Form No. AC08
Page 1 of 10 Rev.No.00;Rev.Date xx.xx.2015
Jansons Institute of Technology Karumathampatti, Coimbatore – 641 659
COURSE DELIVERY PLAN
Faculty Name : K.Prabhu Staff code : jit0152
Subject Name : Engineering Economics & Cost Analysis Subject code : MG2451
Academic Year : 2015 – 2016 Semester : VIII
Program & Branch : B.E Mechanical Engineering Section : -
Sl. No. Course Objectives (As given in the Syllabus) Mapping with corresponding program objectives
1. To learn about the basics of economics and cost analysis related to
engineering so as to take economically sound decisions
1. To Gain practical Mechanical Engineering knowledge in a broad range
of industries
2. To practice mechanical engineering in support of the design of
engineered systems through the application of the fundamental
knowledge, skills, and tools of mechanical engineering.
3. To enhance their skills through formal education and training,
independent inquiry, and professional development.
4. To work independently as well as collaboratively with others, while
demonstrating the professional and ethical responsibilities of the
engineering profession
5. To develop leadership qualities in their field of expertise and conduct
themselves in a professional and ethical manner
6. To enable them handle contemporary issues in the field of
Mechanical Engineering
Form No. AC08
Page 2 of 10 Rev.No.00;Rev.Date xx.xx.2015
Sl. No. Course Outcome (As given in the Syllabus) Mapping with corresponding program outcome
1. Student will able to analyze, understand and solve economic problems in
industries
1. Ability to consider realistic constraints such as economic,
environmental, social, ethical, manufacturing capacity with
sustainability by designing a system, component or process to solve
engineering problems in industries
2. Student will learn how to apply value engineering / analysis and
appropriate methods for measuring value
2. Ability to apply knowledge gained in the field of Mechanical
Engineering by conducting experiments with analysis and interpretation
3. Student will develop knowledge in cash flow and methods of cash flow 3. Ability to understand the impact of engineering solutions in a global,
economic, environmental and social context
4. Student will learn how to analyze and select the maintenance type /
time of replacement
4. Ability to handle contemporary issues
5. Student will develop knowledge on depreciation and methods of
depreciation
5. Ability to work professionally and to apply principles of Mechanical
Engineering to design and realize physical systems, components or
processes
6. Ability to develop innovative solutions to the problems in the field of
Mechanical Engineering
Form No. AC08
Page 3 of 10 Rev.No.00;Rev.Date xx.xx.2015
Lecture
Hour
Time
Allocated
(Mins)
Detailed Topics to be covered
Actual
Completion Deviations (with
reasons) if any HOD Principal
Date Period
UNIT I – INTRODUCTION TO ECONOMICS Corresponding course objective No’s met: 01
1
50 Introduction to Economics, Flow in an Economy
10
10
10
10
10
Economics
Resources
Micro-Economics and Macro-Economics
Objectives of Economics
Flow in an Economy
2
50 Law of supply and demand, Concept of Engineering Economics,
Engineering efficiency, Economic efficiency
10
10
10
10
10
supply and demand
Law of supply and demand
Elasticity of supply and demand
Concept of Engineering Economics
Engineering efficiency & Economic efficiency
3
50 Scope of engineering economics- Element of costs
10
10
10
30
Scope of Economics
Cost, Costing & Element of costs
Cost sheet – purposes and proforma
Problems solving
4 50 Element of costs
50 Problems solving
5
50 Marginal cost, Marginal Revenue, Sunk cost, Opportunity cost, V
ratio, Break-even analysis
10
20
20
Marginal cost, Marginal cost and Marginal Revenue
Sunk Cost & Opportunity cost
Contribution, PV ratio, Break even analysis, Margin of safety
6 50 Break-even analysis
Form No. AC08
Page 4 of 10 Rev.No.00;Rev.Date xx.xx.2015
50 Problem solving
7
50 Elementary economic Analysis – Material selection for product
Design selection for a product
10
20
20
Elementary economic Analysis
Material selection problem & procedure
Design selection problem & procedure
8
50 Process planning
10
20
20
Process planning
Process planning procedure
Problem solving
UNIT II – VALUE ENGINEERING Corresponding course objective No’s met: 01
9
50 Make or buy decision
10
20
20
Introduction
Factors affecting Make or buy decision
Approaches of Make or buy decision
10
50 Value engineering – Function, aims, Value engineering procedure
10
10
10
10
10
Introduction, Value & Types
Function
Aims / objectives
Value analysis Vs. Value engineering
Value engineering procedure
11
50 Interest formulae and their applications –Time value of money
10
10
10
10
10
Introduction
Time value of money
Economic Equivalence & calculations
Methods of calculating interest
Types of cash flow
12
50 Single payment compound amount factor & Examples
10
40
Introduction, Formula
Examples & problem solving
Form No. AC08
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13
50 Single payment present worth factor & Examples
10
40
Introduction, Formula
Examples & problem solving
14
50 Equal payment series sinking fund factor & Examples
10
40
Introduction, Formula
Examples & problem solving
15
50 Equal payment series payment Present worth factor & Examples
10
40
Introduction, Formula
Examples & problem solving
16
50 Equal payment series capital recovery factor & Examples
10
40
Introduction, Formula
Examples & problem solving
17
50 Uniform gradient series annual equivalent factor & Examples
10
40
Introduction, Formula
Examples & problem solving
18
50 Effective interest rate & Examples
10
40
Introduction, Formula
Examples & problem solving
UNIT III – CASH FLOW Corresponding course objective No’s met: 01
19
50 Methods of comparison of alternatives
10
40
Introduction
Methods of comparison of alternatives
20
50 Present worth method & Examples
5
10
10
25
Introduction
Revenue dominated cash flow diagram & Formula
Cost dominated cash flow diagram & Formula
Examples & problem solving
21 50 Present worth method & Examples
50 Problem solving
22 50 Future worth method & Examples
Form No. AC08
Page 6 of 10 Rev.No.00;Rev.Date xx.xx.2015
5
10
10
25
Introduction
Revenue dominated cash flow diagram & Formula
Cost dominated cash flow diagram & Formula
Examples & problem solving
23 50 Future worth method & Examples
50 Problem solving
24
50 Annual equivalent method & Examples
5
10
10
25
Introduction
Revenue dominated cash flow diagram & Formula
Cost dominated cash flow diagram & Formula
Examples & problem solving
25 50 Annual equivalent method & Examples
50 Problem solving
26
50 Rate of return method, Examples in all the methods
10
20
20
Introduction, Formula
Steps, advantages & disadvantages
Examples & problem solving
27 50 Rate of return method, Examples in all the methods
50 Examples & problem solving
UNIT IV - REPLACEMENT AND MAINTENANCE ANALYSIS Corresponding course objective No’s met: 01
28
50 Replacement analysis
5
10
10
25
Introduction
Causes / Reasons for replacement
Factors to be considered for replacing equipments
Failures
29 50 Types of replacement problem
50 Types of replacement problem
30
50 Maintenance analysis, Types of maintenance
5
10
Introduction
Objectives of maintenance
Form No. AC08
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35 Types of maintenance
31 50 Problem on maintenance & replacement
50 Problem solving
32 50 Problem on maintenance & replacement
50 Problem solving
33 50 Determination of economic life of an asset
50 Problem solving
34 50 Replacement of an asset with a new asset
50 Problem solving
35
50 Capital recovery with return and concept of challenger and
defender
15
35
Capital recovery with return
Concept of challenger and defender
36
50 Simple probabilistic model for items which fail completely
10
40
Introduction, Formula
Examples & problem solving
UNIT V - DEPRICIATION Corresponding course objective No’s met: 01
37
50 Depreciation- Introduction
10
10
15
15
Introduction
Definitions
Causes for Depreciation
Reasons for providing Depreciation
38
50 Straight line method of depreciation, Examples
10
40
Introduction, Formula
Examples & problem solving
39
50 Declining balance method of depreciation, Examples
10
40
Introduction, Formula
Examples & problem solving
40 50 Sum of the years digits method of depreciation, Examples
10 Introduction, Formula
Form No. AC08
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40 Examples & problem solving
41
50 Sinking fund method of depreciation/ Annuity method of
depreciation, Examples
10
40
Introduction, Formula
Examples & problem solving
42 50 Service output method of depreciation, Examples
10
40
Introduction, Formula
Examples & problem solving
43
50 Evaluation of public alternatives- introduction, Examples
10
40
Introduction, Formula
Examples & problem solving
44
50 Inflation adjusted decision, procedure to adjust inflation
5
10
35
Introduction
procedure to adjust inflation
Examples & problem solving
45
50 Examples on comparison of alternatives and determination of
economic life of asset.
5
10
35
Introduction
Inflation adjusted economic life of machine
Examples & problem solving
Note: where tutorial is included in the syllabus, course plan also to indicate the hours during which tutorials are planned meeting the syllabus
requirements on the total hours of tutorials to be covered.
Form No. AC08
Page 9 of 10 Rev.No.00;Rev.Date xx.xx.2015
Assignments (Minimum of 2 assignments):
Unit and Portions Mode of assignment* Planned Date Actual Date Remarks
1 unit & 2 unit
30 % of portions Home Assignments
2 unit & 3 unit
30 % of portions Home Assignments
4 unit & 5 unit
40 % of portions Home Assignments
Note(*): Mode of Assignment can be individual/ group/ class/ home assignments/ seminar presentations/ mini projects as decided by the individual faculty
etc.
CIA Test Planning:
Test No. Portions to be completed Portions covered in the test Date of test Remarks
1 1 unit & 2 unit - 30 % of portions
2 2 unit & 3 unit - 30 % of portions
3 4 unit & 5 unit - 40 % of portions
Any other method identified by the faculty in order to ensure the achievement of the course objective / outcome:
Method Supporting course objective Course Outcome Method of assessment
Form No. AC08
Page 10 of 10 Rev.No.00;Rev.Date xx.xx.2015
TEXT BOOKS:
1. Panneer Selvam.R, “Engineering Economics”, Prentice Hall of India Ltd, New Delhi, 2001.
2. Suma Damodaran, ”Managerial Economics”, Oxford university press 2006.
REFERENCES:
1. Chan S.Park, “Contemporary Engineering Economics”, Prentice Hall of India, 2002.
2. Donald.G.Newman, Jerome.P.Lavelle, “Engineering Economics and analysis” Engg. Press, Texas, 2002.
3. Degarmo, E.P., Sullivan, W.G and Canada, J.R, “Engineering Economy”, Macmillan, New York, 1984
4. Grant.E.L, Ireson.W.G, and Leavenworth, R.S, “Principles of Engineering Economy”, Ronald Press, New York,1976.
5. Smith, G.W., “Engineering Economy”, Lowa State Press, Iowa, 1973.
6. Truett & Truett, “Managerial economics- Analysis, problems & cases” Wiley India 8th edition 2004.
7. Luke M Froeb / Brian T Mccann, “Managerial Economics – A problem solving approach” Thomson learning 2007
Date: Course Faculty HOD Principal
MG2451
ENGINEERING ECONOMICS AND COST ANALYSIS
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- V ratio, Elementary economic Analysis – Material selection for product
Design selection for a product, Process planning.
1.1 INTRODUCTION
Efficient functioning of any business organization would enable it to provide goods/services at a
lower price. In the process of managing organizations, the managers at different levels should
take appropriate economic decisions which will help in minimizing investment, operating and
maintenance expenditures besides increasing the revenue, savings and such other gains of the
organization.
These can be achieved through Engineering Economics which deals with the methods that enable
one to make economic decisions towards minimizing costs and/or maximizing benefits to
business organizations.
This chapter discusses the elements of economics and the interaction between its various
components.
This is followed by an analysis of the need and scope of engineering economics. Later, elements
of cost and break-even analysis are presented.
1.2 ECONOMICS
It is a study of economic problems of the people concerning production, consumption, exchange
and distribution of wealth.
