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ENGINEERING

ECONOMICS

(As per New Syllabus of Leading Universities)

Mrs. Parameshwari, M.Com., M.B.A., Dr. S. Ramachandran, M.E., Ph.D.,

Prof. R. Devaraj, M.E., (Ph.D.,)

Professors

School of Mechanical Engineering

Sathyabama University.

Chennai – 600 119

AIR WALK PUBLICATIONS

(Near All India Radio)

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First Edition: 25.01-2017

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MG6863 ENGINEERING ECONOMICS

UNIT I: INTRODUCTION TO ECONOMICS

Introduction to Economics- Flow in an economy, Law of supply and demand, Concept

of Engineering − Economics − Engineering efficiency, Economic efficiency, Scope of

engineering economics − Element of costs, Marginal cost, Marginal Revenue, Sunk

cost, Opportunity cost, Break-even analysis, P − V ratio, Elementary economic Analysis

− Material selection for product, Design selection for a product, Process planning.

UNIT II: VALUE ENGINEERING

Make or buy decision, Value engineering − Function, aims, Value engineering

procedure. Interest formulae and their applications − Time value of money, Single

payment compound amount factor, Single payment present worth factor, Equal payment

series sinking fund factor, Equal payment series payment Present worth factor − equal

payment series capital recovery factor − Uniform gradient series annual equivalent

factor, Effective interest rate, Examples in all the methods.

UNIT III: CASH FLOW

Methods of comparison of alternatives − Present worth method (Revenue dominated

cash flow diagram), Future worth method (Revenue dominated cash flow diagram, Cost

dominated cash flow diagram), Annual equivalent method (Revenue dominated cash

flow diagram, Cost dominated cash flow diagram), rate of return method, Examples in

all the methods.

UNIT IV: REPLACEMENT AND MAINTENANCE ANALYSIS

Replacement and Maintenance analysis − Types of maintenance, types of replacement

problem, determination of economic life of an asset, Replacement of an asset with a

new asset − capital recovery with return and concept of challenger and defender, Simple

probabilistic model for items which fail completely.

UNIT V: DEPRECIATION

Depreciation − Introduction, Straight line method of depreciation, − Declining balance

method of depreciation − Sum of the years digits method of depreciation, − Sinking

fund method of depreciation/Annuity method of depreciation, service output method of

depreciation − Evaluation of public alternatives − Introduction − Examples − Inflation

adjusted decisions − Procedure to adjust inflation, Examples on comparison of

alternatives and determination of economic life of asset.

CONTENTS

CHAPTER – 1: INTRODUCTION TO ECONOMICS 1.1 – 1.62

1.1. Introduction 1.1

1.2. Definition of economics 1.2

1.2.1. Uses of economics 1.3

1.2.2. Macro economics and micro economics 1.4

1.2.3. Importance of economics 1.4

1.3. Flow in an economy 1.5

1.4. Demand 1.9

1.4.1. Law of demand 1.9

1.4.2. Demand curve 1.10

1.4.3. Characteristics of law of demand 1.11

1.4.4. Elasticity of demand 1.11

1.4.5. Factors influencing demand 1.14

1.5. Supply 1.17

1.5.1. Law of supply 1.18

1.5.2. Supply curve 1.18

1.5.3. Determinants of supply or factors influencing supply 1.19

1.6. Supply – demand equilibrium 1.20

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1.7. Concept of engineering economics 1.21

1.8. Efficiency 1.22

1.8.1. Technical efficiency 1.22

1.8.2. Economic efficiency 1.22

1.8.3. Various ways of improving productivity 1.25

1.9. Scope of engineering economics 1.26

1.10. Elements of cost 1.29

1.10.1. Fixed cost 1.29

1.10.2. Variable cost 1.30

1.10.3. Semi-variable cost or mixed cost 1.32

1.10.4. Selling price of a product 1.32

1.10.5. Other terms 1.33

1.10.6. Break Even Analysis (BEA) 1.39

1.10.7. Profit Volume Ratio (P/V ratio) 1.45

1.11. Elementary economic analysis 1.55

1.11.1. Material selection for a product 1.56

CHAPTER – 2: VALUE ENGINEERING 2.1 – 2.60

2.1. Make (or) buy decision 2.1

2.1.1. Criteria for make or buy decision 2.2

2.2. Techniques / approaches of make or buy decisions 2.3

Contents ii

2.2.1. Simple cost analysis 2.3

2.2.2. Economic analysis 2.4

2.2.3. Break even analysis 2.8

2.3. Value 2.11

2.3.1. Types of value 2.11

2.3.2. Value analysis terms 2.13

2.4. Value analysis 2.14

2.5. Value engineering 2.16

2.5.1. Objectives/aims of value engineering 2.17

2.5.2. Benefits of value engineering 2.17

2.5.3. Functions 2.18

2.5.4. Value analysis and value engineering 2.18

2.5.5. Steps/phases involved in value analysis 2.19

2.5.6. Ten principle (commandments) of value analysis 2.23

2.6. Time value of money 2.24

2.7. Cash flow diagrams 2.25

2.8. Equivalence 2.26

2.8.1. Technique of equivalence 2.26

2.9. Interest formulas and their applications 2.28

2.10. Methods of calculating interest payments 2.32

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2.10.1. Single – payment compound amount 2.32

2.10.2. Single payment present worth amount 2.34

2.10.3. Equal payment series compound amount 2.37

2.10.4. Equal payment series sinking fund 2.39

2.10.5. Equal payment series present worth amount 2.42

2.10.6. Equal payment series capital recovery amount 2.44

2.10.7. Uniform gradient series annual equivalent amount 2.47

2.10.8. Interest factors 2.52

2.11. Effective interest rate 2.52

Solved university problems 2.57

CHAPTER – 3: CASH FLOW 3.1 – 3.58


3.2. Present worth method 3.2

3.3. Revenue – dominated cash flow diagram 3.2

3.4. Cost – dominated cash flow diagram 3.3

3.5. Exercise problems based on present worth method 3.4

3.6. Future worth method 3.16

3.6.1. Revenue dominated cash flow diagram 3.16

3.6.2. Cost-dominated cash flow diagram 3.17

3.7. Exercise problems on future worth method 3.18

Contents iv

3.8. Annual equivalent method 3.30

3.8.1. Revenue dominated cash flow diagram 3.30

3.8.2. Steps in solving revenue – dominated cash flow

diagram 3.31

3.8.3. Cost-dominated cash flow diagram 3.32

3.8.4. Steps in solving cost-dominated cash flow diagram 3.32

3.8.5. Special case 3.33

3.9. Alternate approach 3.33

3.10. Exercise problems on annual equivalent method 3.34

3.11. Rate of return method 3.48

3.11.1. Cash flow diagram on rate of return 3.48

3.12. Exercise problems on rate of return method 3.49

CHAPTER – 4: REPLACEMENT AND

MAINTENANCE ANALYSIS

4.1 – 4.44


4.1.1. Reasons for replacement 4.2

4.1.2. Need for maintenance 4.2

4.1.3. Maintenance costs 4.3

4.2. Types of maintenance 4.4

4.2.1. Breakdown maintenance 4.4

4.2.2. Preventive maintenance 4.5

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4.2.2.1. Scheduled maintenance 4.8

4.2.2.2. Predictive maintenance 4.8

4.3. Types of replacement problems 4.10

4.4. Replacement of items (assets) that deteriorate with time 4.10

4.4.1. Determination of economic life of an asset 4.11

4.4.2. Replacement of existing asset with a new asset 4.12

4.4.2.1. Capital recovery with return 4.12

4.4.2.2. Concept of challenger and defender 4.13

4.5. Simple probabilistic model for items which fail completely 4.35

CHAPTER – 5: DEPRECIATION 5.1 – 5.55


5.1.1. Definition 5.2

5.1.2. Need for providing depreciation 5.2

5.1.3. Causes of depreciation 5.3

5.1.4. Terms used for depreciation 5.4

5.1.5. Methods of calculating depreciation 5.4

5.2. Straight line method or fixed instalment method or original

cost method

5.5

5.3. Written down value method (or) diminishing balance method

(or) reducing balance method (or) declining balance method

5.9

5.4. Sum Of Year’s Digits Depreciation (SOYD) 5.14

5.5. Depreciation fund method (or) sinking fund method (or)

annuity method

5.20

Contents vi

5.6. Insurance policy method 5.26

5.7. Service output method of depreciation 5.26

5.8. Evaluation of public alternatives 5.27

5.9. Inflation 5.36

5.9.1. Three levels of inflation 5.37

5.9.2. Effects of inflation 5.39

5.9.3. Causes of inflation 5.39

5.9.4. Control of inflation 5.40

5.9.5. Different types of inflation 5.43

5.9.6. Deflation 5.44

5.10. Inflation adjusted decisions 5.46

5.11. Inflated adjusted economic life of machine 5.49

Short Questions and Answers S.Q.A. 1 – S.Q.A. 26

Appendix — Interest Tables A.1 – A.40

Index I.1 – I.2

vii Engineering Economics – www.airwalkpublications.com

CHAPTER – 1

INTRODUCTION

TO ECONOMICS

Introduction to Economics- Flow in an economy, Law of supply and demand,

Concept of Engineering − Economics − Engineering efficiency, Economic

efficiency, Scope of engineering economics − Element of costs, Marginal

cost, Marginal Revenue, Sunk cost, Opportunity cost, Break-even analysis,

P − V ratio, Elementary economic Analysis − Material selection for product,

Design selection for a product, Process planning.

