contemporary engineering economics, 4 th edition, © 2007 cost-volume-profit analysis lecture no. 30...

Contemporary Engineering

Economics, 4th edition, © 2007

Cost-Volume-Profit Analysis

Lecture No. 30Chapter 8Contemporary Engineering EconomicsCopyright © 2006



Illustration of Full Cost Concept

+ + +

+

DirectMaterialCost

=

Direct LaborCost

Prime Cost

OverheadCost

=

SellingCost

General andAdministrative Cost

FullProductionCost (or InventoryCost) Full

Cost



Break-Even Chart(Fixed Manufacturing Overhead)- (Depreciation)

Fixed Selling and Administrative Expense

Variable Selling and Administrative Expense

Variable Mfg., Overhead Direct Labor$600

500

400

300

200

100

10 18 20 30 40 50 60

Point of Desired Profit

Total Cost LineCash Cost Line

Direct Material

DesiredProfit

(Fixed Manufacturing Overhead)- (Depreciation)

DEPRECIATION

Fixed Selling and Admins Expense

Variable Selling and Admins Expense

Variable Mfg., Overhead

Direct Labor

Units of Product (in thousands)

Dol

lars

(in

th

ousa

nds)



Cost Data for Break-Even Chart

Unit Variable Costs

Direct Materials $2.00

Direct Labor 1.00

Variable Manufacturing Overhead 1.00

Variable Selling and Administrative Expenses

1.00

Total Unit Variable Cost $5.00

Fixed manufacturing overhead (including Depreciation of $10,000) = $70,000Fixed Selling and Administrative Expenses = $30,000Selling Price/Unit = $10Desired Profit before Taxes = $100,000



Def: Difference between the unit sales price and the unit variable cost

MC = Sales price – Variable cost

Application: Break-even volume analysis:

Break - even volume =Fixed costs

MC

Unit Marginal Contribution



Break-Even Analysis FormulasP F

R V

Q N

F NV NQ

NF

Q V

NQFQ

Q V

RFVQ

Q V

V

Q

q

Profit = Fixed costs

= Revenue = Variable cost per unit

= Price per unit = Number of units of volume

Cost = Revenue

at break - even point

Marginal contribution per unit ($)

1- Marginal contribution rate (MCR, %)

1



Sales at break - even point for total cost:

Fixed costs

Marginal Contribution Rate

Sales at break - even point for cash costs:

Fixed cost - Depreciation

MCR

Sales required for desired pre - tax profit level:

Fixed costs + Desired Profit

MCR

F

MCR

Useful Break-even Sales Formulas



Profit-Volume Graph

PROFITS($000’s)

LOSSES($000’s)

10 20 30 40 50 60

$100

0

$100

$200

$100 $200 $300 $400 $500 $600

Point of Desired Profit

Profit Line

Slope of profit line is the marginal contribution

$200

UNITS OF PRODUCT (000’s)

SAME COST DATA AS USED FOR BREAK-EVEN CHART

Fixed cost



Effect of Variable Costs on Sales Company 1 Company 2 Company 3

Number of Units Sold 70,000 70,000 70,000

Unit Selling Price $10.00 $10.00 $10.00

Unit Variable Cost 7.00 6.50 8.00

Unit Marginal Contribution 3.00 3.50 2.00

% Marginal Contribution 30% 35% 20%

Total Marginal Contribution $210,000 $245,000 $140,000

Fixed Costs 150,000 150,000 150,000

Net Profit (loss) before taxes $60,000 $95,000 ($10,000)

The Profit/Volume Graph shows profits (losses) at different operatinglevels for the three companies.



$200

$100

0

$100

$200

20 40 60 80 100

35% MCR 30% MCR

20% MCR

2

3

1

Units of Product Sold(000’s)

•An increase in the selling price with variable costs fixed has the same analysis

Break-even Chart



Effect of Fixed Costs

Selling price per unit = $6.00Variable cost per unit = $3.00 Unit marginal Contribution = $3.00Current fixed costs = $600,000Desired profit level = $150,000Required sales units = (600,000 + 150,000)/3 = 250,000 unit

Fixed costs increase = $60,000 (ex. addtl. advertising expenditure)Reqd. Sales units to maintain profits = 810,000/3 = 270,000 units



400

200

0

200

600660

100,000 200,000

Increase in sales unitsrequired to maintain the same level of profit

Effects of Fixed CostsP

rofi

t an

d L

oss



Present Operation

Variable Cost Increase

Selling Price Decrease

Unit Selling Price

$10.00 $10.00 $9.00

Unit variable Cost

$7.50 $8.25 $7.50

Unit marginal contribution

$2.50 (25%) $1.75 (17.5%) $1.50 (16.6%)

Fixed Costs $150,000 $150,000 $150,000

Price Reduction and Increase in Variable Costs



Price Reductions and Increase in Variable Cost

10% reduction in sales price

0

150

60 86.7 100

PRESENT

10% increasein variable costProfits

(000’s)

Losses(000’s)



Option 1: Adding overtime or Saturday operations: 36Q

Option 2: Second-shift operation: $13,000 + 31.50Q

Break-even volume:

36Q = $13,000 + 31.50Q

Q = 3,000 units

Example 8.4 Break-Even Analysis



Example 8.7 Profit-Maximization Problem

30 for 0 1,000Total revenue function:

30,000 10( 1,000) for 1,000 7,000

5,000 7 for 0 6,000Total cost function:

47,000 12( 6,000) for 6,000 7,000

Q Q

Q Q

Q Q

Q Q

23 5,000 for 0 1,000

Net profit function: 3 15,000 for 1,000 6,000

25,000-2Q for 6,000 7,000

Q Q

Q Q

Q



Net Profit Calculation as a Function of Production Volume



Weekly Profits as a Function of Time

contemporary engineering economics, 4 th edition, © 2007 cost-volume-profit analysis lecture no. 30...

Documents

administrative cost

total unit variable

unit variable cost mc

cost data

th edition

production cost

cost general

inventory cost