Economics is the science that deals with the production and consumption of goods and services
and the distribution and rendering of these for human welfare.
The following are the economic goals / objectives of economy:
A high level of employment
Price stability
Efficiency
An equitable distribution of income
Economic Growth
1.3 FLOW IN ECONOMY
Fig. Flow of goods, services, resources and money payments in a simple economy.
Households and businesses are the two major entities in a simple economy.
Business organizations use various economic resources like land, labor and capital which
are provided by households to produce consumer goods and services which will be used
by them.
Business organizations make payment of money to the households for receiving various
resources.
The households in turn make payment of money to business organizations for receiving
consumer goods and services.
This cycle shows the interdependence between the two major entities in a simple
economy.
1.4 LAWS OF SUPPLY AND DEMAND
Laws of supply
Laws of supply - states that the quantity of a commodity supplied varies directly with the price,
other determinants of supply remaining constant.
If the cost of inputs increases, then naturally, the cost of the product will go up. In such a
situation, at the prevailing price of the product the profit margin per unit will be less.
The producers will then reduce the production quantity, which in turn will affect the
supply of the product.
For instance, if the prices of fertilizers and cost of labor are increased significantly, in
agriculture, the profit margin per bag of paddy will be reduced.
So, the farmers will reduce the area of cultivation, and hence the quantity of supply of
paddy will be reduced at the prevailing prices of the paddy.
If there is advancement in technology used in the manufacture of the product in the long
run, there will be a reduction in the production cost per unit.
This will enable the manufacturer to have a greater profit margin per unit at the
prevailing price of the product. Hence, the producer will be tempted to supply more
quantity to the market.
Weather also has a direct bearing on the supply of products. For example, demand for
woolen products will increase during winter. This means the prices of woolen goods will
be increased in winter.
So, naturally, manufacturers will supply more volume of woolen goods during winter.
Factors influencing supply
The shape of the supply curve is affected by the following factors:
Selling price: As the price increases, sellers like to sell more and vice-versa.
Cost of production: As cost of production rise due to increase in the variable factors,
supply decreases.
Cost of the inputs:
The change in technology affects the supply function.
If the objective of firm is sales maximization, the supply would be larger.
If the number of producers producing the same product increases, the market supply
increases.
During inflationary period, if sellers expect a further rise in prices, supply will decrease
in the market.
Imposition of taxes by the government will reduce the supply.
Weather
Prices of related goods
Law of demand
Law of demand states that other things being equal demand increases when price falls and
contracts when price rises.
Market demand is the total quantity demanded by all the purchasers together.
Elasticity of Demand - Elasticity of demand may be defined as the degree of responsiveness of
quantity demanded to a Change in price.
An interesting aspect of the economy is that the demand and supply of a product are
interdependent and they are sensitive with respect to the price of that product.
From Fig. it is clear that when there is a decrease in the price of a product, the demand
for the product increases and its supply decreases.
Also, the product is more in demand and hence the demand of the product increases.
At the same time, lowering of the price of the product makes the producers restrain from
releasing more quantities of the product in the market.
Hence, the supply of the product is decreased. The point of intersection of the supply
curve and the demand curve is known as the equilibrium point.
At the price corresponding to this point, the quantity of supply is equal to the quantity of
demand. Hence, this point is called the equilibrium point.
Factors influencing demand
The shape of the demand curve is influenced by the following factors:
Income of the people
Prices of related goods
Tastes of consumers
Population and its distribution
Consumer’s expectations
Assumptions of Law of Demand
There is no change in consumers Tastes and preferences
Income of the people remains constant
Prices of other goods should not change
There is no substitute for the commodity
The commodity should not confer any distinction
The demand for the commodity is continuous
People should not expect any change in the price of the commodity
1.5 CONCEPT OF ENGINEERING ECONOMICS
Science is a field of study where the basic principles of different physical systems are
formulated and tested.
Engineering is the application of science. It establishes varied application systems based
on different scientific principles.
From the discussions in the previous section, it is clear that price has a major role in
deciding the demand and supply of a product.
Hence, from the organization’s point of view, efficient and effective functioning of the
organization would certainly help it to provide goods/services at a lower cost which in
turn will enable it to fix a lower price for its goods or services.
The following section discusses the different types of efficiency and their impact on the
operation of businesses and the definition and scope of engineering economics.
.
1.6 TYPES OF EFFICIENCY
Efficiency of a system is generally defined as the ratio of its output to input. The efficiency can
be classified into technical efficiency and economic efficiency.
Technical efficiency
It is the ratio of the output to input of a physical system. The physical system may be a diesel
engine, a machine working in a shop floor, a furnace, etc.
The technical efficiency of a diesel engine is as follows:
In practice, technical efficiency can never be more than 100%.
This is mainly due to frictional loss and incomplete combustion of fuel, which are considered to
be unavoidable phenomena in the working of a diesel engine.
Economic efficiency
Economic efficiency is the ratio of output to input of a business system.
‘Worth’ is the annual revenue generated by way of operating the business and ‘cost’ is the total
annual expenses incurred in carrying out the business. For the survival and growth of any
business, the economic efficiency should be more than 100%.
Economic efficiency is also called ‘productivity’. There are several ways of improving
productivity.
Increased output for the same input
Decreased input for the same output
By a proportionate increase in the output which is more than the proportionate increase in
the input
By a proportionate decrease in the input which is more than the proportionate decrease in
the output
Through simultaneous increase in the output with decrease in the input.
1.7 DEFINITION AND SCOPE OF ENGINEERING ECONOMICS
As stated earlier, efficient functioning of any business organization would enable it to provide
goods/services at a lower price.
In the process of managing organizations, the managers at different levels should take
appropriate economic decisions which will help in minimizing investment, operating and
maintenance expenditures besides increasing the revenue, savings and other related gains of the
organization.
Definition
Engineering economics deals with the methods that enable one to take economic decisions
towards minimizing costs and/or maximizing benefits to business organizations.
Scope
The issues that are covered are elementary economic analysis, interest formulae, bases for
comparing alternatives, present worth method, future worth method, annual equivalent method,
rate of return method, replacement analysis, depreciation, evaluation of public alternatives,
inflation adjusted investment decisions, make or buy decisions, inventory control, project
management, value engineering, and linear programming.
1.8 ELEMENTS OF COSTS
Costing or cost accounting means classifying, recording and allocating the appropriate
expenditure for determining the cost of production and achieved by keeping a continuous record
of all the costs involved in manufacturing.
Costing or cost accounting gives the actual expenditure incurred on the production of the
component based on the records of expenditure on various activities involved.
Fixed Costs and Variable Costs:
The Fixed Costs are the items of expenditure which remain more or less constant irrespective of
the quantity or volume of production. Examples of fixed costs are: Supervisory charges, cost of
lighting, cost of cleaning the works, operator charges, rent of building, interest on capital,
depreciation of plant and building.
The Variable Costs are those items of expenditure which vary with quantity or volume of
production. Examples are: direct material cost, cost of energy or fuel consumed, cost of tools
used, cost of consumables, repair and maintenance charges and storage charges.
The total cost of the product can be divided into following two major groups:
Direct costs are costs of those factors which directly contribute to the final product and hence
can be directly charged or allocated to the manufacture of a specific product. Examples: cost of
raw materials, cost of labor processing the materials, cost of equipment and special tooling, jigs
and fixtures used in the manufacturing of the product.
Indirect costs are costs which cannot be directly allocated to the manufacture of a particular
product. Examples: Wages of inspection and supervisory staff, selling and distribution expenses,
administrative expenses, overhead charges, and cost of indirect materials like lubricants,
coolants, grease, repair and maintenance cost.
Elements of Cost: For the purpose of calculations, the total cost of the product is divided into
the following:
(A) Material cost, (B) Labor cost, (C) Other expenses.
(A) Material Cost
Material cost consists of the cost of materials which are used in the manufacture of product. It is
divided into the following:
Direct material cost: It is the cost of those materials which are directly used for the manufacture
of the product and become a part of the finished product. This expenditure can be directly
allocated and charged to the manufacture of a specific product or job and includes the scrap and
waste that has been cut away from original bar or casting.
Indirect material cost: In addition to direct materials a number of other materials are necessary
to help in the conversion of direct materials into final shape. Though these materials are
consumed in the production, they don’t become a part of the finished product and their cost
cannot be directly booked to the manufacture of a specific product. Such materials are called
indirect materials. The indirect materials include oils, general tools, grease, sand papers,
coolants, cotton waste etc. The cost associated with indirect materials is called indirect material
cost.
In some cases certain direct materials like nails, screws, glue, putty etc., are used in such small
quantity that it is not considered worthwhile to identify and charge them as direct materials. In
such cases these materials are also charged as indirect materials.
(B) Labor Cost
It is the expenditure made on the salaries, wages, overtime, bonuses, etc. of the employees of the
enterprise. It can be classified as:
Direct labor cost: Direct laborer is one who actually works and processes the materials to
convert it into the final shape. The cost associated with direct labor is called direct labor cost.
The direct labor cost can be identified and allocated to the manufacture of a specific product.
Examples of the direct labor are the workers operating lathes, milling machines or welders, or
assemblers in assembly shop. The direct labor cost may be allocated to a product or job on the
basis of time spent by a worker on a job.
Indirect labor cost: Indirect laborer is one who is not directly employed in the manufacturing of
the product but his services are used in some indirect manner. The indirect labor includes
supervisors, inspectors, foreman, storekeeper, gatekeeper, maintenance staff, crane driver etc.
The cost associated with indirect labor is called indirect labor cost. The indirect labor costs
cannot be identified with a particular job or product but are charged on the total number of
products made during a particular period in a plant.
To make the concept of direct and indirect labor cost clear, consider an operator working on a
drilling machine. The operator in this case is direct labor whereas the man supervising the job,
inspector and storeman supplying the material are indirect labor.
(C) Other Expenses
In addition to the material cost and labor cost, several other expenses such as rent of building,
depreciation of plant and machinery, cost of packing materials, transport and distribution
expenses, wages and salaries of administrative staff and executives are also incurred by the
manufacturer. All this expenditure including the indirect material cost and indirect labor cost is
called other expenses.
Simply, we can say that except direct material and direct labor costs all other expenditure
incurred by the manufacturer is known as “Other Expenses”. Expenses are further classified as:
(a) Direct expenses: Direct expenses include all that expenditure which can be directly allocated
and charged to a particular job. The direct expenses include cost of special jigs or fixtures,
patterns, tooling made for job, or cost of research and development work done for that specific
job.
(b) Indirect expenses: Except direct expenses, all other indirect expenditure incurred by the
manufacturer is called indirect expenses. The indirect expenses are also called overhead
expenses or on-cost.
The indirect expenses are further classified as:
(i) Factory expenses.
(ii) Administrative expenses.
(iii) Selling and distribution expenses.
(i) Factory expenses: Factory expenses comprise of the indirect expenses incurred from the
receipt of the order to the completion of production. In addition to indirect material and indirect
labor cost it includes rent of factory building, license fee, electricity and telephone bills of
factory, insurance charges etc.
Factory expenses are also called “Works expenses”, or “Factory or Works overhead”.
(ii) Administrative expenses: Administrative expenses or office expenses include the
expenditure incurred on control and administration of the factory. It includes the salaries of
office and administrative staff, rent of office building, postage and telephone charges, water and
electricity charges for office, Director’s fee, legal and audit charges etc. Administrative expenses
are also known as ‘Administrative overheads’.
(c) Selling and distribution expenses: This is the expenditure incurred on Sales Department for
selling the product, i.e., wages, salaries, commission and travelling allowances of salesmen and
officers in Sales Department, cost of advertisement, packing, delivery and distribution expenses,
rent of warehouses etc.