1.1. INTRODUCTION

Economics is the science, which studies human behaviour when he is

struggling to satisfy his needs by using available sources. Economic problem

arises when there is a scarcity of sources. Then the people try to use the

alternative sources to satisfy their needs. Normally, the income of a person is

limited but his desire is unlimited. He earns Rs. 20,000/- per month, but he

wants to buy a car of cost Rs. 4,00,000/-. In this situation, he has to adopt

some criterion to fulfill his desire from his limited income. He can utilize an

attractive car loan scheme or he can borrow money from somebody.

Similarly, for an Engineer (Engineering Economist) who wants to be an

Entrepreneur, the resources like land, raw materials, labour, capital etc., are

scarce. To overcome this difficulty, he has to take decision about production,

marketing and distribution. The following are the important issues on which

the engineer (engineering economist) has to take decisions.

1. What commodities should be produced?

2. What is the quantity of production or output level?

3. What is the technology to be adopted?

4. Where should the goods be produced?

5. What should be the size of the factory?

6. What price should he charge?

7. What wages he should pay?

8. How much should he allot for advertisement?

9. How much should he borrow from the bank?

10. What is his own investment?

1.2. DEFINITION OF ECONOMICS

1. Economics is the study of activities involved in the production and

exchange of goods.

2. Economics analyses the trends in prices, output and unemployment.

3. Economics studies how people choose to use scarce or limited

productive resources like land, labour, equipment and technical

knowledge to produce various goods and to distribute these goods to

various members of the society for their consumption.

4. Economics is the study of money, banking, capital and wealth.

5. Economics helps to know why nations export some goods and import

others and analyses the effects of putting economic barriers at national

level.

1.2 Engineering Economics – www.airwalkpublications.com

By seeing all different types of definitions, we can conclude as follows.

Economics is the study of how people use scarce resources to produce

valuable commodities and distribute them among different groups.

1.2.1. Uses of Economics

1. Economics’ knowledge serves us in managing our personal lives.

2. It makes us understand the society.

3. It gives the design of better economic policies.

4. Learning about the stock market and interest rates may help people

manage their own finances better.

5. Knowledge about price theory and antitrust policy may improve the

skill of lawyer.

6. Awareness of determinants of cost and revenue will make the

managers take better business decisions.

7. The engineer, doctor, investor and farmer should understand about

accounting and regulations to make the highest profit from their

business.

8. Some study economics because they hope to make money.

9. Some study economics because of the fact that they will be illiterate

if they cannot understand the laws of supply and demand.

10. Some study economics to learn how budget deficits and inflation will

affect their future. Some study economics to pass in examination.

11. As a voter, one should know what are budget deficit, taxes and foreign

trade.

12. As a head of a family, one should know economics to decide how

much to spend and how much to save.

Introduction to Economics 1.3

13. Economics is used to solve business problems and household

problems.

14. It helps us understand the causes of poverty.

15. It is used to understand the essential national issues.

1.2.2. Macro economics and Micro Economics

Macroeconomics studies the functioning of the economy as a whole. It

analyses the following:

1. Determination of national income and output.

2. Overall inflation.

3. Unemployment rates.

4. Total money supply.

5. Investigating why some nations flourish while others stagnate.

Microeconomics analyses the behaviour of individual components like

industries, firms and households. It analyses the following.

1. How individual prices are set?

2. Behaviour of labour union.

3. Taxes on people, work and its effects.

4. Savings.

5. Investigating why some people are fabulously rich while others are

begging on streets.

1.2.3. Importance of Economics

1. If you want to buy a car, you should know which car would give

more kilometers per litre of fuel. People buy a small car as it is

economical. When you want to buy a motorbike, you will go for Hero

Honda since it is giving 90 km/litre of petrol. Even though Yamaha


engine is very good, middle class people buy only Hero Honda for

economical mileage.

2. When you search a house for rent, you will not select the house in

the main bazaar. Because, you have to give more rent for a house

located in main business area. So you should know the economical

condition of the street in which you find house for rent.

3. When you go for foreign countries, you will not go to Africa or

Malaysia or Pakistan or Srilanka. Because our country is economically

better than the above countries. You would normally go to the U.S

or Dubai for earning money. People go to these countries to earn

more and become economically sound. Therefore, it is essential to

know the economical conditions of the country.

4. When you are giving loan to someone, you should know the

economical condition of the person to whom you give loan. If you

give loan to everyone randomly, one day, you will come to a position

to ask loan from others. Bank gives loan to customers by knowing

their economical conditions, to whether they have the capability to

repay or not.

5. Person earning Rs. 30,000/- per month, will be given Bank loan of

Rs. 9,00,000/- (i.e. 30 times of his salary) for constructing house. In

this case, the person will repay (principal + interest) Rs. 10,000/- per

month towards house loan and remaining Rs. 20,000/- will be used

for monthly expenditure including food and clothes. For Bank and

other similar Govt. Sectors, knowing the economical conditions of the

customers is very much important.

1.3. FLOW IN AN ECONOMY

Income in an economy flows from one part to another whenever a

transaction takes place. New spending generates new income, which generates

further new spending, and further new income, and so on. Spending and


income continue to circulate around the macro economy in what is referred

to as the circular flow of income. The circular flow of income forms the

basis for all models of the macro-economy, and understanding the circular

flow process is key to explaining how national income, output and expenditure

is created over time.

The circular flow of income model illustrates the interdependencies of

different factors in the economy. In the basic version (Refer Fig. 1.1), the

economy is modeled as consisting only of households and firms. Money flows

to workers in the form of wages, and money flows back to firms in exchange

for products.

Fig. 1.1: Basic Model of Circular Flow of Income.

Households provide factors of production, such as labour to firms. (Four

factors of production are land, labour, capital and human enterprise). Firms

use these factors to produce goods and services which they sell to the

households. The households then spend money on the goods and services

produced by firms. This money is then used by firms to pay the households

for their work, through wages. This process repeats itself and forms the circular

flow of income.


From the Fig. 1.2 we can see that the expenditure on goods and services

is equal to the income received by households. Therefore in an economy

National income = National expenditure

However, not all income generated will be spent on domestically

produced goods. Some of the income is saved, used to pay taxes or spent on

imported goods and services. Therefore savings, taxation and imports are

leakages in the circular flow of income.

Likewise, sometimes there is extra spending in the economy from

investment, government expenditure and spending on exports which will be

added to the circular flow of income. These are called injections. This is

illustrated in the Fig. 1.2.

Fig. 1.2: Full Circular Flow of Income.

The actual money flows through the economy are far more complicated.

Economists have expanded on the ideas of the circular flow of income model

to better depict the complexity of modern economies.


Summary

ä Firms and households interact and exchange resources in an economy.

ä Households supply firms with the factors of production, such as labour

and capital, and in return, they receive wages and dividends.

ä Firms supply goods and services to households. Consumers pay firms

for these. This spending and income circulate around the economy in

the circular flow of income.

ä Saving income removes it from the circular flow. This is a

withdrawal of income.

ä Taxes are also a withdrawal of income, whilst government spending

on public and merit goods, and welfare payments, are injections into

the economy.

ä International trade is also included in the circular flow of income.

Exports are an injection into the economy, since goods and services

and sold to foreign countries and revenue is earned from the sale.

Imports are a withdrawal from the economy, since money leaves the

country when goods and services are bought from abroad.

ä The economy reaches a state of equilibrium when the rate of

withdrawals = the rate of injections.

ä It is important to remember that income = output = expenditure in

the circular flow.

ä An injection into the circular flow of income is money which enters

the economy. This is in the form of government spending, investment

and exports.

ä A withdrawal from the circular flow of income is money which

leaves the economy. This can be from taxes, savings and imports.


ä The amount of savings in an economy is equal to the amount of

investment.

ä If there are net injections into the economy, there will be an

expansion of national output.

ä If there are net withdrawals from the economy, there will be a

contraction of production, so output decreases.

1.4. DEMAND

If there is a demand for a particular product, then the producers will

come forward to produce it. If goods and services are able to satisfy human

needs, then people show interest to buy them.

If there is a demand for a commodity, then only it will be produced

and sold in the market. So knowing the ‘demand’ for a product is the essential

duty for industrialists and businessmen. Therefore, the demand plays an

important role.

Meaning of Demand

Demand means the desire to buy goods by adequate purchasing power.

Mere desire cannot buy goods. A beggar may have desire to buy a car.

However, he doesn’t have the purchasing power. Therefore, Beggar’s desire

is not a demand. If a rich person desires to buy a car, his desire is considered

as demand because he has the capacity to buy a car.

1.4.1. Law of Demand

Higher the price, lower the demand and lower the price, higher the

demand, other things remaining same. i.e. if the price of a product rises,

then the demand for that product will fall. And if the price of a product falls,

then the demand for that product will rise. This is considered as Law of

Demand.


Demand Schedule: The following table gives the relationship of price with

demand. The Price – Quantity (demand) relationship is shown in the Table 1.1.

This table is known as “Demand Schedule”.

