Fundamentals of Engineering Economy PDF

Chapter-1: FUNDAMENTALS OF ENGINEERING ECONOMY 1 FUNDAMENTALS OF ENGINEERING ECONOMY CHAPTER STRUCTURE 1.1 DEFINITIONS AND CONCEPTS OF ECONOMICS 1.1.1 Microeconomics 1.1.2 Macroeconomics 1.1.3 Gross Domestic Product (GDP...

Chapter-1: FUNDAMENTALS OF ENGINEERING ECONOMY 1 FUNDAMENTALS OF ENGINEERING ECONOMY CHAPTER STRUCTURE 1.1 DEFINITIONS AND CONCEPTS OF ECONOMICS 1.1.1 Microeconomics 1.1.2 Macroeconomics 1.1.3 Gross Domestic Product (GDP) 1.1.4 Managerial Economics 1.1.5 Law of Demand and Supply 1.1.6 Market Equilibrium 1.2 INTRODUCTION TO ENGINEERING ECONOMY 1.2.1 Introduction to Engineering Economy 1.2.2 Principles of Engineering Economy 1.2.3 Engineering Economy and The Design Process 1.1 DEFINITIONS AND CONCEPTS OF ECONOMICS In general, Economics is the study of how individuals and societies choose to utilize scares resources to satisfy their unlimited wants. Different economists have defined economics in their own words. There is no consensus among the economists about a precise definition of economics. Therefore, it is said that whenever six economists are gathered, there are seven opinions. Adam Smith, the father of modern economics, defined economics as a science of wealth. He also assumed that economics is the subject that tells us how to make a nation wealthy. There are several branches of economics. Of these, two are the most important. These are microeconomics and macroeconomics. Both of these terms have been derived from Greek words “mikros” and “makros” respectively meaning “small” and “big” respectively. 1.1.1 MICROECONOMICS Microeconomics is defined as the branch of economics which deals with the individual parts of an economy. In other words, it is the part of economic analysis which is concerned with the behavior of individual units: consumers, households, and firms. It examines how consumers choose between goods and services, how workers choose between jobs and business firms decide what to produce, how to produce and for whom to produce. According to K.E. Boulding, "Microeconomics is the study of particular firms, particular households, individual prices, wages, incomes, individual industries, particular commodities. Thus, microeconomics is the branch of economics which deals with the decision making of individual units in an economy. It studies Individual units of the economy than the economy as a whole. The main objective of microeconomics is the study of price determination in the market. Therefore, it is also called price theory. Microeconomics is based on the assumptions like existence of fun employment, free market economy, perfect competition and partial equilibrium analysis. Microeconomics is also known as the microscopic analysis because it is concerned with microscopic study of various elements of the economy. The scope of microeconomics includes the topics like consumption, production, exchange, distribution and welfare economics. Course: MGTS 301 (ENGINEERING ECONOMICS), Kathmandu University By: Punya Ram Sujakhu (9841395153) Page 1 of 11  Chapter-1: FUNDAMENTALS OF ENGINEERING ECONOMY The concept of microeconomics can be summarized as follows: − Microeconomics studies the individual parts of an economy. − Microeconomics is concerned with individual firms and consumers. − Microeconomics is based on the assumptions of full employment, partial equilibrium analysis and perfect competition. − Microeconomics is applicable only in the free market economy. − Microeconomics is also known as the price theory. − The major variables of microeconomics are individual demand and supply, relative price, output of an individual firm, etc. The main usages of microeconomics are − Helpful to formulate economics policies − Helpful to study human behavior − Helpful in efficient allocation of resources − Useful to study international trade 1.1.2 MACROECONOMICS Macroeconomics is defined as the branch of economics which deals with the economy as a whole. In other words, macroeconomics is tile study of very large, economy-wide aggregate variable like national income, money, price level, unemployment, economic growth, etc. Therefore, it is also known as aggregative economics. It examines how price level is determined and how resources are allocated at the economic system as a whole. The concept of macroeconomics can be cleared by tile following definitions: According to N. G. Mankiw, ”Macroeconomics is the study of economy wide phenomena including inflation, unemployment and economic growth." Thus, macroeconomics is the study of behavior and performance of the economy as a whole. It explains how equilibrium national income and employment ate determined in the economy. Therefore, it is also known as the 'Theory of Income and Employment'. The scope of macroeconomics is large and includes the theory of national income, theory of employment, theory of money, and theory of general price level. Theory of economic growth and theory or international trade. The concept of macroeconomics can be summarized as follows: − Macroeconomics studies economy as a whole. − Macroeconomics is an aggregate economics. − Macroeconomics is called theory of income and employment. − The objectives of macroeconomics are to determine aggregate output, employment and general price level and their rate of change. − The major variables of macroeconomics are national income, total consumption, total saving, total Investment, etc. The main uses or importance of macroeconomics are − Helpful to understand the working of the economy. − Helpful in formulating economic policies. − Helpful In international comparisons. − Evaluate performance of the economy. Course: MGTS 301 (ENGINEERING ECONOMICS), Kathmandu University By: Punya Ram Sujakhu (9841395153) Page 2 of 11  Chapter-1: FUNDAMENTALS OF ENGINEERING ECONOMY 1.1.3 GROSS DOMESTIC PRODUCT (GDP) Gross domestic product is defined as the market value of all the final goods and services produced within the domestic territory of a country in a year. In order to calculate the gross domestic product, all the goods and services produced within the country are multiplied by their respective prices and summed up. Symbolically, GDP = P1Q1 + P1Q2 +... + PnQn Where P = Market price of final goods and services Q = Quantity of goods and services GDP consist of private consumption + gross private investment + government investment + government spending + (exports – imports). GDP is usually calculated by the national statistical agency of the country following the international standard. The world’s GDP was 94,935. USD Billion in 2021. The US had 22,939.58 USD Billion by the end of 2021 and GDP in Nepal is expected to reach 29.30 USD Billion by the end of 2021. GDP includes only the final goods and services. All the intermediate goods and services are excluded from the measurement of GDP. The expression “final goods and services” refers to the goods and services produced for final use whereas “intermediate goods are the goods produced by one firm which are used in further processing by another. For example, flour is an intermediate product because it is used to produce bread and bread is the final product as it is used for final consumption. The features of GDP are as follows: − GDP is the money value or marker value of all the final