1.9 COST OF PRODUCT (LADDER OF COSTS)
The components of cost discussed above can be grouped as follows:
1. Prime cost = Direct material cost + Direct labour cost + Direct expenses
2. Factory cost = Prime cost + Factory expenses
3. Production cost = Factory cost + Administrative expenses
4. Total or Ultimate cost = Production cost + Selling and distribution expenses.
5. Selling price = Ultimate cost + Profit
The above relations can be illustrated on a chart (Ladder of costs)
1.10 EXAMPLES
1. Calculate prime cost, factory cost, production cost, total cost and selling price per item from
the data given below for the year 2003-04:
Particulars Rs.
Cost of raw material in stock as on 1-04-2003 25,000
Raw material purchased 40,000
Direct labor cost 14,000
Direct expenses 1,000
Factory / Works overhead 9,750
Administrative expenditure 6,500
Selling and distribution expenses 3,250
No. of items produced 650
Cost of raw material in stock as on 31-03-2004 15,000
Net profit/item is 10 percent of total cost of the product.
Solution:
For 650 units produced during 2003-04
(i) Direct material used = Stock of raw material on 1-04-2003 + raw material purchased
– Stock of raw material on 31-03-2004 = 25,000 + 40,000 – 15,000 = Rs. 50,000
(ii) Direct labor = Rs. 14,000
(iii) Direct expenses = Rs. 1,000
Prime cost = 50,000 + 14,000 + 1,000 = Rs. 65,000
Factory cost = Prime cost + Factory expenses = 65,000 + 9,750 = Rs. 74,750
Production cost = Factory cost + Administrative expenses = 74,750 + 6,500 = Rs. 81,250
Total cost = Production cost + Selling expenses = 81,250 + 3,250 = Rs. 84,500
Selling price = 84,500 + 10 percent of 84,500 = 84,500 × 1.10 = Rs. 92,950
Prime cost/item = 65,000 / 650 = Rs. 100
Factory cost/item = 74,750 / 650 = Rs. 115
Production cost/item = 81,250 / 650 = Rs. 125
Total cost/item = 84,500 / 650 = Rs. 130
Selling price/item = 92,950 / 650 = Rs. 143
2. From the following data for a sewing machine manufacturer, prepare a statement showing
prime cost, Works/factory cost, production cost, total cost and profit.
Particulars Rs.
Value of stock of material as on 1-04-2003 26,000
Material purchased 2,74,000
Wages to labor 1,20,000
Depreciation of plant and machinery 8,000
Depreciation of office equipment 2,000
Rent, taxes and insurance of factory 16,000
General administrative expenses 3,400
Water, power and telephone bills of factory 9,600
Water, lighting and telephone bills of office 2,500
Material transportation in factory 2,000
Insurance and rent of office building 2,000
Direct expenses 5,000
Commission and pay of salesman 10,500
Repair and maintenance of plant 1,000
Works Manager salary 30,000
Salary of office staff 60,000
Value of stock of material as on 31-03-2004 36,000
Sale of products 6,36,000
Solution:
(i) Material cost = Opening stock value + Material purchases – Closing balance
= 26,000 + 2,74,000 – 36,000 = Rs. 2,64,000
Prime cost = Direct material cost + Direct labor cost + Direct expenses
= 2,64,000 + 1,20,000 + 5,000 = Rs. 3,89,000
(ii) Factory overheads are:
Rent 16,000
Depreciation of plant and machinery 8,000
Water, power and telephone bills of factory 9,600
Material transportation in factory 2,000
Repair and maintenance of plant 1,000
Work Manager salary 30,000
Factory overheads 66,600
Factory cost = Prime cost + Factory expenses = 3,89,000 + 66,600 = Rs. 4,55,600
(iii) Administrative/office expenses are:
Depreciation of office equipment 2,000
General administrative expenses 3,400
Water, lighting and telephone bills of office 2,500
Rent, insurance and taxes on office building 2,000
Salary of office staff 60,000
Office expenses 69,900
Production cost = Factory cost + Office expenses = Rs. 4,55,600 + Rs. 69,900 = Rs. 5,25,500
(iv)Selling overheads are:
Commission and pay to salesmen = Rs. 10,500
Total cost = Production cost + Selling expenses = 5,25,500 + 10,500 = Rs. 5,36,000
(v) Profit = Sales – Total cost = 6,36,000 – 5,36,000 = Rs. 1,00,000
1.11 OTHER COST
1. Marginal Cost
Marginal cost of a product is the cost of producing an additional unit of that product. Let the cost
of producing 20 units of a product be Rs. 10,000, and the cost of producing 21 units of the same
product be Rs. 10,045. Then the marginal cost of producing the 21st unit is Rs. 45.
2. Marginal Revenue
Marginal revenue of a product is the incremental revenue of selling an additional unit of that
product. Let, the revenue of selling 20 units of a product be Rs. 15,000 and the revenue of selling
21 units of the same product be Rs. 15,085. Then, the marginal revenue of selling the 21st unit is
Rs. 85.
3. Sunk Cost
This is known as the past cost of an equipment/asset. Let us assume that an equipment has been
purchased for Rs. 1,00,000 about three years back. If it is considered for replacement, then its
present value is not Rs. 1,00,000. Instead, its present market value should be taken as the present
value of the equipment for further analysis. So, the purchase value of the equipment in the past is
known as its sunk cost. The sunk cost should not be considered for any analysis done from now
onwards.
4. Opportunity Cost
In practice, if an alternative (X) is selected from a set of competing alternatives (X, Y), then the
corresponding investment in the selected alternative is not available for any other purpose. If the
same money is invested in some other alternative (Y), it may fetch some return. Since the money
is invested in the selected alternative (X), one has to forego the return from the other alternative
(Y). The amount that is foregone by not investing in the other alternative (Y) is known as the
opportunity cost of the selected alternative (X). So the opportunity cost of an alternative is the
return that will be foregone by not investing the same money in another alternative.
Consider that a person has invested a sum of Rs. 50,000 in shares. Let the expected annual return
by this alternative be Rs. 7,500. If the same amount is invested in a fixed deposit, a bank will pay
a return of 18%. Then, the corresponding total return per year for the investment in the bank is
Rs. 9,000. This return is greater than the return from shares. The foregone excess return of Rs.
1,500 by way of not investing in the bank is the opportunity cost of investing in shares.
1.12 TERMS USED IN BREAK-EVEN ANALYSIS
(i) Fixed cost: Fixed costs remain fixed in the short-run. Examples are rent, insurance,
depreciation, factory supervisor's salaries, directors' salaries, and so on.
(ii) Variable costs: The variable cost per unit varies with the volume of production. The variable
costs include cost of direct materials, direct labor, direct expenses and operating supplies such as
lubricating oil and so on.
(iii) Total cost: The total of fixed and variable costs.
(iv) Total revenue: The sales proceeds (selling price per unit x number of units sold).
(v) Contribution margin: The contribution margin is the difference between the selling price per
unit and the variable cost per unit. It is also determined as (fixed cost per unit +profit per unit).
(vi) Profit = Contribution - Fixed cost.
(vii) Contribution margin ratio: It is the ratio between contribution per unit and the selling price
per unit.
(viii) Margin of safety in units: The excess of actual sales (in units) minus the breakeven point
(in units).
(ix) Margin of safety in sales volume: The excess of actual sales (in rupees) minus the break-
even point (in rupees).
(x) Angle of incidence: The angle formed where total cost curve cuts the total revenue curve
(xi) PN ratio: The ratio between the contribution and sales.
1.13 ASSUMPTIONS IN THE BREAK-EVEN ANALYSIS
The following assumptions are made while plotting a break-even chart:
The total cost of production can be divided into two categories - (a) Fixed cost, (b)
Variable cost.
Fixed cost remains constant i.e., it is independent of the quantity produced and includes
executive’s salaries, rent of building, depreciation of plant and equipment etc.
The variable cost varies directly and proportionately with the volume of production. If
V = Variable cost per unit and Q is the quantity produced, variable cost = V x Q.
The selling price does not change with change in the volume of sales. If P is the selling
price per unit, the total sales income = P x Q.
The firm deals with only one product, or the sales mix remains unchanged.
There is a perfect synchronization between production and sales. This assumes that
everything produced is sold and there is no change in the inventory of finished goods.
Productivity per worker and efficiency of plant, etc., remains mostly unchanged.
Any change in anyone of the above factors will affect the break-even point and the profits will be
affected by factors other than volume. Hence, the result of the break-even analysis should be
interpreted subject to the limitations of the above assumptions.
1.14 PLOTTING THE BREAK-EVENCHART
The cost and the sales income (revenue) in rupees are plotted along the vertical axis.
The quantity (volume of production) is plotted along the horizontal axis.
Fixed cost is represented by a straight line parallel to the horizontal axis.
The variable costs are superimposed upon the horizontal line representing the fixed cost.
This top line then represents the total cost line.
The sales income line passes through the origin.
The point of intersection of the sales income line and the total cost line represents the
break-even point.
The shaded area between the total cost line and the sales income line on the left hand side
of B.E.P. indicates loss; whereas the shaded area on the right hand side of B.E.P. shows
profit.
1.15 Break-Even Analysis
The main objective of break-even analysis is to find the cut-off production volume from where a
firm will make profit.
Let s = selling price per unit
v = variable cost per unit
FC = fixed cost per period
Q = volume of production
The total sales revenue (S) of the firm is given by the following formula:
S = s Q
The total cost of the firm for a given production volume is given as
TC = Total variable cost + Fixed cost = v Q + FC
The linear plots of the above two equations are shown in Fig.
The intersection point of the total sales revenue line and the total cost line is called the
break-even point.
The corresponding volume of production on the X-axis is known as the break-even sales
quantity.
At the intersection point, the total cost is equal to the total revenue.
This point is also called the no-loss or no-gain situation.
For any production quantity which is less than the break-even quantity, the total cost is
more than the total revenue.
Hence, the firm will be making loss.
For any production quantity which is more than the break-even quantity, the total revenue will be
more than the total cost. Hence, the firm will be making profit.
Profit = Sales – (Fixed cost + Variable costs)
= s Q – (FC + v Q)
The formulae to find the break-even quantity and break-even sales quantity:
The contribution is the difference between the sales and the variable costs. The margin of safety
(M.S.) is the sales over and above the break-even sales. The formulae to compute these values
are
Contribution = Sales – Variable costs
Contribution/unit = Selling price/unit – Variable cost/unit
M.S. = Actual sales – Break-even sales
= Profit × sales / Contribution
M.S. as a per cent of sales = (M.S./Sales) 100
1.16 Break-even point
The point of intersection of the total cost line and the income line is called as the break-even
point. The break-even point is that junction here income and costs are exactly in balance. Thus
there is neither profit nor loss for that particular volume of production.
Break-even point indicates minimum operating level below which it is dangerous to fall. As the
performance reaches towards this non-profit point, corrective measures should be taken to cut
down the cost, (increase output or raise selling price.) The spread to the right of BEP shows the
profit potential while to the left represents the loss potential BEP is also called as the "no-profit-
no-loss point."
1.17 Margin of Safety
Margin of safety is the distance between the break-even point and the output being produced. A
large margin of safety indicates that the business can earn profit even if there is a great reduction
in output. If the margin of safety is relatively small then it indicates that the profit will be
considerably small even if there is a small drop in output. A low margin of safety level indicates
high fixed costs and profits are not possible unless the output level is sufficient enough to absorb
fixed costs.
Margin of safety is generally expressed as:
Ratio of budgeted sales to sales at BEP.
Ratio of actual sales to sales at BEP.
Percentage of budget to BEP.
Percentage of budget to actual sales at BEP.
Percentage of the difference between actual sales and break-even sales to budgeted sales.
In case unsatisfactory margin of safety the following measures should be taken:
Increase in the sale price.
Reduction in fixed costs.
Reduction in variable costs.
Increase in output.
Stop production of non-profitable items and pay more attention towards profitable items.