Table 1.1: Demand Schedule

Price Quantity Demanded

Rs. 10 100 units

Rs. 8 150 units

Rs. 6 200 units

Rs. 4 250 units

The meaning of the above table is that if the price of a product is Rs. 10,

then 100 units of products will be sold. If the price is Rs. 8, then 150 units

of products will be sold. That is, the demand increases with the decrease in

price.

1.4.2. Demand Curve

The Demand Curve is plotted by using the data from the demand

schedule. Price is marked in the ordinate (‘y’ axis) and ‘Quantity demanded’

is marked in the abscissa (x axis). The demand curve slopes downward from

left to right indicating that when price rises, less is demanded and when price

falls, more is demanded. This kind of slope is called ‘Negative slope’.

Fig. 1.3: Demand Curve


The demand curve explains only Price − Quantity relationship. However,

normally demand varies not only with price. It also varies with other factors.

The relationship between demand and other factors are not shown in the

Demand Curve.

A demand curve is used to know

1. What is the maximum quantity that will be sold at a particular price?

2. What shall be the maximum price, for a particular quantity?

1.4.3. Characteristics of Law of Demand

1. Inverse relationship: If the price rises, then demand falls and if the

price falls, then demand rises.

2. Price is an independent variable.

3. Demand is a dependent variable.

4. Other things remain the same: There are so many factors apart from

price affecting the demand. We assume other factors remain same and

concentrate on the relationship between the price and demand only.

Reasons for Law of Demand

(a) Income effect: When price rises, the consumer’s income is reduced.

Therefore, the consumer has to curtail his expenditure on all commodities

including the commodity for which price has risen.

(b) Substitution effect: When a price of petrol rises people buy gas as a

substitute. So, demand for petrol decreases.

1.4.4. Elasticity of Demand

Elasticity of demand is defined as the degree of response of quantity

demanded to a change in price. It represents the rate of change in the quantity

demanded due to a change in price.


e = elasticity of demand

e = Proportionate change in the quantity demanded

Proportionate change in price

= Change in quantity demanded ⁄ Quantity demanded

Change in price ⁄ Price

= (Q2 − Q1) ⁄ Q1

(P2 − P1) ⁄ P1

Example: Q1 = 5000 ; Q2 = 8000 ; P1 = 20 ; P2 = 15,

then e = (8000 − 5000) ⁄ 5000

(15 − 20) ⁄ 20

= 0.6

− 0.25 = − 0.24

The price elasticity is negative. It shows the inverse relationship between

price and demand.

Total revenue is equal to price times quantity (P × Q). If consumers buy 5

units at Rs. 3 each then the total revenue is Rs. 15. If a price decrease leads

to a decrease in total revenue, this is a case of inelastic demand; if a price

decrease leads to an increase in total revenue, this is the case of elastic

demand; and if a price decrease leads to no change in total revenue, this is

the borderline case of unit-elastic demand.

Income Elasticity

Income elasticity is defined as the degree of responsiveness of quantities

demanded to a change in income. A change in income influences the change

in demand. The income elasticity can be measured by using the following

formula.

e1 = % change in demand

% change in income

where e1 = Income elasticity


Suppose a consumer’s income is Rs. 30,000/- per month and he

purchases 1 kg. of sweets per month for his children. If his income increases

to Rs. 60,000/- per month, then he is prepared to purchase 2 kg of sweets

per month.

Cross Elasticity of Demand (ec)

ec = % change in demand of a product

% change in price of another related product

The demand increase or decrease depends on the price of its substitutes.

If the price of LG TV is reduced, then the demand for Samsung TV will be

reduced. Therefore LG TV price affects Samsung TV demand. If there is an

increase in price of coffee, then the demand for tea will increase. Therefore,

coffee’s price affects the tea’s demand. The demand’s increase or decrease

depends on the prices of its complements also. For example, an increase in

demand for transistors will lead to an increase in the demand for dry battery

cells. A decrease in price of fountain pens leads to an increase in their demand

and hence increases the demand for ink.

An increase in the price of petrol decreases the demand for cars. The

high price of sugar will affect the demand for both coffee and tea. Cross

elasticity is defined as the proportionate change in the demand of a particular

product in response to the change in price of another related product.

Substitute goods: 1. Tea and Coffee, 2. Butter and margarine, 3. Coal and

gas, 4. Gas cooker and electric cookers, 5. Fountain pen and dot pen, 6. Petrol

and Diesel.

Complementary goods: 1. Sugar and Tea, 2. Petrol and Car, 3. Electricity

and Electric cookers, 4. Pipes and Pipe tobacco, 5. Pen and Ink.


1.4.5. Factors influencing demand

1. Nature of the product.

2. Multiple use of the product.

3. Income of the buyer.

4. Substitute products.

5. Proportion of income spent on the product.

6. Urgency of the Demand.

7. Fashion and Habit.

8. Durability of the product.

9. Price level.

10. Standard of living of the people.

11. Complementary products.

12. Possibility of postponement of consumption.

13. Purchase frequency of a product.

14. Consumer’s taste.

15. Consumer’s preference.

16. Advertisement.

1. Nature of the commodity: The demand for goods which satisfies the

essential basic need − food (especially rice) − will not change even if its price

increases. Therefore, it is inelastic. At the same time, the demand for silk

sarees varies with respect to the prices. Therefore, it is elastic. By the above

examples, we can conclude that the elasticity depends on the nature of the

product. So nature of product affects the demand.


2. Multiple use of the product: Take steel and electricity. Steel can be used

for many purposes. Electricity can be used for many purposes. A commodity

having a variety of uses has a comparatively elastic demand. A small fall in

its price will bring forth demand from many areas and hence demand is elastic.

For example, if electricity unit price is increased, then people will curtail its

use for non-essential purposes. So more the unit price, less is the demand. So

‘multiple uses’ of a commodity affects the elasticity.

3. Substitutes: If auto fares rises, people will use city buses or electric trains

as a substitute. Therefore, a commodity having number of substitutes has

relatively elastic demand. If a commodity’s price rises, its consumption will

be curtailed by using its substitutes. If a commodity has no substitute, then

the demand will be inelastic and hence people have no alternative and they

have to buy the product even though its price rises. So the substitutes affect

the demand.

4. Income of the buyers: Rich people will not bother about the price of milk

or fruits or biscuits. So the demand is inelastic. But poor people cannot do

so. As far as poor people are concerned, the demand is elastic. Therefore, the

income of the buyer is responsible for the elasticity and it affects the demand.

5. Proportions of income spent on the commodity: The Example of Match

box and Salt. We normally spend very very less proportion of our income to

buy match box and salt. Therefore, we will not bother about the rise of price

of these products. Hence, the demand will not change although the price rises.

Therefore, it is inelastic.

6. Urgency of the demand: E.g. Medicine for patient. Umbrella at the time

of raining. For a patient, the medicine is an urgent need. He will not bother

about its price and he will buy the medicine at any cost. Due to urgency, the

demand becomes inelastic. At the time of rains, the price rise of umbrella will

not affect its demand.


7. Fashion, habit and social custom

Fashion: When the day to day fashion requires branded T-shirt, people rush

to a Branded showroom. The demand will not be affected even though the

cost is more. Then we conclude that fashion products have inelastic demand.

Nowadays studying B.E is a fashion for all. People will not mind spending

more money for studying B.E. So the demand for B.E. admission is more,

even though the cost is more.

Habit: Those who are addicted to bad habits will not bother about the cigarette

price hike and the liquor price hike. Therefore, habit makes the demand

inelastic.

Social Custom: E.g. Marriage. People will not stop spending money for

marriage function. Even though it is costly, some people will conduct the

marriage function in a grand way. They will not bother about the marriage

hall’s rent. They will not bother about the cost of jewels, sarees, meals etc.

So the product, commodity, function related to social customs are inelastic.

8. Durability of the products: More durable and repairable a commodity is,

the higher is its elasticity of demand. If a commodity is durable and repairable,

then it can be repaired instead of buying a new one. Shoes can be repaired

instead of buying new ones. Tables and chairs can be repaired instead of

buying new ones. Therefore, the durable goods have elastic demand.

9. Price level: If the price level is high, the elasticity is high. If the price

level is low, the elasticity is less. A fall in cell phone price makes a large

number of people buy these products. So high price products have elastic

demand.

10. Standard of living and cost of living: The place where the standard of

living and cost of living is more, the elasticity of demand is less and vice

versa. It is similar to how income affects the elasticity of demand.


11. Complementary products: Ink and pen, petrol and car and electricity and

electrical appliances are complementary products. If the price of the car falls,

then the demand for petrol increases. If the pen’s price falls, then ink’s demand

increases. Therefore, the complementary product affects the elasticity of

demand.

12. Possibility of postponement of consumption: Gold price sometimes

increases and sometimes decreases. Normally people buy golden ornaments as

an asset. Therefore, if the price of gold is high, then they will postpone the

purchase, hoping that its price will decrease or their savings may increase in

future. Therefore, this possibility of postponement affects the elasticity of

demand.

13. Purchase Frequency of a product: If a product is frequently purchased,

then people will be keen on its price. So this type of product is price elastic.

Example: Industrial products.

1.5. SUPPLY

Supply means the quantity of goods, which are offered for sale at a

given price. Supply and demand are two important terms used in economics.

The demand analyses the buyer side of market, while the supply analyses the

seller side of market.