goods and services produced within a country. − GDP includes the money value of only final goods and services produced in a year. − GDP is calculated at the current market prices. − GDP includes only those goods which have market value and brought in the market for sale. − Transfer payments like pension, unemployment allowance, etc. are not included in GDP because these payments do not contribute in any way to the production. − GDP does not include capital gains. − Whether the resources arc domestically-owned or foreign-owned does not matter. As long as the resources are located within the country, the value of the output they produce is included in GDP. 1.1.4 MANAGERIAL ECONOMICS Managerial economics is a special branch of economics. It is the application of economic principles and methods to business practices. In other words, it is an application of economic theory to the business practice for decision making and forward planning. Decision making is the process of selecting one action out of several alternative actions and forward planning is the process of thinking in advance or it implies planning in advance for the future. According to Edwin Mansfield, "Managerial economics is concerned with ways in which business executives and other policy makers should make decisions” Thus, managerial economics is based on both microeconomics and macroeconomics since it is concerned with the study of problems and principles of an individual firm or an individual industry and it uses the monetary policy, trade cycle, industrial policy of the government for the successful management of a firm. Managerial economics gives knowledge to the manger of the firm regarding best use of the resources and achieving goal of the firms. Course: MGTS 301 (ENGINEERING ECONOMICS), Kathmandu University By: Punya Ram Sujakhu (9841395153) Page 3 of 11  Chapter-1: FUNDAMENTALS OF ENGINEERING ECONOMY The scope of managerial economics is − Demand analysis and forecasting − Theory of Production and cost analysis − Price theory or theory of exchange − Theory of profit − Theory of capital and investment 1.1.5 LAW OF DEMAND AND SUPPLY The demand and supply are most important factors or forces determining price and quantity in the free market economy. Demand is related with the economic activities of the consumers and supply is related with the economic activities of the producers or the suppliers. These two factors are like two blades of a scissors. It means that as only one blade of a scissors does not function. likewise one force of the market either demand or supply also cannot function without another. The integration of these two forces of the market is necessary to determine the equilibrium price and quantity of output. In this context, this part of the unit deals with the demand, supply and market equilibrium. 1. Law of Demand In general, the demand for a commodity is its quantity which consumers are able and willing to purchase at each possible price during a given period of time, other things remaining the same. And, the law of demand states the inverse relationship between the quantity demanded and price of a commodity. According to this law, the demand for a commodity increases with a fall in its price and decreases with a rise in its price, other things remaining the same. Thus, this law implies that price and quantity demanded are inversely related. Course: MGTS 301 (ENGINEERING ECONOMICS), Kathmandu University By: Punya Ram Sujakhu (9841395153) Page 4 of 11  Chapter-1: FUNDAMENTALS OF ENGINEERING ECONOMY According to Prof. Alfred Marshall, "Demand refers to the quantities of a commodity that the consumers are able and willing to buy at each possible price during a given period of time, other things being equal". Marshall states the law of demand as "other things remaining the same, the amount demanded increases with a fall in price and diminishes with a rise in price". The law of demand is based on the following assumptions: − No change in income of the consumer − No change in price of related goods − No change in tastes and preferences of the consumers − No change in fashion and habit of the consumer − No changes in size and composition of population − No expectations of change in the future price of the commodity. Based on these assumptions, the law of demand can be explained with the help of a demand schedule and demand curve. A demand schedule is a tabular presentation of different prices of a commodity and its corresponding quantity demanded per-unit of time. In other words, it is a table, which shows the relationship between the price of a commodity and the quantity demanded. And, a demand schedule is a tabular presentation of different prices of a commodity and its corresponding quantity demanded per-unit of time. In other words, it is a table, which shows the relationship between the price of a commodity and the quantity demanded. A hypothetical demand schedule and demand curve is given below. 2. Law of Supply The quantities of a good that individual firm is willing and able to offer in sale over a given time period is defined as supply. In general, more goods are offered for sale at higher price, i.e. supply increases with the increase in price. Therefore, the relation between price and quantity supplied is positive and direct. The functional relationship between price and quantity supplied gives the law of supply. According to this law, other things remaining the same, the quantity supplied of a commodity is directly related to the price of the commodity. It means that when price rises, the quantity supplied increases, and when price falls, the quantity supplied decreases. Course: MGTS 301 (ENGINEERING ECONOMICS), Kathmandu University By: Punya Ram Sujakhu (9841395153) Page 5 of 11  Chapter-1: FUNDAMENTALS OF ENGINEERING ECONOMY The law of supply is based on the following assumptions: − No change in price of inputs or factors of production. − No change in state of technology. − No change in goal of producers. − No change in number of producers. − No change in price of other goods. − No change in tax and subsidy policy of the government. On the basis of these assumptions, the law of supply can be explained with the help of supply schedule and supply curve. A supply schedule is a tabular presentation of the various quantities of a commodity offered for sale at various prices at given period of time. 1.1.6 MARKET EQUILIBRIUM In the ordinary sense, equilibrium means balance in opposite forces. In the context of market analysis, equilibrium refers to a state of market in which quantity demanded for a commodity equals to the quantity supplied of the commodity. The equality of demand and supply gives an equilibrium price. It means that equilibrium price is the price at which quantity demanded equals to quantity supplied. Similarly, equilibrium quantity is the quantity demanded and supplied at the equilibrium price. In order to analyze how equilibrium price is determined, we need to integrate the demand and supply curves. For this purpose, let us use the example of potato. The hypothetical market demand and supply schedules for potato are given below. Quantity Demanded Quantity Supplied Surplus (+) or Price (Rs/kg) Pressure on Price (Kgs) (KGs) Shortage (-) 5 50 10 -40 Upward Curve 10 40 20 -20 (disequilibrium) 15 30 30 0 Equilibrium 20 20 40 20 Downward Curve 25 10 50 40 (disequilibrium) Course: MGTS 301 (ENGINEERING ECONOMICS), Kathmandu University By: Punya Ram Sujakhu (9841395153) Page 6 of 11  Chapter-1: FUNDAMENTALS OF ENGINEERING ECONOMY In Figure, DD and SS are the demand and supply curves respectively. These two curves are intersecting each other at point E, which is the equilibrium point. Hence, equilibrium price is Rs. 15 and equilibrium quantity of output is 30 units. When price exceeds equilibrium price Rs. 15, quantity supplied exceeds quantity demanded. This is known as the excess supply or surplus, Let us suppose, price increases to Rs. 20. When price increases to Rs, 20, quantity demanded decreases to 20 units and quantity supplied increases 40 units. In this situation, there is an excess supply equal to 20 units. On the other hand, if price is below equilibrium price Rs. 15, quantity demanded exceeds quantity supplied. This is known as the excess demand or Shortage. Let us suppose, price decreases to Rs. 10. When price decreases to Rs. 10, quantity demanded is 40 units and quantity supplied is 20 units. 1.2.1 INTRODUCTION TO ENGINEERING ECONOMY The Accreditation Board for Engineering and Technology states that engineering “is the profession in which a knowledge of the mathematical and natural sciences gained by study, experience, and practice is applied with judgment to develop ways to utilize, economically, the materials and forces of nature for the benefit of mankind.”In this definition, the economic aspects of engineering are emphasized, as well as the physical aspects. Clearly, it is essential that the economic part of engineering practice be accomplished well. Thus, engineers use knowledge to find new ways of doing things economically. In general, engineering economy deals with the concepts and techniques of analysis useful in evaluating the worth of systems, products, and services in relation to their costs. Fundamentally, engineering economy involves formulating, estimating, and evaluating the economic outcomes when alternatives to accomplish a defined purpose are available. Another way to define engineering economy is as a collection of mathematical techniques that simplify economic comparison. Engineering economy is a collection of techniques that simplify comparisons of alternatives on an economic basis. In defining what engineering economy is, it might also be helpful to define what it is not. Engineering economy is not a method or process for determining what the alternatives are. On the contrary, engineering economy begins only after the alternatives have been identified. If the best alternative is actually one that the engineer has not even recognized as an alternative, then all of the engineering economic analysis Course: MGTS 301 (ENGINEERING ECONOMICS), Kathmandu University By: Punya Ram Sujakhu (9841395153) Page 7 of 11  Chapter-1: FUNDAMENTALS OF ENGINEERING ECONOMY tools in will not result in its selection. Real-world decisions usually include many other factors in the decision making process. For example, in determining whether to build a nuclear-powered, gas-fired, or coal-fired power plant, factors such as safety, air pollution, public acceptance, water demand, waste disposal, global warming, and many others would be considered in identifying the best alternative. Objectives and Basis of Engineering Economy In addition to the economic aspects of decision making, nonmonetary factors (attributes) often play a significant role in the final recommendation. Examples of objectives other than profit maximization or cost minimization that can be important to an organization include the following: 1. Meeting or exceeding customer expectations 2. Safety to employees and to the public 3. Improving employee satisfaction 4. Maintaining production flexibility to meet changing demands 5. Meeting or exceeding all environmental requirements 6. Achieving good public relations or being an exemplary member of the community Why Engineering Economy is important to Engineers? Decisions made by engineers, managers, corporation presidents, and individuals are commonly the result of choosing one alternative over another. Decisions often reflect a person's educated choice of how to best invest funds. The decision of how to invest capital will invariably change the future, hopefully for the better; that is, it will be value adding. Engineers play a major role in capital investment decisions based on their analysis, synthesis, and design efforts. The factors considered in making the decision are a combination of economic and noneconomic factors. For many corporations, especially larger ones, many of the projects and services are international in scope. They may be developed in one country for application in another. People and plants located in sites around the world routinely separate product design and manufacturing from each other, and from the customers who utilize the product. The approaches presented here are easily implemented in multinational settings or within a single country or location. Correct use of the techniques of engineering economy is especially important, since virtually any project-local, national, or international-will affect costs and/or revenues. It is used to answer many different questions 1. Which engineering projects are worthwhile? - Has the mining or petroleum engineer shown that the mineral or oil deposits is worth developing? 2. Which engineering projects should have a higher priority? - Has the industrial engineer shown which factory improvement projects should be funded with the available dollars? 3. How should the engineering project be designed? - Has civil or mechanical engineer chosen the best thickness for insulation? Some typical applications of engineering economy are listed below Manufacturing Company
Addition (expansion) to an existing plant.
Improvements to a material handling system.
Selecting between numerical controlled milling machines produced by different manufacturers. Course: MGTS 301 (ENGINEERING ECONOMICS), Kathmandu University By: Punya Ram Sujakhu (9841395153) Page 8 of 11  Chapter-1: FUNDAMENTALS OF ENGINEERING ECONOMY
Selecting the preferred conceptual (preliminary) design for a new consumer product.
Selecting the preferred detailed design for an application. Service Company
Selecting the best type (and model) of light truck for use in a service fleet.
Determining the preferred location of a distribution center.
Selecting an upgraded computer system to integrate and improve the accomplishment of a number of present functions in an organization.
Selecting the preferred conceptual (preliminary) design for a new consumer service and its basic delivery process.
Selecting the preferred detailed design for a service (e.g., a home health care service involving professional nursing care to meet the periodic needs of patients). Government Organization
Evaluating the contracting of garbage pickup and disposal versus continued accomplishment by a city work force.
Analyzing the significant repair and upgrading of a highway bridge versus its replacement with a new structure.
Selecting the preferred conceptual (preliminary) design for a new elementary school.
Evaluating the life cycle cost for a new major weapon system.