Mathematically:
Margin of Safety = (Sales - Sales at BEP / Sales) x 100
= Profit x Sales / (Sales - Variable costs)
1.18 Angle of Incidence
The angle between the sales income line and the total cost line is called as angle of incidence. A
large angle of incidence indicates large profit and extremely favorable business position
management aims to widen the angle of incidence to improve the rate of profitability. A narrow
angle shows that even though fixed overheads are recovered, the profit accrued shows a low rate
of return. This indicates a large part of variable costs in total cost.
1.10 Profit/Volume Ratio (P/V Ratio)
P/V ratio is a valid ratio which is useful for further analysis. Profit volume ratio measures the
profitability in relation to sales. The contribution at given output is defined to be the difference
between total sales and total variable costs. The P/V ratio is the ratio of contribution to sales. It
represents the relationship between contribution and turn-over. So, it is a measure to compare
profitability of different products. Higher the P/V ratio, the high yielding is the product.
The different formulae for the P/V ratio are as follows:
P/V ratio = Contribution / Sales = Sales − Variable costs / Sales
The relationship between BEP and P/V ratio is as follows:
BEP =Fixed cost / P/V ratio
Uses of P/V ratio
The P/V ratio can be used to study a variety of problems viz.:
Determination of B.E.P.
To know profit for given sales volume.
To now sales volume for achieving some desired profit.
P/V ratio can be increased by
Increasing the selling price.
Changing the mix of sales.
Reduction in variable costs.
1.19 ADVANTAGES OF BREAK-EVEN CHART
Management can employ break-even chart to project the cost and income picture under various
anticipated future conditions and for alternative business programme. Hence, the chart is useful
to the management.
To show the relative importance of different classes of costs, how they vary with volume
of production, and how they may be controlled.
To show the impact of changes in sales volume on profit.
To predict the effect of price and cost changes on the break-even point.
To show the gain needed in sales volume (or productivity) to maintain profits when
prices or costs change in a specific way e.g. when prices decline but wages and the cost
of material do not.
To select the proper size plant or to predict the effect of changes in plant size or
modernization of plant on the break-even point. Therefore, through break-even chart
management can estimate what amount of investment in plant capacity is economically
justified for the projected volume of sales.
To compare the profitability of two or more firms.
1.20 LIMITATIONS OF BREAK-EVEN ANALYSIS
In practice all the costs are not always either fixed costs or variable costs. There are some
semi-variable overhead costs.
In the long run all costs are variable, so the break-even analysis holds good only for short
run requirements.
Break even analysis assumes, that profits are a function of output ignoring the fact that
they are also affected by technological changes, improved management, improvement in
quality, versatility, etc.
It is suitable only when the firm produces one type of product.
1.21 APPLICATION OF BREAK-EVEN ANALYSIS
Make or Buy Decision
Choosing a Product Mix when there is a Limiting Factor
Drop or add decision
Impact of changes in cost or selling price on BEP
Determining the BEP when there is an increase in the fixed cost
1.22 EXAMPLE:
Alpha Associates has the following details:
Fixed cost = Rs. 20,00,000
Variable cost per unit = Rs. 100
Selling price per unit = Rs. 200
Find
(a) The break-even sales quantity,
(b) The break-even sales
(c) If the actual production quantity is 60,000, find (i) contribution; and (ii) margin of
safety by all methods.
Solution
Fixed cost (FC) = Rs. 20,00,000
Variable cost per unit (v) = Rs. 100
Selling price per unit (s) = Rs. 200
(a) Break-even quantity = FC / s – v = 20,00,000 / 100 = 20,000 units
(b) Break-even sales = (FC / s – v) x s = 20,000 x 200 = Rs. 40,00,000
(c) (i) Contribution = Sales – Variable cost = s x Q – v x Q = 200 x 60000 – 100 x 60000
= 1,20,00,000 – 60,00,000
= Rs. 60,00,000
(ii) Margin of safety M.S. = Sales – Break-even sales = 60,000 x 200 – 40,00,000 =
= Rs. 80,00,000
M.S. as a per cent of sales = 80,00,000 / 1,20,00,000 x 100 = 67%
1.23 Elementary Economic Analysis
Whether it is a business situation or a day-to-day event in somebody’s personal life, there are a
large number of economic decisions making involved. One can manage many of these decision
problems by using simple economic analysis.
For example, an industry can source its raw materials from a nearby place or from a far-off
place. In this problem, the following factors will affect the decision:
Price of the raw material
Transportation cost of the raw material
Availability of the raw material
Quality of the raw material
Consider the alternative of sourcing raw materials from a nearby place with the following
characteristics:
The raw material is more costly in the nearby area.
The availability of the raw material is not sufficient enough to support the operation of
the industry throughout the year.
The raw material requires pre-processing before it is used in the production process. This
would certainly add cost to the product.
The cost of transportation is minimal under this alternative.
On the other hand, consider another alternative of sourcing the raw materials from a far-off place
with the following characteristics:
The raw material is less costly at the far off place.
The cost of transportation is very high.
The availability of the raw material at this site is abundant and it can support the plant
throughout the year.
The raw material from this site does not require any preprocessing before using it for
production
1.24 EXAMPLES FOR SIMPLE ECONOMIC ANALYSIS
In this section, the concept of simple economic analysis is illustrated using suitable examples in
the following areas:
Material selection for a product
Design selection for a product
Design selection for a process industry
Building material selection for construction activities
Process planning/Process modification
1.24.1 Material Selection for a Product/Substitution Of Raw Material
The cost of a product can be reduced greatly by substitution of the raw materials. Among various
elements of cost, raw material cost is most significant and it forms a major portion of the total
cost of any product.
So, any attempt to find a suitable raw material will bring a reduction in the total cost in any one
or combinations of the following ways:
Reduced machining/process time
Enhanced durability of the product
Cheaper raw material price
Therefore, the process of raw material selection/substitution will result in finding an alternate
raw material which will provide the necessary functions that are provided by the raw material
that is presently used.
In this process, if the new raw material provides any additional benefit, then it should be treated
as its welcoming feature.
EXAMPLE
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?
Solution:
(a) Cost of using aluminium metal for the jet engine part:
Weight of aluminium casting/unit = 1.2 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 x1.2 + 150 = 96 + 150 = Rs. 246
(b) Cost of jet engine part made of steel/unit:
Weight of steel casting/unit = 1.35 kg
Cost 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 x 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
1.24.2 Design Selection for a Product
The design modification of a product may result in reduced raw material requirements, increased
machinability of the materials and reduced labor.
Design is an important factor which decides the cost of the product for a specified level of
performance of that product.
The elementary economic analysis applied to the selection of design for a product is illustrated
with example problems.
EXAMPLE
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 labor is Rs. 200 per hour. The operating cost of the grinder
including labor is Rs. 150 per hour. Which design should be adopted if 1,00,000 units are
required per year and what is the economic advantage of the best alternative?
Solution
Operating cost of lathe including labor = Rs. 200 per hr
Operating cost of grinder including labor = Rs. 150 per hr
(a) Cost of design A
No. of hours of lathe time per 1,000 units = 16 hr
No. of hours of grinder time per 1,000 units = 4.5 hr
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 x 200 + 4.5 x 150 = Rs. 3,875
Total cost of design A/1,00,000 units = 3,875 x 1,00,000/1,000 = Rs. 3,87,500
(b) Cost of design B
No. of hours of lathe time per 1,000 units = 7 hr
No. of hours of grinder time per 1,000 units = 12 hr
Total cost of design B/1,000 units = Cost of lathe operation/1,000 units + Cost of grinder
operation/1,000 units
= 7 x 200 + 12 x 150 = Rs. 3,200
Total cost of design B/1,00,000 units = 3,200 x 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.
1.25 Process Planning
Process plan
It is the detailed instructions for making a part or a component. It includes such information as
the operations, their sequence, machines, tools, speeds and feeds, dimensions, tolerances, stock
removed, inspection procedures and time standards (i.e., cycle time).
Process planning
It may be defined as the determination of the processes and the sequence of operations required
for making the product. It consists of devising, selecting and specifying processes, machine tools
and other equipment to transform the raw material into finished product as per the specifications
called for by the drawings.
Process planning can be defined as an act of preparing a detailed processing documentation for
the manufacture of a piece part or assembly.
Process Planning Activities
Analysis of the finished part requirements as specified in the engineering design
Determining the sequence of operation required
Selecting the proper equipment to accomplish the required operations
Calculating the specific operation setup times and cycle times on each machine
Documenting the established process plans
Communicating the manufacturing knowledge to the shop floor
1. Analyze finished part requirements
Component drawing should be analyzed to identify its features, dimensions, and
tolerance specifications
Part’s requirement defined by its features, dimensions, and tolerance specifications will
determine corresponding processing requirements
2. Determine operating sequence
Basic aim is to determine the type of processing operation that has the capability to
generate various types of features, given the tolerance requirements
There are two ways of viewing decision process
First view is to consider processing evaluation of part from rough state to finished final
state. In this view material is removed or modified on rough part in stages in order to
transform it into finished part
Second view is to consider part evaluation from finished state back to rough/ initial state.
In this view material is added back onto the part.
3. Select machines
Machine selection requires determining how the part would be processed on each of the
alternative machines so that best machine can be selected
At this phase, firm has to decide whether to make or buy the component part
Break even analysis is most convenient method for selecting optimum method of
manufacture or machine amongst the competing ones
Factures which influence the selection of machine are,
Ø Economic considerations
Ø Production rate and unit cost of production
Ø Durability and dependability
Ø Lower process rejection
Ø Minimum set-up and put away times
Ø Longer productive life of machines or equipment
Ø Functional versatility
4. Material selection parameters
Function
Appearance
Reliability
Service life
Environment
Compatibility
Productivity
Cost
5. Calculate processing time
Determination of set-up times requires knowledge of available tooling and sequence of
steps necessary to prepare the machine for processing given work piece
For establishing accurate set-up times, detailed knowledge of equipment capacity,
tooling, and shop practice required
Calculation of part processing time requires determination of sequence of processing
steps on each machine. This is called as OUTPLANNING
After calculation of processing time, appropriate times for loading, part unloading,
machine indexing, and other factors involved in one complete cycle for processing a part
must be included to compute the expected machine cycle time
Allowances are added with machine cycle time to calculate standard cycle time for
processing one piece
Appropriate machine rates are added with calculated cycle time to calculate expected
standard cost for given operation
6. Document process planning
Process plan is documented as job routing or operation sheet
Operation sheet also called “route sheet”, “instruction sheet”, “traveler”, “planner”
Information provided by route sheet are,
Ø Part identification
Ø Description of processing steps in each operation
Ø Operation sequence and machines
Ø Standard set-up and cycle times
Ø Tooling requirements for each operation
Ø Production control information showing the planning lead time at each operation
Reasons for documentation
To have a record on hoe a part is processed in order to plan future parts with similar
design requirements in a consistent manner
To provide a record for future job quoting, cost estimating, and standard costing systems
To act as a vehicle for communication
7. Communicate process knowledge
Communication is essential to ensure that part will be processed according to most
economical way
Process documentation and communication provide basis for improved part consistency
and quality in manufacturing
Process Planning Sheet
The whole information determined by the process planning is recorded in a tabular form in a
sheet called process planning sheet. This document is provided to the shop personnel for their
use. The character of this sheet will vary for different organizations depending upon the
production conditions and degree of details required.
In general the following data is listed for each component of the product in the process sheet.
Information regarding the main product, of which the component being manufactured is a
part i.e., name and part number of the main product.
Name, part number, drawing number of the component and number off i.e., no. of
components required per product.
Information concerning the blank i.e., raw material used, size and weight of stock.
Operations are listed in proper sequence along with the shops in which these operations
will be performed.
Information regarding machines used for each operation.
Data on jigs, fixtures and other special tools required.
Inspection devices needed for inspection.
Cutting data i.e., speeds, feeds & depth of cut for each machining operation.
Elements of standard time such as set-up time, handling time and machining time for the
job.