Supply Schedule

Supply schedule is useful to analyse the relationship of supply with

respect to the price. If the price of the product is more, then many more

suppliers will be interested to supply. So more the price, more the supply will

be. The following table is called as supply schedule, which reveals the truth

that ‘when price is more, supply is more’. And this table is called as “Supply

Schedule”.


Table 1.2: Supply Schedule

Price in Rs. Quantity supplied in units

10 100

8 80

6 60

3 30

1.5.1. Law of supply

When the price of a commodity rises, its supply increases and when

the price falls, the supply decreases provided other things remain same.

i.e., If the price of a commodity is more, the supply will be more. If the price

goes down, the supply will decline.

1.5.2. Supply Curve

Supply is plotted in the x-axis in terms of Quantity. Price is marked in

the y-axis. For different price, different quantity will be supplied.

From the supply curve, we can find the relationship of supply with

respect to price.

Fig. 1.4: Supply Curve


1.5.3. Determinants of Supply or Factors influencing supply

Most of the factors affecting the demand will also affect the supply.

Following factors are important which affect the supply.

1. Price.

2. Cost of production.

3. Method of production.

4. Prices of substitutes.

5. Prices of complementary products

6. Fluctuation of price.

7. Number of sellers in the markets.

8. Natural causes − Rain, storm and cyclone.

9. Strikes, Bandhs and Lockouts.

10. Technology Development.

11. Fashion.

12. Government Policy.

13. Society, social status and social changes.

14. Cost of living.

15. Standard of living.

Elasticity of Supply

The responsiveness of change in supply to the change in price is called

as Elasticity of Supply. Supply is elastic when change in price affects the

supply. Supply is inelastic, when change in price does not affect the supply.

Elasticity of supply = % change in supply

% change in price


Factors determining the elasticity of supply

1. Availability of resources [men, machines, materials and time].

2. Available time between supply and demand.

3. Technological improvements.

4. Different methods used to produce goods.

5. Raw materials availability.

6. Market structure.

7. Government policy.

8. Taxation.

9. Number of sellers.

1.6. SUPPLY – DEMAND EQUILIBRIUM

Supply increases with prices because the suppliers earn greater profits

and can easily cover their costs. Demand increases with lower prices because

the products become more affordable and the buyers get more value for their

money. Because people only buy a product if the benefit is at least equal to

its cost, and because people’s preferences vary widely, a lower product price

will have a benefit worth the cost for more people, thus increasing demand.

This is why when demand and supply quantities are plotted according to price,

the supply curve moves upward with price, while the demand curve moves

downward with price. When the amount demanded is equal to the amount

supplied, then equilibrium is achieved, known as the market equilibrium (or

supply-demand equilibrium), where the quantity is equal to the equilibrium

quantity and the price is equal to the equilibrium price. At this price, the

supply curve and demand curve intersect and the point of intersection is known

as the equilibrium point. Furthermore, if prices are different from the

equilibrium price, then the law of supply and demand states that the price

of any product will adjust until the supply equals the demand.


Fig. 1.5: Supply-Demand Market Equilibrium

1.7. CONCEPT OF ENGINEERING ECONOMICS

Economics, as a science, deals with the problem of allocation of scarce

resources among competing ends and giving maximum satisfaction at minimum

cost.

The role of engineers today, apart from planning and building, also

includes problem solving, managerial decision making, etc. An engineering

economist draws on the accumulated knowledge of engineering and economics

to identify the alternative uses of limited resources and select the most suitable

course of action.

So, Engineering Economics is devoted to problem solving, decision

making, optimization and determination of equilibrium. The decision maker’s

objective is to arrive at the best combination of goods to be consumed or

produced, or of inputs to be employed. This helps in the efficient and effective

functioning of an organization enabling it to fix a lower price for its

goods/services.


1.8. EFFICIENCY

The main economic activity is to achieve economic optimisation

i.e. maximum possible efficiency. In general terms, efficiency can be defined

as the ratio of a system’s output to its input.

Efficiency (%) = Output

Input × 100

Efficiency is classified into two types

ä Technical (engineering) efficiency.

ä Economic efficiency.

1.8.1. Technical Efficiency

An industry is engaged in production of a particular commodity. Its job

is to transform a set of given inputs into some useful outputs. If the industry

earns the maximum profit by using efficient production method (using method

study and time study), by minimizing waste scraps, then the company is

technically efficient.

If an organisational unit is engaged in supplying adequate goods

according to the demand, then it is technically efficient. For example,

reliability and quickness of a courier service system in its deliveries proves

that it is technically efficient. If a motor bike runs more kilometers per litre

fuel, then it is technically efficient. Technical efficiency means doing a job in

the cheapest possible way. i.e., production of given level of output from the

lowest possible inputs. Maximise the output from the given set of inputs by

minimizing loss or wastage.

1.8.2. Economic Efficiency

Economic efficiency is also called as Business efficiency. Economic

efficiency will be obtained only after technical efficiency is obtained.

Economic efficiency depends on


1. Scarce resources like men, machines, materials, money and time.

2. Alternative way of using scarce resources.

By using scarce resources, you can produce product A or product B.

Only one product out of 2 will give maximum profit. Find which product will

give you more profit, do it in a best method and be economically efficient.

Economic efficiency can be generically expressed as

Economic efficiency (%) = Output

Input × 100

= Worth (Annual revenue)

Cost (Total annual expenses) × 100

An organisation is economically efficient if it is technically efficient and

if it succeeds in utilizing its scarce resources in the most desirable way. Most

desirable way means that

ä Maximising social welfare in case of a society.

ä Maximizing the utility in case of individual consumer.

In case of an organisation profit

ä Maximising the profit

ä Maximising the sales.

ä Maximising the growth rate.

ä Maximising the value of the organisation.

ä Maximising the survival in the business for long period.

ä Maximising any combination of above all.


Technical efficiency is a prerequisite for economic efficiency. If an

organisation is technically inefficient so that it can not find out the best method

or best machine, then it can not be economically efficient. Economic efficiency

is obtained by the following activities.

1. Efficient selection of goods to be produced.

2. Efficient selection of resources.

3. Efficient allocation of resources.

4. Efficient choice of methods of production.

5. Efficient allotment of goods produced among the consumers.

How to measure Technical efficiency

One can measure technical efficiency by using physical indicators such

as

(i) Capital − output ratio.

(ii) Capital − labour ratio.

(iii) Actual cost − standard cost ratio.

How to measure economic efficiency

It is very difficult to measure economic efficiency precisely. Some

methods are:

1. Using optimization model such as linear programming.

2. Using total productivity.

3. Using total profitability.

Large corporations having sophisticated planning machinery may adopt

the linear programming method. However, small-scale industries and Medium

type industries adopt their own ad-hoc methods to measure the economic

efficiency and they adopt these methods to increase economic efficiency. The


firms may set some target for productivity or profitability for themselves. If

they achieve those targets, then they are economically efficient. Otherwise not.

Productivity is the ratio of output to input. In other words, it is the ratio of

gross revenue to the total cost of production. Profitability is the return on

capital invested in the business.

1.8.3. Various ways of improving productivity (i.e. Economic efficiency)

ä Increased output for no change in input: This can be achieved

through small or creative changes in the process which involve an

insignificant cost but largely contribute in saving process time and

resources, there by increasing productivity.

ä Decreased input for same output: By decreasing inputs to produce

the same level at output, the productivity ratio increases. For example,

a substitute raw material available at a lower price contributes to

decreased input.

ä Proportionate increase in the output is more than proportionate

increase in the input: Here, for example, by extending the product

line to fully utilize the existing facilities will result in an increase in

revenue which will be much more than the proportionate increase in

the input cost. This will increase the economic efficiency.

ä Proportionate decrease in input is more than the proportionate

decrease in output: If a uneconomical product is removed from the

existing product mix, a decrease in revenue and decrease in input cost

(material costs, operation costs, etc.) occurs. But the decrease in input

is more than the decrease in output, which will result in a net increase

in productivity.

ä Increase in output with simultaneous decrease in input: Improving

existing technologies or introducing new and advanced technologies

allows more work to be done with less time, cost and effective

utilization of resources. Even if the cost of new technology is high,


in the long-run, the high initial cost would break-even resulting in

increased revenues and decreased inputs. Thus increased productivity

is achieved.

1.9. SCOPE OF ENGINEERING ECONOMICS

Engineering economics plays a vital role in all engineering decisions. It

is the application of economic techniques to the evaluation of design and

engineering alternatives, its role being to assess the appropriateness of a

given project, estimate its value and justify it from an engineering standpoint.

Engineering economics deals with the methods that enable engineers’ to

make economic decisions towards minimising costs and/or maximising profits

to business organizations. The role of engineering economists in decision −making is

ä to identify alternative uses for limited resources and obtain appropriate

data.

ä to analyse the data to determine the better alternative

The following topics generally fall under the scope of engineering

economics.

ä Elementary economic analysis.

ä Make or buy decisions.

ä Value engineering.

ä Linear programming.

ä Interest formulae.

ä Bases for comparing alternatives, present worth method, future worth

method, annual equivalent method, rate of return method.


ä Replacement analysis.

ä Depreciation.

ä Evaluation of public alternatives, inflation adjusted investment

decisions.

These topics of engineering economics constitute its subject matter.