Determining the preferred replacement cycle for medium sized backhoes in the highway department equipment fleet. 1.2.2 PRINCIPLES OF ENGINEERING ECONOMY The development, study, and application of any discipline must begin with a basic foundation. We define the foundation for engineering economy to be a set of principles that provide a comprehensive doctrine for developing the methodology. Once a problem or need has been clearly defined, the foundation of the discipline can be discussed in terms of seven principles. 1. Develop the Alternatives Carefully define the problem! Then the choice (decision) is among alternatives. The alternatives need to be identified and then defined for subsequent analysis. 2. Focus on the Differences Only the differences in expected future outcomes among the alternatives are relevant to their comparison and should be considered in the decision. 3. Use a Consistent Viewpoint The prospective outcomes of the alternatives, economic and other, should be consistently developed from a defined viewpoint (perspective). 4. Use a Common Unit of Measure Using a common unit of measurement to enumerate as many of the prospective outcomes as possible will simplify the analysis of the alternatives. Course: MGTS 301 (ENGINEERING ECONOMICS), Kathmandu University By: Punya Ram Sujakhu (9841395153) Page 9 of 11  Chapter-1: FUNDAMENTALS OF ENGINEERING ECONOMY 5. Consider All Relevant Criteria Selection of a preferred alternative (decision making) requires the use of a criterion (or several criteria). The decision process should consider both the outcomes enumerated in the monetary unit and those expressed in some other unit of measurement or made explicit in a descriptive manner. 6. Make Risk and Uncertainty Explicit Risk and uncertainty are inherent in estimating the future outcomes of the alternatives and should be recognized in their analysis and comparison. 7. Revisit Your Decisions Improved decision making results from an adaptive process; to the extent practicable, the initial projected outcomes of the selected alternative should be subsequently compared with actual results achieved. 1.2.3 ENGINEERING ECONOMY AND DESIGN PROCESS An engineering economy study is accomplished using a structured procedure and mathematical modeling techniques. The economic results are then used in a decision situation that normally includes other engineering knowledge and input. A sound engineering economic analysis procedure incorporates on the basic of principles discussed as above and involves several steps. We represent the procedure in terms of the seven steps listed below. 1. Problem definition The first step of the engineering economic analysis procedure (problem definition) is particularly important, since it provides the basis for the rest of the analysis. A problem must be well understood and stated in an explicit form before the project team proceeds with the rest of the analysis. The term problem is used here generically. It includes all decision situations for which an engineering economy analysis is required. Recognition of the problem is normally stimulated by internal or external organizational needs or requirements. Operating problems within a company (internal need) or a customer expectation about a product or service (external requirement) are examples. Once the problem is recognized, its formulation should be viewed from a systems perspective. Evaluation of the problem includes refinement of needs and requirements, and information from the evaluation phase may change the original formulation of the problem. In fact, redefining the problem until a consensus is reached may be the most important part of the problem-solving process! 2. Development of the alternatives. The second step of the engineering economic analysis procedure is development of the alternatives. To development of the alternatives, two factors should be considers, (1) searching for potential alternatives and (2) screening them to select a smaller group of feasible alternatives for detailed analysis. The difference between good alternatives and great alternatives depends largely on an individual’s or group’s problem-solving efficiency. 3. Development of the outcomes and cash flows for each alternative Step 3 of the engineering economic analysis procedure incorporates Principles 2, 3, and 4 and uses the basic cash-flow approach employed in engineering economy. A cash flow occurs when money is Course: MGTS 301 (ENGINEERING ECONOMICS), Kathmandu University By: Punya Ram Sujakhu (9841395153) Page 10 of 11  Chapter-1: FUNDAMENTALS OF ENGINEERING ECONOMY transferred from one organization or individual to another. Thus, a cash flow represents the economic effects of an alternative in terms of money spent and received. 4. Selection of a Decision criterion The selection of a decision criterion (Step 4 of the analysis procedure) incorporates Principle 5 (consider all relevant criteria). The decision maker will normally select the alternative that will best serve the long-term interests of the owners of the organization. It is also true that the economic decision criterion should reflect a consistent and proper viewpoint (Principle 3) to be maintained throughout an engineering economy study. 5. Analysis and comparison of the alternatives. Analysis of the economic aspects of an engineering problem (Step 5) is largely based on cash-flow estimates for the feasible alternatives selected for detailed study. A substantial effort is normally required to obtain reasonably accurate forecasts of cash flows and other factors in view of, for example, inflationary (or deflationary) pressures, exchange rate movements, and regulatory (legal) mandates that often occur. Clearly, the consideration of future uncertainties (Principle 6) is an essential part of an engineering economy study. When cash flow and other required estimates are eventually determined, alternatives can be compared based on their differences as called for by Principle 2. Usually, these differences will be quantified in terms of a monetary unit such as dollars. 6. Selection of the preferred alternative. When the first five steps of the engineering economic analysis procedure have been done properly, the preferred alternative (Step 6) is simply a result of the total effort. Thus, the soundness of the technical- economic modeling and analysis techniques dictates the quality of the results obtained and the recommended course of action. Step 6 is included in Activity 5 of the engineering design process (specification of the preferred alternative) when done as part of a design effort. 