A typical process sheet is shown in Table.
The process planning sheet is prepared by the process engineer in consultation with the
tool engineer, industrial engineer, or methods engineer.
USES OF PROCESS SHEET
A process sheet is a very important document which forms a basis for all planning,
scheduling and dispatching functions.
Also it helps in advance planning and for purchase of raw materials design and
manufacture of special tools, jigs, fixtures and inspection devices.
It helps in estimating the cost of the product before it is an actually manufactured.
It also helps in planning for man power required for doing the job.
MG2451
ENGINEERING ECONOMICS AND COST ANALYSIS
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.
2.1 INTRODUCTION – Make or buy
In the process of carrying out business activities of an organization, a component/product can be
made within the organization or bought from a subcontractor. Each decision involves its own
costs.
So, in a given situation, the organization should evaluate each of the above make or buy
alternatives and then select the alternative which results in the lowest cost. This is an important
decision since it affects the productivity of the organization.
In the long run, the make or buy decision is not static. The make option of a component/product
may be economical today; but after some time, it may turn out to be uneconomical to make the
same.
Thus, the make or buy decision should be reviewed periodically, say, every 1 to 3 years. This is
mainly to cope with the changes in the level of competition and various other environmental
factors.
Make or Buy Decisions - is a determination whether to produce a component part internally or to
buy it from an outside supplier. The Organization should evaluate the costs and benefits of
manufacturing a product or product component against purchasing it and then select the
alternative which results in the lower cost.
2.1.1 CRITERIA FOR MAKE OR BUY
Criteria for make
The following are the criteria for make:
The finished product can be made cheaper by the firm than by outside suppliers.
The finished product is being manufactured only by a limited number of outside firms
which are unable to meet the demand.
The part has an importance for the firm and requires extremely close quality control.
The part can be manufactured with the firm’s existing facilities and similar to other items
in which the company has manufacturing experience.
Criteria for buy
The following are the criteria for buy:
Requires high investments on facilities which are already available at supplier’s plant.
The company does not have facilities to make it and there are more profitable
opportunities for investing company’s capital.
Existing facilities of the company can be used more economically to make other parts.
The skill of personnel employed by the company is not readily adaptable to make the
part.
Patent or other legal barriers prevent the company for making the part.
Demand for the part is either temporary or seasonal.
2.1.2 APPROACHES FOR MAKE OR BUY DECISION
Types of analysis followed in make or buy decision are as follows:
1. Simple cost analysis
2. Economic analysis
3. Break-even analysis
2.2INTRODUCTION- value analysis
Value analysis is one of the major techniques of cost reduction and cost prevention. It is a
disciplined approach that ensures necessary functions for minimum cost without sacrificing
quality, reliability, performance, and appearance. According to the Society of American Value
Engineers (SAVE), Value Analysis is the systematic application of recognized techniques which
identify the function of a product or service, establish a monetary value for the function and
provide the necessary function reliably at the lowest overall cost.
It is an organized approach to identify unnecessary costs associated with any product, material
part, component, system or service by analyzing the function and eliminating such costs without
impairing the quality, functional reliability, or the capacity of the product to give service.
2.2.1 WHEN TO APPLY VALUE ANALYSIS
One can definitely expect very good results by initiating a VA programme if one or more of the
following symptoms are present:
1. Company’s products show decline in sales.
2. Company’s prices are higher than those of its competitors.
3. Raw materials cost has grown disproportionate to the volume of production.
4. New designs are being introduced.
5. The cost of manufacture is rising disproportionate to the volume of production.
6. Rate of return on investment has a falling trend.
7. Inability of the firm to meet its delivery commitments.
2.2.2 Value Analysis vs. Value Engineering
Often the terms value analysis and value engineering are used synonymously. Though the
philosophy underlying the two is same, i.e. identification of unnecessary cost, yet they are
different. The difference lies in the time and the stage at which the techniques are applied.
Value analysis is the application of a set of techniques to an existing product with a view to
improve its value. It is thus a remedial process.
Value engineering is the application of exactly the same set of techniques to a new product at the
design stage, project concept or preliminary design when no hardware exists to ensure that bad
features are not added. Value engineering, therefore, is a preventive process.
2.2.3 Value
The term ‘value’ is used in different ways and, consequently, has different meanings. The
designer equates the value with reliability; a purchase person with price paid for the item; a
production person with what it costs to manufacture and a sales person with what the customer is
willing to pay.
Value, in value investigation, refers to “economic value”, which itself can be divided into four
types: cost value, exchange value, use value, and esteem value.
Cost value: It is the summation of the labor, material, overhead and all other elements of cost
required to produce an item or provide a service compared to a base.
Exchange value: It is the measure of all the properties, qualities and features of the product,
which make the product possible of being traded for another product or for money.
In a conventional sense, exchange value refers to the price that a purchaser will offer for the
product, the price being dependent upon satisfaction (value) which he derives from the product.
Value derived from the product consists of two parts “use value” and “esteem value”.
Esteem value: It involves the qualities and appearance of a product (like a TV set), which attract
persons and create in them a desire to possess the product.
Therefore, esteem value is the price paid by the buyer or the cost incurred by the manufacturer
beyond the use value.
Use value: It is known as the function value.
The use value is equal to the value of the functions performed. Therefore, it is the price paid by
the buyer (buyer’s view), or the cost incurred by the manufacturer (manufacturer’s view) in order
to ensure that the product performs its intended functions efficiently. The use value is the
fundamental form of economic value. An item without “use value” can have neither “exchange
value” nor “esteem value”.
2.2.4 Applications
The various application areas of value engineering are machine tool industries, industries making
accessories for machine tools, auto industries, import substitutes, etc
2.2.5 Performance
The performance of a product is the measure of functional features and properties that make it
suitable for a specific purpose. Appropriate performance requires that
(a) The product reliably accomplishes the intended use of work or service requirement
(functional requirements)
(b) The product provide protection against accident, harmful effects on body and danger to
human life (safety requirements)
(c) The product give trouble-free service cover during its specified life span (reliability
requirements)
(d) Service and maintenance work can be carried out on the product with ease and with simple
tools (maintainability requirements)
(e) Appearance of the product creates an impression on the buyer and induces in him or her the
desire to own the product (appearance requirements).
Performance and cost must be interwoven. Desired performance at the least cost should be
achieved by selecting appropriate materials and manufacturing operations, which is the measure
of value. Therefore, the value of the product is the ratio of performance (utility) to cost. Thus,
Value = Performance (utility) / Cost
Value can be increased by increasing the utility for the same cost or by decreasing the cost for
the same utility. Satisfactory performance at lesser cost through identification and development
of low cost alternatives is the philosophy of Value analysis.
2.3 FUNCTION
Function is the purpose for which the product is made. Identification of the basic functions and
determination of the cost currently being spent on them are the two major considerations of value
analysis.
Function identifies the characteristics which make the product/component/part/item/device to
work or sell. “Work functions” lend performance value while “sell functions” provide esteem
value.
Verbs like “support”, “hold”, “transmit”, “prevent”, “protect”, “exhibits”, “control”, etc., are
used to describe work functions, while “attract”, enhance”, “improve”, “create”, etc., are used to
describe “sell” functions. For example, in a “bus driver cabin”, the functional analysis of some of
the parts are given in Table
Component of study Functional analysis
Verb Noun Steering
Wheel Control Direction Gear box
Change Speed Brake system Stop
Vehicle Wiper Clear Water
Horn Make Sound
Side mirror Show Side traffic
2.3.1 Classification of the functions
Rarely do all functions assume equal importance. Usually, some functions are more important
than others. Functions can be classified into the following three categories:
1. Primary function
2. Secondary function
3. Tertiary function
1. Primary functions are the basic functions for which the product is specially designed to
achieve. Primary functions, therefore, are the most essential functions whose non-performance
would make the product worthless, e.g. a photo frame exhibits photographs, a chair supports
weight, a fluorescent tube gives light.
2. Secondary functions are those which, if not in-built, would not prevent the device from
performing its primary functions, e.g., arms of a chair provide support for hands. Secondary
functions are usually related to convenience. The product can still work and fulfill its intended
objective even if these functions are not inbuilt and yet they may be necessary to sell the product.
3. Tertiary functions are usually related to esteem appearance. For example, Sun mica top of a
table gives esteem appearance for the table.
2.4 Objectives of value engineering/value analysis
Increased profits – With the cost reduction of a product, the profits of an organization
increased. This results in time reduction. It also ensures greater returns on invested capital. The
competitive position of company also improves.
Improved product Design – With the modification in design, the customer will get a new and
more acceptable product.
Efficiency – It increases the efficiency of employees as it motivates them to come forward with
their creative ideas. It also makes contributions to improve human factors such as creativity,
team work and positive attitude among employees. The team approach also improves the
decision making.
Time consideration – A product has value for the customer if it is available to him on time. So
time element has great importance in value engineering. It may have no value if it arrives later.
Improvement in quality – This results in improvement in quality, reliability, performance and
maintainability of a product.
2.4.1 Aim / objectivesof value engineering/value analysis
The aims of value engineering are as follows:
1. Simplify the product.
2. Improves quality of the product.
3. Promotes standardization and production of quality products are economically achieved
4. Use (new) cheaper and better materials.
5. Modify and improve product design.
6. Improve organizational efficiency.
7. Develop logical approach to solve problems
8. Use efficient processes.
9. Reduce the product cost.
10. Increase the utility of the product by economical means.
11. Save money or increase the profits.
12. Ensures greater returns on investment.
The value content of each piece of a product is assessed using the following questions:
1. Does its use contribute to value?
2. Is its cost proportionate to its usefulness?
3. Does it need all its features?
These three questions pertain to the function of the part which may decide the elimination of
parts.
Is there anything better for the intended use?
Can company or vendor standard be used?
Can a usable part be made by a lower-cost method?
Is it made with the proper tooling, considering volume?
Does the part yield suitable profit?
Can another vendor furnish the same at a lower cost?
2.4.2 Advantages
The advantages of value engineering are as follows:
1. It is a much faster cost reduction technique.
2. It is a less expensive technique.
3. It reduces production costs and adds value to sales income of the product.
2.5 VALUE ANALYSIS PROCEDURE
Some of the most important phases that can be implemented in value analysis procedure are as
follows:
1. The Orientation Phase
2. The Information phase
3. Functional phase
4. Creation phase
5. Evaluation phase
6. Investigation phase
7. The Recommendation and Implementation phase.
1. The Orientation Phase:
In this phase the project for study is identified and selected. It is advisable to chose/select a
specific problem which is manageable e.g. it would be inadvisable to apply value analysis on a
whole car. The fuel injection system or clutch system may be a specific problem. Likewise do
not work on problem as a whole but break it into elements and study each element separately.
Constitute a team consisting of experts of various fields/departments such as from design, Sales
purchase and accounts etc. this phase can be represented as:
Identify and select ……………The project to be studied.
Establish ………………………… Priorities.
Plan …………………………………A specific project.
Constitute…………………………A team.
Prepare…………………………… Terms of reference for the selected project.
Fix …………………………………… Responsibility for data collection.
When we speak of a team, the emphasis is on team work which signifies the subordination or
personal preferences to group consensus.
2. Information phase:
Normally this phase consists of following three portions:
(i) Collection of facts:
This is probably the most tough task and all efforts should be made to collect all the relevant
information rather facts. These may relate to specifications; drawings parts, names of suppliers,
manufacturing methods use, used methods of purchase followed and annual requirements of
various items/materials etc. It should be ensured that information collected is based on facts only.
(ii) Determination of costs:
For each element being studied complete and accurate cost must be obtained. Considerable
importance should be given to the accuracy of these costs since these would form basis for value
analysis. The direct costs (e.g. labor, materials) for each of the assemblies, subassemblies and
parts of the project as well indirect cost (e.g. cost of indirect labor, Materials, jigs & fixtures,
packing materials etc.) should be taken into consideration.