Economic decision making in an industrial setting

(i) Production Decisions

Production is an economic activity which supplies goods and services

for sale in a market to satisfy consumer wants, thereby profit maximisation is

made possible. The business executive has to make the rational allocation of

available resources at his disposal. He may face problems relating to best

combination of the factors to gain maximum profit or how to use different

machine hours for maximum production advantage, etc.

(ii) Inventory Decision

Inventory refers to the quantity of goods, raw material or other resources

that are idle at any given point of time held by the firm. The decision to hold

inventories to meet demand is quite important for a firm and in certain

situations the level of inventories serves as a guide to plan production and is

therefore, a strategic management variable. Having large inventory of raw

materials, intermediate goods and finished goods means blocking of capital.

(iii) Cost Decisions

The competitive ability of the firm depends upon the ability to produce

the commodity at minimum cost. Hence cost structure, reduction of cost and

cost control has come to occupy important places in business decisions. In the

absence of cost control, profits would come down due to increasing cost.


Business decisions about the future require the businessmen to choose

among alternatives, and to do this, it is necessary to know the costs involved.

Cost information about the resources is very essential for business decision

making.

(iv) Marketing Decisions

Within market planning, the marketing executive must make decisions

on target market, market positioning, product development, pricing channels

of distribution, physical distribution, communication and promotion. A

businessman has to take mainly two different but interrelated decisions in

marketing. They are the sales decision and purchase decision.

Sales decision is concerned with how much to produce and sell for

maximising profit. The purchase decision is concerned with the objective of

acquiring these resources at the lowest possible prices so as to maximise profit.

Here the executive’s basic skill lies in influencing the level, timing, and

composition of demand for a product, service, organisation, place, person or

idea.

(v) Investment Decision

The problems of risks and imperfect foresight are very crucial for the

investment decision. In real business situation, there is seldom on investment

which does not involve uncertainties. Investment decision covers issues like

the decisions regarding the amount of money for capital investment, the source

of financing this investment, allocation of this investment among different

projects over time. These decisions are of immense significance for ensuring

the growth of an enterprise on sound lines. Hence, decisions on investment

are to be taken with utmost caution and care by the executive.

(vi) Personnel Decision

An organisation requires the services of a large number of personnel.

These personnel occupy various positions. Each position of the organisation

has certain specific contributions to achieve organisational objectives. Personnel


decisions cover the areas of manpower planning, recruitment, selection, training

and development, performance appraisal, promotion, transfer, etc. Business

executives should take personnel decisions as an essential element.

1.10. ELEMENTS OF COST

The cost of any product or service is the sum of the various elements

of cost. The three basic elements that make up the cost of any product or

service are:

ä Material cost i.e. the cost of input commodities.

ä Labour cost i.e. cost of remuneration of labourers.

ä Expenses/Over heads i.e. other expenses incurred.

Broadly speaking, cost can be classified as illustrated below

1.10.1. Fixed cost

This is a cost that does not vary in the short-term, irrespective of changes

in production or sales levels or other measures of activity. Fixed costs are

basic operating expenses of a business like rents, machinery, interest payments,

insurance, maintenance costs, salaries, etc.


Fig. 1.6: Fixed Cost

The Fixed costs must be paid even if the firm does not produce the

output. They will not change even if the output changes. Therefore, the fixed

costs are the fixed amount of cost that should be paid irrespective of the level

of output.

Production overheads, also known as works overheads or factory

overheads are all indirect expenses incurred in connection with the manufacture

of a product like salary of watchman, welfare activities for labourers, etc.

Administrative overheads are the indirect expenses required the general

administration and management of a business.

Selling and distribution overheads are the expenses pertaining to the

marketing and shipping of products or services to the customers.

1.10.2. Variable cost

Variable costs are the costs that vary with the level of output. Variable

costs vary in direct proportion to the volume of production. Therefore, if the

output increases, then the variable cost increases. If the output decreases, then

the variable cost decreases. However, the variable cost/unit will remain

constant with the changes in volume.


Fig. 1.7: Variable Cost

Examples

1. Steels cost and fiber cost (raw material) to produce cars.

2. Production oriented temporary workers salary for production lines.

3. Electric power to operate factories and so on.

The variable cost is zero, when output is zero.

The total cost is given by the sum of Fixed cost and Variable cost

TC = FC + VC

Direct Material Cost

It is the cost of the raw materials and components used to create a

product e.g. cost of steel is a direct material in the cost of automobile.

Direct labour cost

It is the sum of the wages and benefits paid to the workers who operate

the production equipment and perform the processing and assembly tasks.

Direct expenses

These are expenses that vary in relation to the production volume, other

than direct material and labour costs.


1.10.3. Semi-Variable Cost or Mixed Cost

These costs are neither fixed costs nor variable costs. These costs fall

in between fixed costs and variable costs. For example, take electricity bills.

There will be a fixed charge when we consume below a certain limit. When

we consume more than the limit, then charges will be more. Take Salesman

case: Salesman will earn monthly salary whether he attains the target or not.

Even though he sells nothing, he will get salary. If he sells more than the

target, then he will get commission related to sales volume. Therefore, the

electricity bill and salesman case are the examples for the semi-variable cost.

Fig. 1.8: Semi-Variable Cost

1.10.4. Selling price of a product

It is necessary for businesses to make use of the cost concept for the

following purposes.

1. Determination of profits.

2. Payment of Tax.

3. To fix Bonus.

4. To calculate Dividends.

5. To know how much of goods to produce and sell.


The Industrialists are to know what price should be quoted for tender,

whether to accept the order or not, what channels should be used for sales

and so on.

The procedure adopted to arrive at the selling price of a product is as

follows:

ä Direct material costs + Direct labour costs + Direct expenses = Prime

cost.

ä Prime cost + Factory overhead = Factory cost.

ä Factory cost + Office and administrative overhead = Costs of

production.

ä Cost of production + Opening finished stock – Closing finished stock

= Cost of goods sold.

ä Cost of goods sold + Selling and distribution overhead = Cost of

sales.

ä Cost of sales + Profit = Sales.

ä Sales/Quantity sold = Selling price per unit.

Note: If the opening finished stock is equal to the closing finished stock, then

the cost of production is equal to the cost of goods sold.

1.10.5. Other Terms

1. Marginal Cost

To know how much should be produced and sold, a firm should know

its marginal cost of producing goods and services. Marginal cost is the extra

or additional cost of producing 1 extra unit of output.


For example: If a firm is producing 500 pen drives (USB devices)

Total cost of producing 500 pen drives = Rs. 25,000

Total cost of producing 501 per drives = Rs. 25,090

Difference = Rs. 90

Then the marginal cost of production is Rs. 90/- for the 501st pen drive.

Marginal cost indicates the increase or decrease in the total cost by producing

an additional unit of output.

Marginal costing: Can be defined as the ascertainment of the marginal cost,

which varies directly with the volume of production, by differentiating between

fixed and variable costs and determining its effect on profit. That is, the fixed

overheads are excluded from the cost of production and provide a same cost

per unit upto a certain level of production. So, only variable costs are charged

to cost units.

Marginal revenue: Increase in the gross revenue of a firm by selling one

additional unit of output.

Marginal benefit: Increase in an activity’s overall benefit that is caused by

an unit increase in the level of that activity, all other factors remaining

constant. Also called marginal utility

2. Average Cost: (AC) or Unit cost

Average cost is total cost divided by the number of units produced.

Average cost = Total cost

Output =

TC

Q = AC


3. Actual cost

Actual cost is the actual expenditure incurred for producing a commodity

or service.

1. Actual wages paid.

2. Cost of materials purchased.

3. Interest paid etc. These costs are generally recorded in the Accounts

books.

4. Opportunity Cost

Life is full of choices. In choosing one thing we must give up something

else. When we go to movie, we cannot read a book. When we go to college,

we forgo the opportunity of getting a full time job. Every time a firm makes

a decision, it incurs cost by discarding alternative courses of action. This cost

is called an opportunity cost.

Opportunity cost is the revenue, which would have been earned by using

the goods or services in some other alternate ways. Opportunity Cost is the

benefits forgone by rejecting one course of action to another. Opportunity cost

is the sacrifice involved in accepting the alternative under consideration.

Opportunity costs of a product for a specific purpose is zero. Opportunity costs

are not recorded in the Accounts book. In economical theory, for a manager

to take a wise decision, he should consider the opportunity cost also.

Let us illustrate the concept of opportunity cost by considering the owner

of a computer firm. The owner works 6 days a week without salary. At the

end of the year, the firm earns a profit Rs. 30,000/-. Therefore, the owner

gets the profit of Rs. 30,000/- per year. However, had the owner gone for a

job, then he would have earned Rs. 50,000/- per year.

The profit by the firm = Rs. 30,000 ⁄−

Opportunity cost of owner’s salary = Rs. 50,000 ⁄−

(−) Rs. 20,000 ⁄−

So the firm runs under a loss of Rs. 20,000/-


Using own building for shop (business): If you give your building for rent,

it will fetch you Rs. 3,000/- month. Then you have to subtract Rs. 3,000 as

an opportunity cost from the profit earned per month.

Student from a poor family going to college: His parents spend Rs. 50,000/-

year for his studies. Had he gone for job, he would have earned Rs. 60,000/-

year. Therefore, the opportunity cost of going to college (instead of going for

a job) is Rs. 1,10,000/-.