7. Performance monitoring and post evaluation of results. This final step implements Principle 7 and is accomplished during and after the time that the results achieved from the selected alternative are collected. Monitoring project performance during its operational phase improves the achievement of related goals and objectives and reduces the variability in desired results. Step 7 is also the follow-up step to a previous analysis, comparing actual results achieved with the previously estimated outcomes. Course: MGTS 301 (ENGINEERING ECONOMICS), Kathmandu University By: Punya Ram Sujakhu (9841395153) Page 11 of 11  CHAPTER-2: COST CONCEPTS AND DESIGN ECONOMICS 2 COST CONCEPTS AND DESIGN ECONOMICS 2.1.1 COST CONCEPT AND CLASSIFICATIONS 1. Classification based on Element According to this classification costs are divided into four categories, materials, Labours, other expenses and overheads. There can be a sub classification of the each element for example raw material, components and spare parts, consumable stores, packing materials etc. this classification is important as it helps to find out the total cost and valuation of work in progress. MGTS 301 -ENGINEERING ECONOMY, Kathmandu University By Punya Ram Sujakhu (9841395153) Page 1 of 17  CHAPTER-2: COST CONCEPTS AND DESIGN ECONOMICS a. Direct Materials Direct materials are the material which can be identified in the conveniently measured and which is directly charged on the product. These materials directly enter the product and form of finished product for example, timber in furniture making, cloth in dress making, brick in building a house, raw material like jute in the manufacturing of gunny bags, fruit in canning industry. b. Direct Labours It includes all the labour expended in altering the construction, composition, conformation or condition of the product. It is the labour which can be conveniently identified or attributed wholly to a particular job, product or process or expanded in converting raw materials into finished goods. Wages given for such labour are known as direct wages. c. Other Direct Expenses These expenses are also called chargeable expenses. They are the expenses other than direct material and direct labour and can be identified with and allocation to cost centers or cost units. Direct expenses are those which are incurred for each unit of manufacturing specifically and identifiable with them. For example, royalties paid on the basis of output, hire charge of special plant or machinery carriage and freight on direct material purchased, import duty and octroi paid on the purchases of imported direct materials, amount payable to sub contractor etc. 2. Classification based on functions MGTS 301 -ENGINEERING ECONOMY, Kathmandu University By Punya Ram Sujakhu (9841395153) Page 2 of 17  CHAPTER-2: COST CONCEPTS AND DESIGN ECONOMICS 3. Classification Based on Behaviour Costs sometimes have a definite relationship with the volume of production. They behave differently when the volume of production rises or falls. They are described as follows a. Fixed Cost This is remains fixed in the total amount and does not increase or decrease with the changes in the volume of production. But the fixed cost per unit when the volume of production decrease and vice-versa, and the fixed cost per unit decrease when the volume of production increases. It includes rent and lease, municipal tax, managerial salaries, building insurance, salaries and wages of permanent staff etc. the characteristics of fixed cost are: i. Fixed cost is unaffected in spite of the change in the volume of output. ii. Per unit cost decrease with the increase in output (or Vice Versa) and per unit cost increase with the decrease in output (or Vice Versa). iii. Costs can be allocated to different departments on the basis of agreed principles. iv. Fixed cost is controllable from the top level. b. Variable Costs This cost tends to vary in direct proportion to the volume of output. In other words, when the volume of output increases, the total variable cost also increases and when the volume of output decreases the total variable cost also decrease. But the variable cost per unit remains fixed. It includes direct material, direct wages, power, royalties, normal spoilage, small tools, commission of salesmen etc. it has the following characteristics: i. Variability of the total cost is in direct proportion to the volume of output ii. Allocation and apportionment to departments are comparatively easy and reasonably accurate iii. Such costs can be controlled by functional managers c. Semi-Variable Cost This cost is partly fixed and partly variable. A semi variable cost often has a fixed element below which it will not fall at any level of output. If the levels of production increase the total amount of semi variable cost also increase and per unit cost decreases but not proportionately. These costs have the characteristics of both fixed and variable costs. Electricity charges, telephone charges, water supply charge are the examples of semi variable costs. They dare also called mixed costs, combined costs or semi fixed costs. The characteristics of semi-variable cost Difference between Variable and Fixed Cost Bases Variable Cost Fixed Cost 1. Total Cost The total variable cost change with The total fixed cost does not the change in output change with the change in output 2. Per Unit Cost The per unit variable costs remain The per unit fixed cost changes the same in any level of output with the change in output 3. Controllability Variable costs are controllable Fixed costs are not controllable MGTS 301 -ENGINEERING ECONOMY, Kathmandu University By Punya Ram Sujakhu (9841395153) Page 3 of 17  CHAPTER-2: COST CONCEPTS AND DESIGN ECONOMICS 4. Classification Based on decision making MGTS 301 -ENGINEERING ECONOMY, Kathmandu University By Punya Ram Sujakhu (9841395153) Page 4 of 17  CHAPTER-2: COST CONCEPTS AND DESIGN ECONOMICS 2.1.2 GENERAL ECONOMIC ENVIRONMENT There are numerous general economic concepts that must be taken into account in engineering studies. In broad terms, economics deals with the interactions between people and wealth, and engineering is concerned with the cost-effective use of scientific knowledge to benefit humankind. This section introduces some of these basic economic concepts and indicates how they may be factors for consideration in engineering studies and managerial decisions. 