(iii) Fixation of costs of specifications and requirements:
It has been observed that specifications and requirements are simply statements of the desired
results to be incorporated in the final product. Thus it is desirable to segregate the specifications
and actual requirement by analysis of the facts.
It is often found that over designing at the start of product development is a common
phenomenon. So it is essential to find out what s it that is really required. Thus requirements
should not be based on imposed specifications but oasis should be facts.
3. Function Phase:
The objectives of this phase are
To decide the area of analysis and the functions that it actually performs; because if the
value of an item/product is to be determined it is essential to determine its use or
function.
To relate these functions to the cost and worth of providing them; since the term
functions in “Value Analysis” means that which makes the product work or sell.
From the above, two important relations can be determined and these reveals the importance of
function.One is the relationship between value and function. Another relationship is between
work and sell.Here, the word “work” directly relates to “value” and the word “sell” relates
between value & function.
The rules of conation definitions are:
All the functions should be accomplished in two words-a-verb and a noun.
All the functions must be categorized into two levels of importance basis of primary and
secondary etc.
Basic are those which serve the primary purpose and secondary are those which serve other
purposes not directly accomplishing the basic but supporting it.
As per first rule the objective is to identify simply and unambiguously the tasks to be carried out
by the product/item under consideration. It is preferable if it is done in two words i.e. a verb and
a noun e.g. the various functions of a bulb are-gives light, removes darkness, illuminates space.
Increase visibility etc.
The work and sell functions are expressed by different categories of verbs and nouns: e.g. for
work functions we use action verbs (like support, create, enclose and insulate etc.) and
measurable nouns (like weight, current, density, force and voltage etc.) which establish
quantitative statements. For expressing sell functions; passive verbs (like increase, decrease,
improve etc.) and non measurable nouns (like beauty, convenience, style form and features etc.)
which establish qualitative statements.
After having defined the functions, the next step is to establish the worth of each basic
function.The objective of evaluating functional relationship is to:
Determine which the poor value functions are and whether the value analysis effort
should be continued.
Obtain a reference point from which the cost of alternatives can be compared.
Formulate a target cost, to provide a psychological incentive to discourage a premature
relaxation of the value analysis effort.
In this way establish descending order of importance of the functions with relative value of
importance.
4. Creation Phase:
In value analysis as in method study a persistent critical examination of facts is extremely
important. Creative phase objective is to produce ideas and to formulate alternative ways for
accomplishing the essential functions and improving the value of the problem under
consideration.
This effort starts as soon as enough information has been collected, reviewed and understood.
The first step is to ask and answer questions like:
WHAT (What is achieved)
WHY (Why is it essential)
HOW (How it is achieved?) Why that way?
WHERE (Where does it take place?) Why there?
WHEN (When is it done?) Why then?
WHO (Who does it?) Why that man?
Creative problem solving techniques are utilized to discover alternatives that will provide
essential or required functions at the lowest possible cost. Consider whether the function can be
eliminated whether it can be achieved in simpler way or it can be combined or integrated with
any other Isolate items/ components that contribute nothing to the use function e.g. consider if
the inspection can be eliminated or whether SOC can be replaced by 100% inspection or whether
the tolerances are realistic or if the reduced surface finish is acceptable.
Similarly as are materials concerned consider if.
Cheaper components/parts can be purchased from outside market instead of making.
Whether alternative cheaper materials can be used.
If the design changes can reduce the material used.
If the dimensions can be reduced.
If a new design can reduce the number of components used.
If redesign will combine two or more functions or will eliminate any component/part or
function.
If with redesign excess material, scrap or number of rejects will be reduced.
Thus creativity may be defined as the process of combining already existing elements into
something that is new as far as creator is concerned for the purpose of solving problems.
The followings are the simple steps in creative thinking:
(A) Identification of the problem:
Ask what is the problem
List out the objectives of the problem.
Define the situation of the problem.
Try to develop the challenges.
Define the problem in various ways and from several angles and then try to identify the
teal problem.
(B) Determination of the Facts:
Make all observations.
List out the elements of the problem.
Ask creative question such as what, when how, where, why and who.
Determine what is good regarding the problem,
Do not make assumptions.
Do not assume No without basis or beware of “automatic” No.
(C) Idea Determination:
Apply brain storming.
Use fertile imagination and do not judge the situation.
Incubate your ideas.
(D) Determination of Solution:
Evaluate your ail ideas.
Make a fair comparison.
Determine inter relationships
Anticipate objections if any.
Determine and develop place and time for appropriate action.
5. Evaluation Phase:
The objectives of evaluation phase are:
To select for further analysis the most promising of the ideas generated during the
creative phase.
To subject the ideas to a preliminary screening to identify those which satisfy the
following criteria?
Will the idea work?
Is it cheaper than present design?
Is it feasible to implement?
Will it satisfy the user requirements?
If the answer to any of the above is “no” can it be modified or combined with another to
give a yes answer.
To find out which is the most suitable proposal and obtain its cost?
The generation of a quantity of ideas does not accomplish anything until these ideas are put to
use. Before these can be utilized continued creativity must be applied. This may be done on a
single idea or a combination of ideas.
Now the estimated cost is to be determined on all ideas i.e. what will be the potential cost of
utilizing the ideas (under consideration) and what are the resultant savings implied. After that an
assessment of good and bad features of taking the lowest cost idea or group of ideas should be
made. Attempts should be made to by refinement of an idea and again evaluating it for the
purpose of minimization of bad features.
When such rough solutions along with their estimated costs are established, they are compared to
determine which one will provide the greatest possibility of attaining the value- level target. Now
the selection of ideas which are to be carried through further development is made. The
combined creative ideas that have been refined to basically workable solutions and have greatest
possible return on further investment are subjected to “investigation phase” techniques.
6. Investigation Phase:
The objectives of this phase are:
To bring partially developed or selected untried ideas to fruitarian and to find out their
feasibility and limitation.
To prepare a work plan for converting the selected ideas into tangible proposals.
In this phase, further refining of the selected ideas is made to convert them into workable and
salable solutions. Use company and industrial standards because within a standard lies a tried
and tested solution to a problem. This type of solution is utilized if it also the lowest total cost
approaches.
Adopt the following procedure:
(i) Consul specialists and vendors:
These people must always be consulted because of their specialized knowledge. They can
pinpoint problems in their specialized field and bring new information to effect the solution of
the problem.
(ii) Utilized specialty products, processes and procedures:
The use of these in many cases provide a lower cost way of providing the function or functions
These need evaluation and are utilized when they accomplish a lower total cost than would
standard products, processes and procedures.
7. Recommendation and Implementation Phase:
The objectives of this phase are:
To prepare and submit the planned proposals along with benefits and limitation to the
management.
To review submitted proposals if not acceptable to the management.
The recommendation phase and its included techniques are the culmination and warp up of all
the previous efforts exerted throughout the job plan. Upon these techniques and their diligent
fulfillment hinges success or failure of all the foregoing work. In this phase the selected
alternative is presented to the decision maker.
The selected proposal should contain an accurate description of the change as accurate cost,
whether estimate or factual must be presented as part of the final recommendation so as to
support the validity of the savings potential calculation.
The final recommendation need not in fact should contain all the data accumulated but should
however contain sufficient data for the decision maker to select the course of action to be taken.
After the recommendations have been carefully accepted, the implementation phase should be
carefully monitored and followed up by the value analysis team. It may be noted that most of the
value analysis projects collapse primarily due to the resistance to change by the actual users.
2.6. BASIC PRINCIPLES OF BRAIN STORMING
Some of the important principles of brain storming which are useful in creation phase of value
analysis are
(i) A quality idea comes from quantity of ideas. If the number of ideas generated is more, the
more good solutions do turn up.
(ii) Creative ideas emerge from unconventional thinking. This is possible when members of the
group “talk off the top of their heads” and voice weird ideas as they flash through their minds,
regardless of how stupid or impractical they may appear. Often, non-technical personnel can
prove to be the greatest innovators in technical areas since their viewpoints are objective and
they do not know that some of their ideas are technically not feasible at all. So it is preferable to
include one or two non-technical persons in the study team. Members are to be told by the team
leader in the beginning of the session itself, not to breathe a word of criticism of even the
weirdest idea.
(iii) Spontaneous evaluation of ideas curbs imaginative thinking and retards the flow of creative
ideas. The group should not evaluate the alternatives suggested by its member immediately since
immediate evaluation may curb imaginative thinking and slow down the flow of creative ideas.
(iv) Hitch-hiking on the ideas often leads to better ideas. Participants have to improve upon ideas
of other members either directly or by combining more ideas in addition to contributing ideas of
their own. A brilliant idea may not be a practical one initially, or it may look to be silly or useless
but discussions can convert it into a valuable one.
(v) Creativity is a regenerative process and the recording of ideas as they emerge helps serve as a
catalyst to generate more ideas. Memory may not retain all ideas or recall them when they are
needed. So, a stenographer may be asked to record ideas simultaneously. A tape recorder can
also be used for this purpose or even ideas can be written on a blackboard. These recorded ideas
can be reviewed at some later date.
(vi) When ideas cease to flow, short diversions enable the mind to rebound with new ideas after
recuperation. Members of the syndicate may reach a stage where new ideas do not come. At such
a stage, short diversions—rest, favorite sport, hobby, lunch or tea break, etc.—may be taken
during which members are advised to sleep over the ideas and report fresh after the break. Such
short diversions enable mind to recoup and rebound with new ideas.
2.7 INTEREST FORMULAS AND APPLICATIONS
2.7.1 INTRODUCTION
Interest rate is the rental value of money. It represents the growth of capital perunit period. The
period may be a month, a quarter, semiannual or a year. Aninterest rate 15% compounded
annually means that for every hundred rupeesinvested now, an amount of Rs. 15 will be added to
the account at the end ofthe first year. So, the total amount at the end of the first year will be Rs.
115.At the end of the second year, again 15% of Rs. 115, i.e. Rs. 17.25 will be addedto the
account. Hence the total amount at the end of the second year will beRs. 132.25. The process
will continue thus till the specified number of years.
2.7.2 TIME VALUE OF MONEY
If an investor invests a sum of Rs. 100 in a fixed deposit for five years with aninterest rate of
15% compounded annually, the accumulated amount at the endof every year will be as shown in
Table.
The formula to find the future worth in the third column is
F = P (1 + i)n
Where P = principal amount invested at time 0,
F = future amount
i = interest rate compounded annually,
n = period of deposit.
The maturity value at the end of the fifth year is Rs. 201.14. This means thatthe amount Rs.
201.14 at the end of the fifth year is equivalent to Rs. 100.00at time 0 (i.e. at present). This is
diagrammatically shown in Fig. Thisexplanation assumes that the inflation is at zero percentage.
Alternatively, the above concept may be discussed as follows: If we wantRs. 100.00 at the end of
the nth year, what is the amount that we should depositnow at a given interest rate, say 15%? A
detailed working is shown in Table 3.2
From Table 3.2, it is clear that if we want Rs. 100 at the end of the fifthyear, we should now
deposit an amount of Rs. 49.72. Similarly, if we wantRs. 100.00 at the end of the 10th year, we
should now deposit an amount ofRs. 24.72.
Also, this concept can be stated as follows:A person has received a prize from a finance
company during the recentfestival contest. But the prize will be given in either of the following
two modes:
1. Spot payment of Rs. 24.72 or
2. Rs. 100 after 10 years from now (this is based on 15% interest ratecompounded
annually).
If the prize winner has no better choice that can yield more than 15%interest rate compounded
annually, and if 15% compounded annually is thecommon interest rate paid in all the finance
companies, then it makes nodifference whether he receives Rs. 24.72 now or Rs. 100 after 10
years.
On the other hand, let us assume that the prize winner has his own businesswherein he can get a
yield of 24% interest rate (more than 15%) compoundedannually, it is better for him to receive
the prize money of Rs. 24.72 at presentand utilize it in his business. If this option is followed, the
equivalent amountfor Rs. 24.72 at the end of the 10th year is Rs. 212.45. This example
clearlydemonstrates the time value of money.