5. Incremental Costs (or) Differential Costs

As name implies, incremental cost is the additional cost due to change

in the level of the business activities (or) the nature of the business activities.

The changes in business activities are obtained as follows:

1. Addition of new product line.

2. Change in channel of distribution.

3. Installation of new machines.

4. Replacing old machines by better new machines.

5. Expansion in other markets.

When the firm is new, there is no question of incremental cost. For

firms already established, incremental costs are useful for decision making.

For evaluating the alternatives, the management will analyse the incremental

cost.

6. Sunk Cost

The cost incurred by a decision which can not be recovered is called as

a Sunk cost. Sunk cost once incurred can not be retrieved. Brewery plant

installed at the time of prohibition is an example for Sunk cost. Sunk cost is

just like the fixed cost. Sunk cost is not affected by the change in the level

or the nature of the business activities. Management will not analyse the sunk

cost for decision making. The difference between incremental costs and sunk


costs are explained by means of following example. The components of cost

of machine are given below:

1. Acquisition costs.

2. Service and maintenance costs.

3. Operating costs (manpower, electric power and raw materials).

4. Space occupying costs (depreciation, taxes and insurance to be paid

for a building in which machine is installed).

A management is in a position to decide whether to buy a machine or

hire it.

Table 1.3

If a machine is bought If a machine is hired

1. Acquisition cost is equal to price

of machine + its cartage to the

buyer’s premises + cost of

installation.

1. Acquisition cost is equal to only

rent and no other cost.

2. The management has to bear the

service and maintenance cost.

2 No service and maintenance cost

for Management.

It will be taken care of by the

suppliers of the machine for hire.

3. Operat ing cost and space

occupying cost exist.

3. Opera ting cost and space

occupying cost exist.

In this Table 1.3, the acquisition costs and service and maintenance costs

are different for different alternative decisions. Therefore, these costs are called

as Differential costs.


On the other hand, the operating costs and the space occupying costs

are same for both alternative decisions. Therefore, these costs are called as

Sunk cost. Only the Differential costs should be considered for

decision-making and sunk costs can be ignored because it will occur in both

alternative decisions.

Most of the times, differential costs are considered as variable costs and

sunk costs as fixed costs, but not always. Because in the above example,

operating costs are variable costs but they are not differential costs, they are

sunk costs. Similarly, price of the machine is fixed cost but it is not sunk

cost, it is a differential cost.

7. Recurring cost

A recurring cost is one that occurs at regular intervals and is anticipated.

Variable costs are recurring. Examples: cost to provide electricity to a

production facility, paying rent.

8. Nonrecurring cost

A nonrecurring cost is one that occurs at irregular intervals and is not

generally anticipated. The cost to replace a company vehicle damaged beyond

repair in an accident is a nonrecurring cost, the cost of augmenting equipment

based on older technology to restore its usefulness, emergency maintenance

expenses.

9. Cash cost

Cost that involves a payment of cash or cheque (i.e. not in credit) is

called a cash cost. A cash cost is a cash transaction or cash flow.

10. Book cost

Costs reflected in the accounting system only are called book costs.


It is not a cash flow, but it is an accounting entry that represents some

change in value. When a company records a depreciation charge, no money

changes hands. However, the company is saying in effect that the market value

of its physical, depreciable assets has decreased by that value during the year.

11. Life-cycle cost

Life-cycle costs refer to costs that occur over the various phases of a

product or service life cycle, from needs assessment through design,

production, and operation to decline and retirement. i.e. Life-cycle costs is the

sum total of all the costs incurred during the life cycle of a product.

1.10.6. Break Even analysis (BEA)

The Break Even Analysis is used to analyse the relationship between

cost, volume and profit. It is also called as CVP (cost, volume, and profit)

analysis. Break even analysis is used to find the level at which the total cost

and total revenue becomes equal. It is a lack of sense on the part of

management to run a business without break even analysis. In the case of a

manufacturing concern, if the quantity produced is less than the break even

quantity, a loss is incurred and if the manufactured quantity is greater than

the break even quantity, a profit is made.

Significance of BEA

1. It gives, the minimum number of units to be produced so that there

is no loss.

2. It indicates when the profit is attained.

3. To fix the bonus for employees and other wage calculations, this

analysis is used.


Fig. 1.9: Break Even Point

The break even point can be obtained by graph. In this graph when total

sales line intersects the total cost line, the BEP is obtained.

B.E.P can be obtained in terms of

(a) Number of units (How much minimum number of units should be

produced to avoid loss)

(b) Sales Volume (or) Total Revenue (How much sales volume should

be achieved to avoid loss)

(c) % of estimated capacity (What % of estimated capacity should be

attained to avoid loss).


Concept of Break Even Point

Since we know already what is fixed cost and variable cost, we can

analyse the following example to understand the Break even point concept.

Problem 1.1

The following data refers to the business concern

AIR WALK Publications.

Fixed cost per annum F = Rs. 1,00,000 ⁄ −Variable Cost per unit V = Rs. 6 ⁄ −Sales price per unit S = Rs. 10 ⁄ −Annual Production capacity is 50,000 units.

From above data

1. Fixed cost Rs. 1,00,000 is constant for any number of units

produced.

2. Total variable cost = Variable Cost

Unit × No. of units produced.

3. Total Sales (or) Total Revenue = Price

Unit × No. of units sold.

4. Total cost = FC + VC.

5. Profit = Total Sales − Total cost.

The total cost, sales and profit can be worked out for different production

levels as given in the table.


Q

(V.C/Unit)

No. of

units

Price ×No. of

units

Total

Sales −Total

Cost

Production

Level

(units)

Fixed

Cost

(FC)

Total

Variable

Cost =Rs. 6×Q

(VC)

Total Cost

= FC + VC

= (2) + (3)

Total

Sales

Rs.10 × Q

Profit

(1) (2) (3) (4) (5) (5) − (4)

1 0 1,00,000 0 1,00,000 0 −1,00,000

(Loss)

2 5000 1,00,000 30,000 1,30,000 50,000 −80,000

(Loss)

3 15,000 1,00,000 90,000 1,90,000 1,50,000 −40,000

(Loss)

4. 25,000

BEP in

units

1,00,000 1,50,000 2,50,000 2,50,000

BEP in

Rupees

0

(No loss

& No

profit)

5. 35,000 1,00,000 2,10,000 3,10,000 3,50,000 +40,000

6 45,000 1,00,000 2,70,000 3,70,000 4,50,000 +80,000

From the above table, we can understand the following points.

1. When the company does not produce any thing, the loss is

Rs. 1,00,000, which is equal to F (or FC).


2. When there is an increase in production, the loss goes on reducing

i.e. when 5000 units are produced, the loss is Rs. 80,000. When

15,000 units are produced, the loss is further reduced to Rs. 40,000/-.

3. At a production level of 25,000 units, the unit makes no loss and no

profit. The production level, which makes neither profit nor loss,

is known as the BEP.

At the BEP, the total sales are just sufficient to cover the variable

cost and recover fully the fixed cost.

4. At production levels beyond the BEP, the company earns profits.

Higher level of production earns higher profits.

5. The calculation are valid until the maximum capacity is reached i.e. up

to 50,000 units, the calculations are valid. Beyond this level, even the

fixed costs will change due to additional infrastructure required and

hence fresh calculations have to be made.

Construction and analysis of break even charts

Graphical Method

1. For drawing graph different levels of production are plotted in x axis

and the cost and Revenue (F, TC and Sales) are plotted in y-axis.

2. The data from the table can be plotted in the graph.

3. When the production is 0 unit, the sales revenue is 0 (mark point 0)

and at 45,000 units, it is Rs. 4,50,000 (Mark point C). The sales

revenue line is drawn by joining these points 0 and C.

4. When the production is 0 unit, the total cost is Rs. 1,00,000 (Mark

point A) and at production level of 45,000 units, it is Rs. 3,70,000/-

(Mark Point B). The cost line is drawn to joining these two points

A and B.


Fig. 1.10

5. The above two lines (Total sales line and total cost line) intersect at

production level of 25,000 units. This is the Break Even Point B.E.P.

Analytical method

A simple way of finding out BEP is an follows

BEP = F

S − V

where F = Fixed cost

S = Selling price per unit

V = Variable cost per unit

So BEP = 1,00,000

10 − 6 = 25,000


Contribution: (S − V)

In the formulae BEP = F

S − V

(S − V) represents the portion of the sales revenue, which goes to recover

the fixed cost. Hence, (S − V) is known as ‘contribution’ towards fixed costs

(and profit). The formula can be modified as

BEP = F

C

Where C = S − V = Contribution per unit.

1.10.7. Profit volume ratio (P/V ratio)

P/V ratio is the ratio of contribution to sales. It is generally expressed

as a %. It is also called as contribution ratio.

In the above example,

The P/V ratio = C × 100

S

= 4 × 100

10 = 40%

BEP can be calculated in terms of turnover (in Rupees) on the basis of

P/V ratio. In this case, formula is modified as follows

BEP = F

P ⁄ V ratio

For the above example, the BEP can be calculated by using the modified

formula

BEP = 1,00,000

40% =

1,00,000

0.4 = Rs. 2,50,000

When sales per unit and variable cost per unit is not given, we can use

the above formula.