1. Consumer and Producer Goods and Services The goods and services that are produced and utilized maybe divided conveniently into two classes. Consumer goods and services are those products or services that are directly used by people to satisfy their wants. Food, clothing, homes, cars, television sets, haircuts, opera, MGTS 301 -ENGINEERING ECONOMY, Kathmandu University By Punya Ram Sujakhu (9841395153) Page 5 of 17  CHAPTER-2: COST CONCEPTS AND DESIGN ECONOMICS and medical services are examples. The providers of consumer goods and services must be aware of, and are subject to, the changing wants of the people to whom their products are sold. Producer goods and services are used to produce consumer goods and services or other producer goods. Machine tools, factory buildings, buses, and farm machinery are examples. The amount of producer goods needed is determined indirectly by the amount of consumer goods or services that are demanded by people. However, because the relationship is much less direct than for consumer goods and services, the demand for and production of producer goods may greatly precede or lag behind the demand for the consumer goods that they will produce. 2. Necessities, Luxuries, and Price Demand Goods and services may be divided into two types: necessities and luxuries. Obviously, these terms are relative, because, for most goods and services, what one person considers a necessity may be considered a luxury by another. For example, a person living in one community may find that an automobile is a necessity to get to and from work. If the same person lived and worked in a different city, adequate public transportation might be available, and an automobile would be a luxury. For all goods and services, there is a relationship between the price that must be paid 3. Concept of Utility and Value MGTS 301 -ENGINEERING ECONOMY, Kathmandu University By Punya Ram Sujakhu (9841395153) Page 6 of 17  CHAPTER-2: COST CONCEPTS AND DESIGN ECONOMICS 2.1.3 CLASSIFICATION OF MARKET STRUCTURE 1. Perfect Competition MGTS 301 -ENGINEERING ECONOMY, Kathmandu University By Punya Ram Sujakhu (9841395153) Page 7 of 17  CHAPTER-2: COST CONCEPTS AND DESIGN ECONOMICS 2. Monopolistic Competition MGTS 301 -ENGINEERING ECONOMY, Kathmandu University By Punya Ram Sujakhu (9841395153) Page 8 of 17  CHAPTER-2: COST CONCEPTS AND DESIGN ECONOMICS 3. Monopoly MGTS 301 -ENGINEERING ENGINEERING ECONOMY, ECONOMY Kathmandu University By Punya Ram Sujakhu (9841395153) Page 9 of 17  CHAPTER-2: COST CONCEPTS AND DESIGN ECONOMICS 4. Oligopoly Competition MGTS 301 -ENGINEERING ECONOMY, Kathmandu University By Punya Ram Sujakhu (9841395153) Page 10 of 17  CHAPTER-2: COST CONCEPTS AND DESIGN ECONOMICS 2.1.4 TOTAL REVENUE FUNCTION MGTS 301 -ENGINEERING ECONOMY, Kathmandu University By Punya Ram Sujakhu (9841395153) Page 11 of 17  CHAPTER-2: COST CONCEPTS AND DESIGN ECONOMICS 2.1.5 COST, VOLUME, AND BREAKEVEN POINT RELATIONSHIPS MGTS 301 -ENGINEERING ECONOMY, Kathmandu University By Punya Ram Sujakhu (9841395153) Page 12 of 17  CHAPTER-2: COST CONCEPTS AND DESIGN ECONOMICS MGTS 301 -ENGINEERING ECONOMY, Kathmandu University By Punya Ram Sujakhu (9841395153) Page 13 of 17  CHAPTER-2: COST CONCEPTS AND DESIGN ECONOMICS MGTS 301 -ENGINEERING ECONOMY, Kathmandu University By Punya Ram Sujakhu (9841395153) Page 14 of 17  CHAPTER-2: COST CONCEPTS AND DESIGN ECONOMICS MGTS 301 -ENGINEERING ECONOMY, Kathmandu University By Punya Ram Sujakhu (9841395153) Page 15 of 17  CHAPTER-2: COST CONCEPTS AND DESIGN ECONOMICS MGTS 301 -ENGINEERING ECONOMY, Kathmandu University By Punya Ram Sujakhu (9841395153) Page 16 of 17  CHAPTER-2: COST CONCEPTS AND DESIGN ECONOMICS Present Economy Studies When alternatives for accomplishing a specific task are being compared over one year or less and the influence of time on money can be ignored, engineering economic analyses are referred to as present economy studies. Several situations involving present economy studies are illustrated in this section. The rules, or criteria, shown next will be used to select the preferred alternative when defect-free output (yield) is variable or constant among the alternatives being considered. MGTS 301 -ENGINEERING ECONOMY, Kathmandu University By Punya Ram Sujakhu (9841395153) Page 17 of 17  Engineering Economy Chapter 2: Cost Concepts and Design Economics Copyright ©2012 by Pearson Education, Inc. Engineering Economy, Fifteenth Edition Upper Saddle River, New Jersey 07458 By William G. Sullivan, Elin M. Wicks, and C. Patrick Koelling All rights reserved.  The objective of Chapter 2 is to present various methods for estimating important factors in an engineering economy study. Copyright ©2012 by Pearson Education, Inc. Engineering Economy, Fifteenth Edition Upper Saddle River, New Jersey 07458 By William G. Sullivan, Elin M. Wicks, and C. Patrick Koelling All rights reserved. Estimating the future cash flows for feasible alternatives is a critical step in engineering economy studies. Estimating costs, revenues, useful lives, residual values, and other pertinent data can be the most difficult, expensive, and time- consuming part of the study. Copyright ©2012 by Pearson Education, Inc. Engineering Economy, Fifteenth Edition Upper Saddle River, New Jersey 07458 By William G. Sullivan, Elin M. Wicks, and C. Patrick Koelling All rights reserved.  Results of cost estimating are used for a variety of purposes. Setting selling prices for quoting, bidding, or evaluating contracts. Determining if a proposed product can be made and distributed at a profit. Evaluating how much capital can be justified for changes and improvements. Setting benchmarks for productivity improvement programs. Copyright ©2012 by Pearson Education, Inc. Engineering Economy, Fifteenth Edition Upper Saddle River, New Jersey 07458 By William G. Sullivan, Elin M. Wicks, and C. Patrick Koelling All rights reserved.  Cost-Estimation Techniques (Integrated Approach to Developing the Cash Flow) The integrated cost estimation approach has three major components. 1. Work breakdown structure (WBS) 2. Cost and revenue structure (classification) 3. Estimating techniques (models) Copyright ©2012 by Pearson Education, Inc. Engineering Economy, Fifteenth Edition Upper Saddle River, New Jersey 07458 By William G. Sullivan, Elin M. Wicks, and C. Patrick Koelling All rights reserved.  Copyright ©2012 by Pearson Education, Inc. Engineering Economy, Fifteenth Edition Upper Saddle River, New Jersey 07458 By William G. Sullivan, Elin M. Wicks, and C. Patrick Koelling All rights reserved. 1. Work Breakdown Structure (WBS) A basic tool in project management A framework for defining all project work elements and their relationships, collecting and organizing information, developing relevant cost and revenue data, and management activities. Each level of a WBS divides the work elements into increasing detail. Copyright ©2012 by Pearson Education, Inc. Engineering Economy, Fifteenth Edition Upper Saddle River, New Jersey 07458 By William G. Sullivan, Elin M. Wicks, and C. Patrick Koelling All rights reserved.  