable components.

An algebraic expression representing a cost as a function of fixed and variable components.

Y = F + VX

Y = total costF = fixed componentV = variable cost per unitX = number of units

Vehicle Maintenance = $3,625 + $0.59 X

Cost Functions

Boston Quack-Tours

$0

$4,000

$8,000

$12,000

$16,000

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

Tickets Sold

Veh

icle

Mai

nten

ance

( 17,700, $13,100 )

( 3,300, $5,620 )

High-Low Method

Boston Quack-Tours

$0

$4,000

$8,000

$12,000

$16,000

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

Tickets Sold

Veh

icle

Mai

nten

ance

( 17,700, $13,100 )

( 3,300, $5,620 )

$7,480

14,400

(1) Find the variable cost (slope).

Variable cost:$7,480

14,400= $0.52/unit

Boston Quack-Tours

$0

$4,000

$8,000

$12,000

$16,000

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

Tickets Sold

Veh

icle

Mai

nten

ance

( 17,700, $13,100 )

( 3,300, $5,620 ) Slope = $0.52Slope = $0.52

(2) Find the fixed cost (y-intercept).

~ $4,000

Fixed cost: $13,100 - $0.52 x 17,700 = $3,896

( 17,700,$13,100 )

Boston Quack-Tours

$0

$4,000

$8,000

$12,000

$16,000

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

Tickets Sold

Veh

icle

Mai

nten

ance

y = 0.59x + 3,625

R2 = 0.92

A more precise way to estimate cost functions.

Use trendline function in Excel.

Takes all points into account.

Least-Squares Regression

Boston Quack-Tours

$0

$2,000

$4,000

$6,000

$8,000

$10,000

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

Tickets Sold

Cas

hier

Sal

arie

s

Don’t use a trendlineto estimate.

$8,450

$4,100

Some expenses are fixed within a certain range.

Relevant Range

Boston Quack-Tours

y = -0.01x + 2494.7

R2 = 0.153

$0

$500

$1,000

$1,500

$2,000

$2,500

$3,000

0 5,000 10,000 15,000

Tickets Sold

Off

ice

Exp

ense

Costs cannot be negative!

Consider this a fixed cost equal to the average

amount.

Plausible Cost Functions

Cost-Volume-Profit Analysis

Volume of

output Sales price Variable costs Fixed costs Product mix

An investigation of the interrelationships among:

Per Unit

$ 350

185

$ 165

Total

Sales $ 42,000

Less Variable Expenses 22,200

Contribution Margin $ 19,800

Less Fixed Expenses 13,860

Net Income $ 5,940

Contribution Income Statement

CM: covers fixed expenses & provides profit

The level of sales at which the contribution margin is just enough

to cover fixed expenses

Total fixed expenses

Per unit contribution margin

= 84 units$13,860

165

Break-even point =

=

Break-Even Point

Per Unit

$ 350

185

$ 165

Total

Sales

Less Variable Expenses

Contribution Margin

Less Fixed Expenses

Net Income

At 84 units…

Total

$ 29,400

15,540

$ 13,860

13,860

$ 0

Per Unit

Sales $ 350

Less Variable Expenses 185

Contribution Margin $ 165

= 47.1%$165$350

CM Ratio =

Contribution Margin Ratio

Total fixed expenses

Contribution margin ratio

= $29,400$13,860

.471

Break-even point =

=

Break-Even Point

In sales dollars

How many units must be soldto earn a net income of $8,000?

x = number of units

Sales - Variable - Fixed = Income

350x - 185x - 13,860 = 8,000

165x = 21,860

x = 133

Target Net Profit