Margin of safety (M.S): It is the difference between the expected level of

sales and the break even sales. Margin of safety is used to indicate the amount

of sales that are above the break-even point.

Margin of safety (M − S) = Total sales − Break even sales

= Profit

Contribution × sales

MS interms of percentage = M − S

Total Sales × 100

Applications of Break Even Analysis

The Break Even analysis is used by managers for decision-making in a

number of areas as follows.

1. Pricing decision.

2. Make or buy decisions.

3. Products (or Sales) mix.

4. Utilisation of limiting factors.

5. Alternative methods of production.

6. Discontinuance of product line.

7. Expansion of capacity.

8. Profit planning.

Problem 1.2: The following data are given for a company. Estimated

output = 80,000 units; Fixed cost = Rs. 4,00,000; Variable cost = Rs. 10 per

unit; Selling Price = Rs. 20 per unit. Find out the break even point analytically

and Graphically.

(a) Analytically

BEP = F

S − V =

4,00,000

20 − 10 =

4,00,000

10 = 40,000 units.


(b) Graphically

No. of

units

produced

(Q)

FCTotal VC

= 10 × Q

Total

Cost TC

= FC + VC

Total

Sales =Rs. 20 × Q

Profit =Total

Sales −Total cost

0 4,00,000 0 4,00,000 0 − 4,00,000

80,000 4,00,000 8,00,000 12,00,000 16,00,000 + 4,00,000

1. Plot the no. of units in the ‘x’ axis. Plot the Rupee in lakhs in ‘y’

axis.

2. When ‘0’ units are produced, the total cost is 4 lakhs, Mark this point

as A.

3. When ‘80,000’ units are produced, the total cost is 12 lakhs. Mark

this as B.

4. Joint A and B. This is Total cost line.

5. When ‘0’ units are produced, the total sales is ‘0’.


6. When 80,000 units are produced and sold, the sales revenue is 16 lakhs.

Mark this point as C. Now join ‘0’ and C. This is Total Sales line.

7. The total cost line and total sales line will intersect at point BEP.

From BEP, draw vertical to cut ‘x’ axis. We get 40,000 units. So

BEP = 40,000 units. Similarly, from BEP, draw horizontal to cut ‘y’

axis. We get 8 lakhs. So BEP = 8 lakhs. So from above graph, we

found

BEP in terms of units = 40,000 units and

BEP in terms of money = 8 lakhs.

Problem 1.3: From the following data (a) find out the break even point.

Variable cost per unit = Rs. 15/- Fixed cost = Rs. 54,000/- Selling price per

unit = Rs. 20/- (b) What should be the selling price per unit if the BEP is

brought down to 6,000 units.

Solution

(a) V = Rs. 15; F = Rs.54,000; S = Rs. 20

BEP = F

S − V =

54,000

20 − 15 −

54,000

5 = 10,800 units

(b) BEP = F

S − V

6000 = 54,000

S − 15

S − 15 = 54,000

6000 = 9

S = 15 + 9 = 24 ; So S = Rs. 24

So Selling Price = Rs. 24 ⁄− if the BEP is brought down to 6000 units.


Problem 1.4: The following data relate to a company working at 100%

capacity level in manufacturing business. Fixed Overheads = Rs. 30,000/-

Variable Overheads = Rs. 50,000/-, Direct wages = 40,000/- Direct materials

= 1,00,000/-; Sales = 2,50,000/-. Mark the values in the break-even chart and

determine BEP from the chart. Verify the result by calculations.

Solution

Draw the chart for 0% and 100%

Fixed Overheads = Fixed cost = Rs. 30,000/-

Variable cost = Variable overheads + Direct wages + Direct materials

= 50,000 + 40,000 + 1,00,000 = Rs. 1,90,000/-

Total cost at 0% = 30,000 (A)

Total cost at 100% = 30,000 + 1,90,000 = 2,10,000 (B)

Join A & B to get Total Cost line (TC line)

Total sales at 0% = 0

Total Sales at 100% = Rs. 2,50,000/- (C)

Join 0 & C. This is Total Sales line


This Total Sales line & Total cost line intersect at B.E.P. From B.E.P,

draw horizontal. It cuts at Rs. 1,25,000/- So B.E.P = Rs. 1,25,000/-

Verification

B.E.P = F

P ⁄ V ratio =

F

Contribution ratio =

F

(S − V) ⁄ S

Contribution ratio = S − V

S =

2,50,000 − 1,90,000

2,50,000 = 0.24

BEP = F

Contribution ratio =

30,000

0.24 = Rs. 1,25,000 ⁄−

Problem 1.5: Suguna associates has the following details:

Fixed cost = Rs. 20,00,000

Variable cost per unit = Rs. 100

Selling price per unit = Rs. 200

Find

(1) The break-even point in quantity.

(2) The break-even point in sales [A.U. May 2014]

Solution

Fixed cost (FC) = Rs. 20,00,000

Variable cost per unit (v) = Rs. 100

Selling price per unit (s) = Rs. 200


(1) The break-even point in quantity = FC ⁄ S − V

= 20,00,000 ⁄ (200 − 100)

= 20,000 units.

(2) The break-even point in sales = FC

S − V × S

= 20,00,000

200 − 100 × 200

= Rs. 40,00,000

Problem 1.6: From the following information relating to Geetha Ltd., you are

required to Find out:

(1) P/V ratio (2) BEP (3) Profit (4) Margin of safety.

Total fixed cost = Rs. 4,500

Total variable cost = Rs. 7,500

Total sales = Rs. 15,000 [A.U. May 2013]

Solution

(1) P/V ratio

P/V ratio = Contribution

Sales × 100

Contribution = Sales − Variable costs

= 15,000 − 7,500 = Rs. 7,500

P ⁄ V ratio = 7,500

15,000 × 100 = 50%


(2) BEP

BEP = Fixed cost

P ⁄ V ratio × 100

= 4,500

50% =

4,500

50 × 100

= Rs. 9,000

(3) Profit

Profit = Contribution − Fixed cost

= 7,500 − 4,500 = Rs. 3,000

(4) Margin of safety

Margin of safety = Profit

Contribution × 100

= 3,000

7,500 × 100 = Rs. 6,000

(ii) Also calculate the volume of sales to earn profit of Rs. 6,000.

Profit = Sales − (Fixed cost + variable cost)

6,000 = Sales − (7,500 + 4,500)

Sales = 6,000 + 12,000 = Rs. 18,000

Problem 1.7: A company produces single product which sells for Rs. 20 per

unit. Variable cost is Rs. 15 per unit and Fixed overhead for the year is

Rs. 6,30,000.

Required:

(a) Calculate sales value needed to earn a profit of 10% on sales.

(b) Calculate sales price per unit to bring BEP down to 1,20,000 units.

(c) Calculate margin of safety sales if profit is Rs. 60,000.


Solution

(a) S = V + F + P

S = Sales = Rs. 20 ⁄ unit

V = Variable Cost = Rs. 15 ⁄ unit

F = Fixed Cost = Rs. 6,30,000

P = Profit = 10

100 × 20 = Rs. 2 ⁄ unit

Suppose sales units are x

Then, 20x = 15x + 6,30,000 + 2x

20x − 17x = 6,30,000

∴ x = 6,30,000

3 = 2,10,000 units

Sales value = 2,10,000 × 20 = Rs. 42,00,000

(b) Sales price to down BEP to 1,20,000 units

S = V + F

New BEP

∴ S = 15 + 6,30,000

1,20,000 = Rs. 20.25


(c) M.S Sales = Profit

P ⁄ V ratio ∴

60,000

P ⁄ V where P ⁄ V =

C

S × 100.

i.e., 20 − 15

20 × 100 =

5

20 × 100 = 25%

∴ M.S = 60,000

25 × 100 = Rs. 2,40,000

Problem 1.8: A company has fixed cost of Rs. 90,000, Sales Rs. 3,00,000

and Profit of Rs. 60,000.

Required

(i) Sales volume if in the next period, the company suffered a loss of

Rs. 30,000.

(ii) What is the margin of safety for a profit of Rs. 90,000?

Solution

P/V ratio = Contribution

Sales × 100 =

1,50,000

3,00,000 × 100

= 50%

(i) If in the next period company suffers a loss of Rs. 30,000 then

Contribution = Fixed Cost ± Profit

= Rs. 90,000 − Rs. 30,000 (as it is loss) = Rs. 60,000

Then Sales = Contribution

P ⁄ V ratio or

60,000

0.50 = Rs 1,20,000

So, there will be loss of Rs. 30,000 at sales of Rs. 1,20,000

(ii) Safety = Profit

PV ratio or

90,000

0.5 = Rs. 1,80,000


Alternative solution of this part

Break even Sales = Fixed Cost

PV Ratio =

90,000

0.5 = Rs. 1,80,000

Sales at Profit of Rs. 90,000 = Fixed Cost + Profit

PV Ratio

= 90,000 + 90,000

0.5 =

1,80,000

0.5 = Rs. 3,60,000

Margin of Safety = Sales − Break even Sales

= 3,60,000 − 1,80,000 = Rs. 1,80,000

1.11. ELEMENTARY ECONOMIC ANALYSIS

As studied earlier, the objective of engineering economics is to compare

the economic values of different alternatives and choose the alternative that

results in maximum benefit.