2.7.2 FORMULA
While making investment decisions, computations will be done in many ways. To simplify all
these computations, it is extremely important to know how to use interest formulas more
effectively. Before discussing the effective application of the interest formulas for investment-
decision making, the various interest formulas are presented first.
Interest rate can be classified into simple interest rate and compound interest rate.
In simple interest, the interest is calculated, based on the initial deposit for every interest period.
In this case, calculation of interest on interest is not applicable.
In compound interest, the interest for the current period is computed based on the amount
(principal plus interest up to the end of the previous period) at the beginning of the current
period.
The notations which are used in various interest formulae are as follows:
P = principal amount
n = No. of interest periods
i = interest rate (It may be compounded monthly, quarterly, semiannually or annually)
F = future amount at the end of year n
A = equal amount deposited at the end of every interest period
G = uniform amount which will be added/subtracted period after period to/ from the amount of
deposit A1 at the end of period 1
Single-Payment Compound Amount
Here, the objective is to find the single future sum (F) of the initial payment (P) made at time 0
after n periods at an interest rate i compounded every period.The cash flow diagram of this
situation is shown in Fig.
The formula to obtain the single-payment compound amount is
F = P(1 + i)n = P(F/P, i, n)
Where(F/P, i, n) is called as single-payment compound amount factor.
Single-Payment Present Worth Amount
Here, the objective is to find the present worth amount (P) of a single future sum(F) which will
be received after n periods at an interest rate of i compounded at the end of every interest
period.The corresponding cash flow diagram is shown in Fig.
The formula to obtain the present worth is
P = = F(P/F, i, n)
Where (P/F, i, n) is termed as single-payment present worth factor.
Equal-Payment Series Compound Amount
In this type of investment mode, the objective is to find the future worth of n equal payments
which are made at the end of every interest period till the end of the nth interest period at an
interest rate of i compounded at the end of each interest period. The corresponding cash flow
diagram is shown in Fig.
In Fig, A = equal amount deposited at the end of each interest period
n = No. of interest periods
i = rate of interest
F = single future amount
The formula to get F is
F =A = A(F/A, i, n)
Where (F/A, i, n) is termed as equal-payment series compound amount factor.
Equal-Payment Series Sinking Fund
In this type of investment mode, the objective is to find the equivalent amount (A) that should be
deposited at the end of every interest period for n interest periods to realize a future sum (F) at
the end of the nth interest period at an interest rate of i. The corresponding cash flow diagram is
shown in Fig.
In Fig. A = equal amount to be deposited at the end of each interest period
n = No. of interest periods
i = rate of interest
F = single future amount at the end of the nth period
The formula to get F is
A = F = F (A/F, i, n)
Where (A/F, i, n) is called as equal-payment series sinking fund factor.
Equal-Payment Series Present Worth Amount
The objective of this mode of investment is to find the present worth of an equal payment made
at the end of every interest period for n interest periods at an interest rate of i compounded at the
end of every interest period. The corresponding cash flow diagram is shown in Fig.
Here, P = present worth
A = annual equivalent payment
i = interest rate
n = No. of interest periods
The formula to compute P is
P = A = A (P/A, i, n)
Where (P/A, i, n) is called equal-payment series present worth factor.
Equal-Payment Series Capital Recovery Amount
The objective of this mode of investment is to find the annual equivalent amount (A) which is to
be recovered at the end of every interest period for n interest periods for a loan (P) which is
sanctioned now at an interest rate of I compounded at the end of every interest period.
In Fig P = present worth (loan amount)
A = annual equivalent payment (recovery amount)
i = interest rate
n = No. of interest periods
The formula to compute P is as follows:
A = P = P(A/P, i, n)
Where,
(A/P, i, n) is called equal-payment series capital recovery factor.
Uniform Gradient Series Annual Equivalent Amount
The objective of this mode of investment is to find the annual equivalent amount of a series with
an amount A1 at the end of the first year and with an equal increment (G) at the end of each of
the following n – 1 years with an interest rate i compounded annually. The corresponding cash
flow diagram is shown in Fig.
The formula to compute A under this situation is
A = A1 + G‒
Where(A/G, i, n) is called uniform gradient series factor.
Effective Interest Rate
Let i be the nominal interest rate compounded annually. But, in practice, the compounding may
occur less than a year. For example, compounding may be monthly, quarterly, or semi-annually.
Compounding monthly means that the interest is computed at the end of every month. There are
12 interest periods in a year if the interest is compounded monthly. Under such situations, the
formula to compute the effective interest rate, which is compounded annually, is
Effective interest rate, R = (1 + i/ C )C− 1
Where, i = the nominal interest rate
C = the number of interest periods in a year.
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MG2451
ENGINEERING ECONOMICS AND COST ANALYSIS
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.
3.1 INTRODUCTION
The primary objective of the traditional Income Statement and Balance Sheet is to report to the
interested parties the operational performance and economic position of an enterprise. An
intelligent reader can gather sufficient idea about costs, revenues, profit/loss assets, liabilities and
owners equity from these statements. Under the Companies Act, a company is required to
include the figures of previous year in the financial accounts so that the interested parties may
compare individual figures for better understanding of the corporate performance and economic
position. The schedules attached to published account explain important items for the knowledge
of the concerning parties. The format of published accounts has been revised from time to time
with a view to providing more and more information to the shareholders, creditors and others.
Nobody can deny the usefulness of the traditional form of annual accounts which form an
important basis for making financial decisions.
No doubt the annual accounts in their traditional forms are very important but they suffer from
certain limitations. The serious limitation of a Balance Sheet is that it is a static document as it
shows the economic position at a point of time and fails to show fully the movements or changes
in the assets, liabilities and owners equity. From the financial accounts in their usual form, it is
not clear as to how the funds were generated and how they were utilized between the closing
dates of two Balance Sheets. In order to provide such information, another document known as
Statement of Changes in Financial Position is prepared. This document shows the changes in the
financial position between the closing dates of the Balance Sheets.
In this connection it is important to understand clearly the meaning of the word 'Fund' which is
used in three different senses. In a narrow sense, fund means each and the statement based on
this concept is known as Cash Flow Statement. In a broader sense, fund means all financial
resources which flows through working capital accounts and fixed capital accounts and a fund
flow statement based on this concept is almost a new form of Balance Sheet. The APB
(Accounting Principles Board, U.S.A.) has recommended the preparation and presentation of
statement of changes in financial position according to the broadest sense of the term 'Fund.'
However, the meaning of the 'Fund' in both the narrow as well as broader senses do not find
favor with many academicians and practitioners who prefer to consider Fund in the sense of
Working Capital i.e., Current assets minus Current liabilities. In this chapter, we shall illustrate
the preparation of statement of changes is financial position based on all the three concepts of
Fund.
Funds Flow Statement is known by different names such as: (i) Where Got Where Gone
Statement, (ii) Statement of sources and application of funds, (iii) Statement of changes in
working capital, (iv) Statement showing summary of financial operations, (v) Statement of
sources and application of working capital, (vi) Statement of changes in financial position, (vii)
Funds Flow statement, etc. It may be noted that there is no official name of the statement as its
preparation is still obligatory. Only few enlightened firms in India publish this statement for the
guidance of their members and creditors. However, it is advisable that the title of the statement
reflects the concept of fund on which it is based.
3.2 CASH FLOW STATEMENT
We have seen the preparation of Funds Flow Statement which treated 'Fund’ in the sense of
working capital. The statement of changes in financial position can also be prepared on the basis
of the cash concept of the word 'Fund.' It is knows as Cash Flow Statement if Fund is considered
in the sense of cash.
The preparation of Cash Flow Statement is important to understand the paradoxical situation in
which a firm finds difficulty in honoring its short period business commitments despite the
existence of sufficient working capital as indicated by the Fund Flow Statement (working capital
basis). This happens when a large proportion of working capital is tied up in the form of
inventories and other working assets.
The Fund Flow Statement based on working capital concept does not take into account the
qualitative structure of working capital.
Cash is a peculiar component of working capital. It should be distinguished from other
components in any scheme of short-period financial planning. The Cash Flow Statement enables
a firm to know the availability of cash from different sources and the manner of its utilization.
A projected Cash Flow Statement tells the management about the case position at different
timings. The management can arrange for additional necessary cash in case cash outflow exceeds
the cash inflow in any particular period of time. Similarly surplus cash, if any, can be invested
for effective utilization of cash balances.
3.3 CONSTRUCTION OF CASH FLOW STATEMENT
A Cash Flow Statement is prepared to show the movements of cash between the closing dates of
two Balance Sheets. It starts from the opening cash and ends with the closing balance of cash
showing different sources from where cash was received and the manner in which it was utilized
during the period for which Cash Flow Statement is prepared. The usual transactions resulting in
cash inflows are:
Issue of shares;
Issue of debentures;
Sale of investments;
Sale of assets;
Cash from business operations.
Cash outflows due to its application for various purposes such as-(a) Redemption of preference
shares, (b) Redemption of debentures, (c) Repayment of loans, (d) Payment of taxes, (e) Payment
of dividend, (f) Cash losses due to operations.
The preparation of Cash Flow Statement is not difficult if a complete set of information in the
form of Profit and Loss Account and Balance Sheet is given. An increase of share capital,
debentures and loans clearly means that cash inflow took place due to additional issue of shares
and debentures and obtaining further loans during the year. A decrease in current year’s figures
of the liabilities will mean liquidation of liabilities and hence an application of cash.
A comparison of non-current assets like Land and Buildings, plant and machinery, furniture,
trade investment, etc. will tell whether there had been increase or decrease in cash or an item
resulted in cash inflow or cash outflow. For instance, an increase in current year's amount of
furniture clearly means cash outflow due to purchase of additional furniture. Conversely, a
decrease in current years amount of furniture means sale and hence an application of cash. We
have already seen how variations in non-current assets and liabilities generate or use funds
(cash). Again the general rules can be laid down as under:
Increase in Non-current liability = Cash Inflow, Decrease in Non-current liability = Cash
Outflow
Increase in Non-current asset = Cash Outflow, Decrease in Non-current asset= Cash Inflow
Note: The net cash inflow or outflow can be arrived at only after preparing the relevant account
by allowing for appropriate adjustments, if any.
3.4. FORMAT OF A CASH FLOW STATEMENT
A cash flow statement can be prepared in the following form:
3.5 DIFFERENCE BETWEEN CASH FLOW ANALYSIS AND FUND FLOW
ANALYSIS
Following are the points of difference between Cash Flow Analysis and a Funds Flow Analysis.
1. A Cash Flow Statement is concerned only with the change in cash position while a Fund Flow
Analysis is concerned with change in working capital position between two balance sheet dates.
Cash is only one of the constituents of working capital besides several other constituents such as
inventories, accounts receivable, prepaid expenses.
2. A Cash Flow Statement is merely a record of cash receipts and disbursements. Of course, it is
valuable in its own way but it fails to bring to light many important changes involving the
disposition of resources. While studying the sort-term solvency of a business one is interested
not only in cash balance but also in the assets which can be easily converted into cash.
3. Cash flow analysis is more useful to the management as a tool of financial analysis in short
period as compared to funds flow analysis. It has rightly been said that shorter the period covered
by the analysis, greater is the importance of cash flow analysis. For example, if it is to be found
out whether the business can meet its obligations maturing after 10 years from now, a good
estimate can be made about firm's capacity to meet its long-term obligations if changes in
working capital position on account of operations are observed. However, if the firm's capacity
to meet a liability maturing after one month is to be seen, the realistic approach would be to
consider the projected change in the cash position rather than an expected change in the working
capital position.