Copyright ©2012 by Pearson Education, Inc. Engineering Economy, Fifteenth Edition Upper Saddle River, New Jersey 07458 By William G. Sullivan, Elin M. Wicks, and C. Patrick Koelling All rights reserved. A WBS has other characteristics. Both functional and physical work elements are included. The content and resource requirements for a work element are the sum of the activities and resources of related subelements below it. A project WBS usually includes recurring and nonrecurring work elements. Copyright ©2012 by Pearson Education, Inc. Engineering Economy, Fifteenth Edition Upper Saddle River, New Jersey 07458 By William G. Sullivan, Elin M. Wicks, and C. Patrick Koelling All rights reserved. 2. Cost and Revenue Structure Used to identify and categorize the costs and revenues that need to be included in the analysis. The life-cycle concept and WBS are important aids in developing the cost and revenue structure for a project. Perhaps the most serious source of errors in developing cash flows is overlooking important categories of costs and revenues. Copyright ©2012 by Pearson Education, Inc. Engineering Economy, Fifteenth Edition Upper Saddle River, New Jersey 07458 By William G. Sullivan, Elin M. Wicks, and C. Patrick Koelling All rights reserved. 3. Estimating Techniques (Models) REMEMBER! The purpose of estimating is to develop cash-flow projections—not to produce exact data about the future, which is virtually impossible. Cost and revenue estimates can be classified according to detail, accuracy, and their intended use. Order-of-magnitude estimates (±30%) Semidetailed, or budget, estimates (±15%) Definitive (detailed) estimates (±5%) Copyright ©2012 by Pearson Education, Inc. Engineering Economy, Fifteenth Edition Upper Saddle River, New Jersey 07458 By William G. Sullivan, Elin M. Wicks, and C. Patrick Koelling All rights reserved.  The level of detail and accuracy of estimates depends on time and effort available as justified by the importance of the study, difficulty of estimating the items in question, methods or techniques employed, qualifications of the estimator(s), and sensitivity of study results to particular factor estimates. Copyright ©2012 by Pearson Education, Inc. Engineering Economy, Fifteenth Edition Upper Saddle River, New Jersey 07458 By William G. Sullivan, Elin M. Wicks, and C. Patrick Koelling All rights reserved. A variety of sources exist for cost and revenue estimation. Accounting records: good for historical data, but limited for engineering economic analysis. Other sources inside the firm: e.g., sales, engineering, production, purchasing. Sources outside the firm: U.S. government data, industry surveys, trade journals, and personal contacts. Research and development: e.g., pilot plant, test marketing program, surveys. Copyright ©2012 by Pearson Education, Inc. Engineering Economy, Fifteenth Edition Upper Saddle River, New Jersey 07458 By William G. Sullivan, Elin M. Wicks, and C. Patrick Koelling All rights reserved.  These models can be used in many types of estimates. Indexes technique Unit technique Factor technique Copyright ©2012 by Pearson Education, Inc. Engineering Economy, Fifteenth Edition Upper Saddle River, New Jersey 07458 By William G. Sullivan, Elin M. Wicks, and C. Patrick Koelling All rights reserved.  Indexes, I, provide a means for developing present and future cost and price estimates from historical data. k = reference year for which cost or price is known. n = year for which cost or price is to be estimated (n>k). Cn = estimated cost or price of item in year n. Ck = cost or price of item in reference year k. Indexes can be created for a single item or for multiple items (eqs. 3-1, 3-2). Copyright ©2012 by Pearson Education, Inc. Engineering Economy, Fifteenth Edition Upper Saddle River, New Jersey 07458 By William G. Sullivan, Elin M. Wicks, and C. Patrick Koelling All rights reserved.  Pause and solve In 2002 Acme Chemical purchased a large pump for $112,000. Acme keys their cost estimating for these pumps to the industrial pump index, with a baseline of 100 established in 1992. The index in 2002 was 212. Acme is now (2010) considering construction of a new addition and must estimate the cost of the same type and size of pump. If the industrial pump index is currently 286, what is the estimated cost of the new pump? Copyright ©2012 by Pearson Education, Inc. Engineering Economy, Fifteenth Edition Upper Saddle River, New Jersey 07458 By William G. Sullivan, Elin M. Wicks, and C. Patrick Koelling All rights reserved.  The unit technique is one that is widely known and understood. A “per unit factor” is used, along with the appropriate number of units, to find the total estimate of cost. An often used example is the cost of a particular house. Using a per unit factor of, say, $120 per square foot, and applying that to a house with 3,000 square feet, results in an estimated cost of $120 x 3,000 = $360,000. This techniques is useful in preliminary estimates, but using average costs can be very misleading. Copyright ©2012 by Pearson Education, Inc. Engineering Economy, Fifteenth Edition Upper Saddle River, New Jersey 07458 By William G. Sullivan, Elin M. Wicks, and C. Patrick Koelling All rights reserved.  The factor technique is an extension of the unit technique where the products of several quantities are summed and then added to components estimated directly. C = cost being estimated Cd = cost of the selected component d estimated directly fm = cost per unit of component m Um = number of units of component m Copyright ©2012 by Pearson Education, Inc. Engineering Economy, Fifteenth Edition Upper Saddle River, New Jersey 07458 By William G. Sullivan, Elin M. Wicks, and C. Patrick Koelling All rights reserved.  Parametric cost estimating is the use of historical cost data and statistical techniques (e.g., linear regression) to predict future costs. Parametric models are used in the early design stages to get an idea of how much the product (or project) will cost, on the basis of a few physical attributes (such as weight, volume, and power). Copyright ©2012 by Pearson Education, Inc. Engineering Economy, Fifteenth Edition Upper Saddle River, New Jersey 07458 By William G. Sullivan, Elin M. Wicks, and C. Patrick Koelling All rights reserved. The power-sizing technique (or exponential model) is frequently used for developing capital investment estimates for industrial plants and equipment. (both in $ as of the point in time for which the estimate is desired) (both in the same physical units) Copyright ©2012 by Pearson Education, Inc. Engineering Economy, Fifteenth Edition Upper Saddle River, New Jersey 07458 By William G. Sullivan, Elin M. Wicks, and C. Patrick Koelling All rights reserved.  