Economic analysis to the application of data to a theory of how people

produce, trade and use goods and services. It can be defined as the study of

economic systems or a study of a production process or an industry to

determine if it is operating effectively and how much profits are made

The management function of an engineer is mostly directed towards

economic objectives and monitored by economic measures. The concept of

simple economic analysis is discussed in the following areas:

ä Material selection for a product

ä Design selection for a product

ä Design selection for a process industry

ä Building material selection for construction purposes.

ä Process planning/process modifications.


1.11.1. Material selection for a product

Raw material cost, among the various elements of costs, contributes to

a major portion of the total cost of any product. Hence, a raw material which

is cheaper in price or requires reduced machining time or provides

enhanced durability of the product or has a combination of these, would

bring about a reduction in the total cost of the product.

So, in the process of raw material selection the analysis of different

available raw materials is done to select an alternate raw material which would

provide the necessary functions as well as additional benefits (like cheaper

cost) than the raw material that is currently used. Substitution of the selected

alternate raw material will result in profit maximization.

Design selection of a Product

Design of a product is concerned with the form and functions of a

product. It specifies which materials are to be used, determines the tolerances,

defines the appearance of the product and sets standards for performance. So,

design of a product has direct bearing on the materials, equipments and

processes used in the manufacture of the product.

Therefore, design is a vital factor which decides the cost of the product

for a specified level of performance of that product and any design

modification to the product may result in reduced raw material requirements,

increased machinability of the materials and reduced labour.

Design for selection for a process industry

Process industry is concerned with the processing of bulk resources into

other products, like chemicals, food and beverage.

Process design involves the overall sequences of the operations required

to achieve the required product. The sequences are determined by product

nature, raw materials used, quality and quantity of output required.


Therefore, the choice of appropriate equipments and equipment materials

will result in reduction of costs. Alternate kinds of equipment for the same

service may need to be considered like, for example, water cooled exchangers

vs air coolers, pneumatic conveyors vs screw or bucket elevators, and so on.

Building Material Selection for Construction Purposes

Multiple factors are often considered when evaluating the various

categories of building materials as they have a significant effect on the cost

of the product. Apart from the price of raw materials, their transportation cost

to the location are also to be considered while sourcing them. Also energy

efficient and lower maintenance cost materials weighed against their initial

investment contribute to the reduction in annual expenditures.

Process planning

The activity of developing a manufacturing plan needed to convert the

product design into a physical entity is called process planning. It involves

determining the sequence of processing and assembly steps that must be

accomplished to produce the required part or product according to the given

specifications.

Process planning transforms a product design into a set of instruction

(sequence, machine tool setup etc.) to manufacture machined part economically

and competitively. Hence, it is subject to modifications until the most

economical sequence of operations is identified.

The various steps involved in developing a process plan are discussed as

follows

1. The first step in process planning is the analysis of part requirements.

Detailed study of the component drawings is carried out to identify

the salient features

2. Next is the selection of raw work pieces. Shape, size (dimensions and

weight), material and other attributes are determined.


3. Now, the appropriate types of processing operations and their

sequences to transform the features, dimensions and tolerances of a

part from the raw to the finished state are determined. Also batch

size influences the process sequence.

4. Next is the selection of machine tools for these operations. Basic

criteria for evaluating the suitability of a machine tool to accomplish

an operation are: Unit cost of production, manufacture lead time and

quality.

5. Other factors which influence the selection of machine tool are:

(i) Desired features, dimensions of work piece, dimensional

tolerances and raw material form.

(ii) Process capability size, mode of operation, tooling capabilities

and automatic tool changing capabilities of machine tools.

(iii) Production quantity and order frequency.

6. In this step work holding devices, cutting tools, jigs and fixtures and

inspection equipments are determined.

7. Now the controllable variables of machine condition i.e. cutting speed,

feed and depth of cut for each operation are determined.

8. The operation time is estimated. Also, the total time to complete the

job taking into account the loading and unloading times, handling

times, and other allowances are found out.

9. The details are represented on the process sheet.

In the above process, any modifications are done to determine the most

practical and economical sequence to manufacture a component/product.


Problem 1.9: In the design of a jet engine part, the designer has a choice of

specifying either an aluminium alloy casting or a steel casting. Either material

will provide equal service, but the aluminium casting will weigh 1.2 kg as

compared with 1.35 kg for the steel casting. The aluminium can be cast for

Rs. 80.00 per kg. and the steel one for Rs. 35.00 per kg. The cost of machining

per unit is Rs. 150.00 for aluminium and Rs. 170.00 for steel. Every kilogram

of excess weight is associated with a penalty of Rs. 1,300 due to increased

fuel consumption. Which material should be specified and what is the

economic advantage of the selection per unit? (AU – Nov. 2013)

Solution

Cost of using aluminium metal for the jet engine part:

Weight of aluminium casting/unit = 12 kg

Cost of making aluminium casting = Rs. 80.00 per kg

Cost of machining aluminium casting per unit = Rs. 150.00

Total cost of jet engine part made of aluminium/unit

= Cost of making aluminium casting/unit +

Cost of machining aluminium casting/unit

= 80 × 1.2 + 150 = 96 + 150

= Rs. 246

Cost of jet engine part made of steel/unit

Weight of steel casting unit = 1.35 kg

Cos of making steel casting = Rs. 35.00 per kg

Cost of machining steel casting per unit = Rs. 170.00

Penalty of excess weight of steel casting = Rs. 1,300 per kg


Total cost of jet engine part made of steel/unit = Cost of making steel

casting/unit + Cost of machining steel casting/unit + Penalty for excess weight

of steel casting

= 35 × 1.35 + 170 + 1,300 (1.35 − 1.2)

= Rs. 412.25

Decision

The total cost/unit of a jet engine part made of aluminium is less than

that for an engine made of steel

Hence, aluminium is suggested for making the jet engine part. The

economic advantage of using aluminium over steel/unit is

Rs. 412.25 – Rs. 246 = Rs. 166.25

Problem 1.10: Two alternatives are under consideration for a tapered fastening

pin. Either design will serve the purpose and will involve the same material

and manufacturing cost except for the lathe and grinder operations.

Design A will require 16 hours of lathe time and 4.5 hours of grinder

time per 1,000 units. Design B will require 7 hours of lathe time and 12 hours

of grinder time per 1,000 units. The operating cost of the lathe including

labour is Rs. 200 per hour. The operating cost of the grinder including labour

is Rs. 150 per hour. Which design should be adopted if 1,00,000 units are

required per year.

Solution

Operating cost of lathe including labour = Rs. 200 per hour.

Operating cost of grinder including labour = Rs. 150 per hour

Cost of design A

No. of hours of lathe time per 1,000 units = 16 hours

No. of hour of grinder time per 1,000 units = 4.5 hours


Total cost of design A/1,000 units = Cost of lathe operation per 1,000 units

+ Cost of grinder operation

per 1,000 units.

= 16 × 200 + 4.5 × 150

= Rs. 3,875

Total cost of design A/1,00,000 units = 3,875 × 1,00,000 ⁄ 1,000

= Rs. 3,87,500

Cost of design B

No. of hours of lathe time per 1,000 units = 7 hours

No of hours of grinder time per 1,000 units = 12 hours

Total cost of design B/1,000 units = Cost of lathe operation/1,000 units

+ Cost of grinder

operation/1,000 units.

= 7 × 200 + 12 × 150

= Rs. 3,200

Total cost of design B/1,00,000 units = 3,200 × 1,00,000 ⁄ 1,000

= Rs. 3,20,000

Decision

The total cost/1,00,000 units of design B is less than that of design A.

Hence, design B is recommended for making the tapered fastening pin

Economic advantage of the design B over design A per 1,00,000 units.

= Rs 3,87,500 − Rs 3,20,000 = Rs. 67,500

Problem 1.11: For the design of a building in a remote area the designer has

to select the material for window frames. The materials are not available

locally and have to be transported from a distance of 1800 km to the site.

The price of steel frames is Rs. 1100 each and of aluminium frames is

Rs. 1600 each. Their weights are 70 kgs and 35 kgs per each unit respectively.


The transport charges are Rs. 1.5 per kg. per 100 kms Which is the most

suitable material on the basis of its economic advantage?

Solution

Distance between building site and purchase site = 1800 km

Transportation cost = Rs. 1.5 ⁄ kg ⁄ 100 km.

For steel window frame

Price/unit = Rs. 1100

Weight/unit = 70 kgs

⇒ Transportation cost = 70 × 1.5 × 1800

100 = Rs. 1,890

∴ Total cost of steel frame/unit = Price ⁄ unit + Transportation cost ⁄ unit

= 1100 + 1890 = Rs. 2990

For aluminium window frame

Price/unit = Rs. 1600

Weight/unit = 35 kgs.

⇒ Transportation cost = 35 × 1.5 × 1800

100 = Rs. 945

Total cost of aluminium frame/unit = 1600 + 945 = Rs. 2,545

Frame above we can observe that the cost of aluminium frame is less

than the steel frame.

Therefore, the economic advantage/unit of aluminium frame over steel

frame is

= 2990 − 2545 = Rs. 445.

Since, there is an economic advantage of Rs. 445/unit for the aluminium

frame, it is recommended.

*********


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