4. Cash is part of working capital and, therefore, an improvement in cash position results in
improvement in the funds position but the reverse is not true. In other words "inflow of cash"
results in "inflow of funds" but inflow of funds may not necessarily result in "inflow of cash"
Thus, a sound funds position does not necessarily mean a sound cash position but a sound cash
position generally means a sound funds position.
5. Another distinction between a cash flow analysis and a funds flow analysis can be made on the
basis of the techniques of their preparation. An increase in a current liability or decrease in a
current asset results in decrease in working capital and vice versa. While an increase in a current
liability or decrease in a current asset (other than cash) will result increase in cash and vice versa.
Some people, as stated before, use the term 'funds' in a very narrow sense of ,cash' only. In such
an even the two terms 'Funds' and 'Cash' will have synonymous meanings.
3.6 UTILITY OF CASH FLOW ANALYSIS
A Cash Flow Statement is useful for short-term planning. A business enterprise needs sufficient
cash to meet its various obligations in the near future such as payment for purchase of fixed
assets, payment of debts maturing in the near future, expenses of the business, etc.
A historical analysis of the different sources and applications of cash will enable the
management to make reliable cash flow projection for the immediate future. It may then plan out
for investment of surplus or meeting the deficit, if any. Thus, a cash flow analysis is an important
financial tool for the management. Its chief advantages are as follows:
1. Helps in efficient cash management. Cash flow analysis helps in calculating financial policies
and cash position. Cash is the basis for all operations and hence a projected cash flow statement
will enable the management to plan and coordinate the financial operations properly. The
management can know how much cash is needed, from which source it will be derived, how
much can be generated internally and how much could be obtained from outside.
2. Helps in internal financial management. Cash flow analysis provides information about funds
which will be available from operations. This will help the management in determining policies
regarding internal financial management, e.g., possibility of repayment of long-term debt,
dividend policies, planning replacement of plant and machinery, etc.
3. Discloses the movements of cash. Cash flow statement discloses the complete story of cash
movement. The increase in, or decrease of, cash, and the reason therefore can be known. It
discloses the reasons for low cash balance in spite of heavy operating profits or for heavy cash
balance in spite of low profits. However, comparison of original forecast with the actual results
highlights the trends of movements of cash which may otherwise go undetected.
4. Discloses success or failure of cash planning. The extent of success or failure of cash planning
can be known by comparing the projected cash flow statement with the actual cash flow
statement and necessary remedial measures can be taken.
3.7 LIMITATIONS OF CASH FLOW ANALYSIS
Cash flow analysis is a useful tool of financial analysis. However, it has its own limitations.
These limitations are as under:
1. Cash flow statement cannot be equated with the Income Statement. An income Statement
takes into account both cash as well as non-cash items, and, therefore, net cash flow does not
necessarily mean net income of the business.
2. The cash balance as disclosed by the cash flow statement may not represent the real liquid
position of the business since it can be easily influenced by postponing purchases and other
payments.
3. Cash flow statement cannot replace the Income Statement or the Funds Flow Statement.
Each of them has a separate function to perform.
3.8 PRESENT WORTH METHOD OF COMPARISON
In this method of comparison, the cash flows of each alternative will be reduced to time zero by
assuming an interest rate i. Then, depending on the type of decision, the best alternative will be
selected by comparing the present worth amounts of the alternatives.
The sign of various amounts at different points in time in a cash flow diagram is to be decided
based on the type of the decision problem.
In a cost dominated cash flow diagram, the costs (outflows) will be assigned with positive sign
and the profits, revenue, salvage value (all inflows), etc. will be assigned with negative sign.
In a revenue/profit-dominated cash flow diagram, the profit, revenue, salvage value (all inflows
to an organization) will be assigned with positive sign. The costs (outflows) will be assigned
with negative sign.
In case the decision is to select the alternative with the minimum cost, then the alternative with
the least present worth amount will be selected. On the other hand, if the decision is to select the
alternative with the maximum profit, then the alternative with the maximum present worth will
be selected.
3.8.1 REVENUE-DOMINATED CASH FLOW DIAGRAM
A generalized revenue-dominated cash flow diagram to demonstrate the present worth method of
comparison is
P represents an initial investment and Rj the net revenue at the end of the jth year. The interest
rate is i, compounded annually. S is the salvage value at the end of the nth year.
To find the present worth of the above cash flow diagram for a given interest rate, the formula is
PW(i) = – P + R1[1/(1 + i)1] + R2[1/(1 + i)
2] + ... + Rj[1/(1 + i)
j] + Rn[1/(1 + i)
n] + S[1/(1 + i)
n]
In this formula, expenditure is assigned a negative sign and revenues are assigned a positive sign.
If we have some more alternatives which are to be compared with this alternative, then the
corresponding present worth amounts are to be computed and compared. Finally, the alternative
with the maximum present worth amount should be selected as the best alternative.
3.8.2 COST-DOMINATED CASH FLOW DIAGRAM
A generalized cost-dominated cash flow diagram to demonstrate the present worth method of
comparison is
P represents an initial investment, Cj the net cost of operation and maintenance at the end of the
jth year, and S the salvage value at the end of the nth year.
To compute the present worth amount of the above cash flow diagram for a given interest rate i,
we have the formula
PW(i) = P + C1[1/(1 + i)1] + C2[1/(1 + i)
2] + ... + Cj[1/(1 + i)
j]+ Cn[1/(1 + i)
n] – S[1/(1 + i)
n]
In the above formula, the expenditure is assigned a positive sign and the revenue a negative sign.
If we have some more alternatives which are to be compared with this alternative, then the
corresponding present worth amounts are to be computed and compared. Finally, the alternative
with the minimum present worth amount should be selected as the best alternative.
3.9. FUTURE WORTH METHOD
In the future worth method of comparison of alternatives, the future worth of various alternatives
will be computed. Then, the alternative with the maximum future worth of net revenue or with
the minimum future worth of net cost will be selected as the best alternative for implementation.
3.9.1 REVENUE-DOMINATED CASH FLOW DIAGRAM
A generalized revenue-dominated cash flow diagram to demonstrate the future worth method of
comparison is presented in
P represents an initial investment, Rj the net-revenue at the end of the jth year, and S the salvage
value at the end of the nth year.
The formula for the future worth of the above cash flow diagram for a given interest rate, i is
FW(i) = –P(1 + i)n + R1(1 + i)
n–1 + R2(1 + i)
n–2 + ... + Rj(1 + i)
n–j + ... + Rn + S
In the above formula, the expenditure is assigned with negative sign and the revenues are
assigned with positive sign.
If we have some more alternatives which are to be compared with this alternative, then the
corresponding future worth amounts are to be computed and compared. Finally, the alternative
with the maximum future worth amount should be selected as the best alternative
3.9.2 COST-DOMINATED CASH FLOW DIAGRAM
A generalized cost-dominated cash flow diagram to demonstrate the future worth method of
comparison is given in
P represents an initial investment, Cj the net cost of operation and maintenance at the end of the
jth year, and S the salvage value at the end of the nth year.
The formula for the future worth of the above cash flow diagram for a given interest rate, i is
FW(i) = P(1 + i)n + C1(1 + i )
n–1 + C2(1 + i)
n–2 + ... + Cj(1 + i)
n–j + ... + Cn – S
In this formula, the expenditures are assigned with positive sign and revenues with negative sign.
If we have some more alternatives which are to be compared with this alternative, then the
corresponding future worth amounts are to be computed and compared. Finally, the alternative
with the minimum future worth amount should be selected as the best alternative.
3.10. ANNUAL EQUIVALENT METHOD
In the annual equivalent method of comparison, first the annual equivalent cost or the revenue of
each alternative will be computed. Then the alternative with the maximum annual equivalent
revenue in the case of revenue-based comparison or with the minimum annual equivalent cost in
the case of cost based comparison will be selected as the best alternative.
3.10.1 REVENUE-DOMINATED CASH FLOW DIAGRAM
A generalized revenue-dominated cash flow diagram to demonstrate the annual equivalent
method of comparison is presented in
P represents an initial investment, Rj the net revenue at the end of the jth year, and S the salvage
value at the end of the nth year.
The first step is to find the net present worth of the cash flow diagram using the following
expression for a given interest rate, i:
PW(i) = –P + R1/(1 + i)1 + R2/(1 + i)
2 + ... + Rj/(1 + i)
j + ... + Rn/(1 + i)
n + S/(1 + i)
n
In the above formula, the expenditure is assigned with a negative sign and the revenues are
assigned with a positive sign.
In the second step, the annual equivalent revenue is computed using the following formula:
Where (A/P, i, n) is called equal payment series capital recovery factor.
If we have some more alternatives which are to be compared with this alternative, then the
corresponding annual equivalent revenues are to be computed and compared. Finally, the
alternative with the maximum annual equivalent revenue should be selected as the best
alternative.
3.10.2 COST-DOMINATED CASH FLOW DIAGRAM
A generalized cost-dominated cash flow diagram to demonstrate the annual equivalent method of
comparison is presented in
P represents an initial investment, Cj the net cost of operation and maintenance at the end of the
jth year, and S the salvage value at the end of the nth year.
The first step is to find the net present worth of the cash flow diagram using the following
relation for a given interest rate, i.
PW(i) = P + C1/(1 + i)1 + C2/(1 + i)
2 + ... + Cj/(1 + i)
j + ... + Cn/(1 + i)
n – S/(1 + i)
n
In the above formula, each expenditure is assigned with positive sign and the salvage value with
negative sign. Then, in the second step, the annual equivalent cost is computed using the
following equation:
Where (A/P, i, n) is called as equal-payment series capital recovery factor.
As in the previous case, if we have some more alternatives which are to be compared with this
alternative, then the corresponding annual equivalent costs are to be computed and compared.
Finally, the alternative with the minimum annual equivalent cost should be selected as the best
alternative.
If we have some non-standard cash flow diagram, then we will have to follow the general
procedure for converting each and every transaction to time zero and then convert the net present
worth into an annual equivalent cost/revenue depending on the type of the cash flow diagram.
Such procedure is to be applied to all the alternatives and finally, the best alternative is to be
selected.
3.10.3 ALTERNATE APPROACH
Instead of first finding the present worth and then figuring out the annual equivalent
cost/revenue, an alternate method which is as explained below can be used. In each of the cases
presented in Sections 3.10.1 and 3.10.2, in the first step, one can find the future worth of the cash
flow diagram of each of the alternatives.
Then, in the second step, the annual equivalent cost/revenue can be obtained by using the
equation:
Where (A/F, i, n) is called equal-payment series sinking fund factor.
3.11. RATE OF RETURN METHOD
The rate of return of a cash flow pattern is the interest rate at which the present worth of that cash
flow pattern reduces to zero. In this method of comparison, the rate of return for each alternative
is computed. Then the alternative which has the highest rate of return is selected as the best
alternative.
In this type of analysis, the expenditures are always assigned with a negative sign and the
revenues/inflows are assigned with a positive sign.
A generalized cash flow diagram to demonstrate the rate of return method of comparison is
presented in
In the above cash flow diagram, P represents an initial investment, Rj the net revenue at the end
of the jth year, and S the salvage value at the end of the nth year.
The first step is to find the net present worth of the cash flow diagram using the following
expression at a given interest rate, i.
PW(i) = – P + R1/(1 + i)1 + R2/(1 + i)
2 + ... + Rj/(1 + i)
j + ... + Rn/(1 + i)
n + S/(1 + i)
n
Now, the above function is to be evaluated for different values of i until the present worth
function reduces to zero, as shown in Fig.
In the figure, the present worth goes on decreasing when the interest rate is increased. The value
of i at which the present worth curve cuts the X-axis is the rate of return of the given
proposal/project. It will be very difficult to find the exact value of i at which the present worth
function reduces to zero.
So, one has to start with an intuitive value of i and check whether the present worth function is
positive. If so, increase the value of i until PW(i) becomes negative. Then, the rate of return is
determined by interpolation method in the range of values of i for which the sign of the present
worth function changes from positive to negative.