Pause and solve Acme Logistics provides “Less than truck load” (LTL) services throughout the U.S. They have several hubs where they use cross-docking to move goods from one trailer to another. Acme built its last hub 10 years ago, and it had 36 dock doors. The cost index at that time was 140, and the total cost was $6 million. Acme plans a new hub that will have 48 dock doors. The cost index now is 195, and Acme will use a capacity factor of 0.82. What is the estimated cost of the new hub? Copyright ©2012 by Pearson Education, Inc. Engineering Economy, Fifteenth Edition Upper Saddle River, New Jersey 07458 By William G. Sullivan, Elin M. Wicks, and C. Patrick Koelling All rights reserved.  A learning curve reflects increased efficiency and performance with repetitive production of a good or service. The concept is that some input resources decrease, on a per-output-unit basis, as the number of units produced increases. Copyright ©2012 by Pearson Education, Inc. Engineering Economy, Fifteenth Edition Upper Saddle River, New Jersey 07458 By William G. Sullivan, Elin M. Wicks, and C. Patrick Koelling All rights reserved. Most learning curves assume a constant percentage reduction occurs as the number of units produced is doubled. Copyright ©2012 by Pearson Education, Inc. Engineering Economy, Fifteenth Edition Upper Saddle River, New Jersey 07458 By William G. Sullivan, Elin M. Wicks, and C. Patrick Koelling All rights reserved. Learning curve example: Assume the first unit of production required 3 hours time for assembly. The learning rate is 75%. Find (a) the time to assemble the 8th unit, and (b) the time needed to assemble the first 6 units. Copyright ©2012 by Pearson Education, Inc. Engineering Economy, Fifteenth Edition Upper Saddle River, New Jersey 07458 By William G. Sullivan, Elin M. Wicks, and C. Patrick Koelling All rights reserved.  Cost Estimation in the Design Process To ensure that products can be sold at competitive prices, cost must be a major factor in the design of the product. Both a bottom-up approach and a top-down approach can be used to determine product costs and selling price. Copyright ©2012 by Pearson Education, Inc. Engineering Economy, Fifteenth Edition Upper Saddle River, New Jersey 07458 By William G. Sullivan, Elin M. Wicks, and C. Patrick Koelling All rights reserved.  “Bottom-up” cost estimating is commonly used to make decisions about what to produce and how to price products. Major types of costs to estimate are tooling costs, manufacturing labor costs, material costs, supervision, factory overhead, and general and administrative costs. Copyright ©2012 by Pearson Education, Inc. Engineering Economy, Fifteenth Edition Upper Saddle River, New Jersey 07458 By William G. Sullivan, Elin M. Wicks, and C. Patrick Koelling All rights reserved.  Value Engineering The objective of value engineering (VE) is to provide required product functions at a minimum cost. VE necessitates a detailed examination of a product’s functions, and the cost of each, in addition to a through review of product specifications. Performed by a team of specialists from a variety of disciplines (design, manufacturing, marketing, etc.), and the team focuses on determining the most cost- effective way to provide high value at an acceptable cost to the customer. Copyright ©2012 by Pearson Education, Inc. Engineering Economy, Fifteenth Edition Upper Saddle River, New Jersey 07458 By William G. Sullivan, Elin M. Wicks, and C. Patrick Koelling All rights reserved.  VE is most appropriately applied early in the life cycle where there is more potential for cost savings. It is applied repeatedly during the design phase as new information becomes available. The VE function appears within the design to cost loop and is critical part of obtaining a total manufacturing cost that is less than the target cost. Copyright ©2012 by Pearson Education, Inc. Engineering Economy, Fifteenth Edition Upper Saddle River, New Jersey 07458 By William G. Sullivan, Elin M. Wicks, and C. Patrick Koelling All rights reserved.  Copyright ©2012 by Pearson Education, Inc. Engineering Economy, Fifteenth Edition Upper Saddle River, New Jersey 07458 By William G. Sullivan, Elin M. Wicks, and C. Patrick Koelling All rights reserved.  Copyright ©2012 by Pearson Education, Inc. Engineering Economy, Fifteenth Edition Upper Saddle River, New Jersey 07458 By William G. Sullivan, Elin M. Wicks, and C. Patrick Koelling All rights reserved.  CHAPTER-3: TIME VALUE OF MONEY 3 TIME VALUE OF MONEY 3.1 TIME VALUE OF MONEY 3.1.1 INTRODUCTION TO TIME VALUE OF MONEY Time value of money is the most importance concepts in finance. It means that the value of a rupee received in one year from now is not the same as the value of a rupee received today. In other words, most of us would prefer to received cash sooner rather than later and to spend later rather than sooner. Money has time value because it earns interest on the principal and also on the previously earned interest. As a result, a rupee invested today can grow a rupee plus interest and interest on interest at some future date. For example, if we invest Rs. 1000 at the rate of 10 percent, annually it becomes Rs 1100 in one year later. Hence, Rs 1000 is called present value of Rs 1100. It means, the future value Rs 1100 is the result of present value Rs 1000. Money has time value because 1. Inflation: Money in hand today has more purchasing power. 2. Risk factor: the present is certain as comparing to future, so it is required to compensate the uncertainty. 3. Time preference: it is human behavior that every one prefers to receive money as earlier as possible. 4. Liquidity preference: Capital can be employed productively. 5. Sacrifice of present consumption: For making investment one must save his earning and saving from current earning is not possible without sacrificing present consumption. And, people do not like to sacrifice their presence consumption if they do not get reward for it. 3.1.2 SIMPLE INTEREST AND COMPOUND INTEREST 1 SIMPLE INTEREST Simple interest is interest that is paid (earned) on only the original amount, or principal, borrowed (lent). The dollar amount of simple interest is a function of three variables: the original amount borrowed (lent), or principal; the interest rate per time period; and the number of time periods for which the principal is borrowed (lent). The formula for calculating simple interest is Simple Interest (SI) = P*i*n Where, P = Principal or Original amount borrowed i = Interest rate per time period n = No. of time Periods (years) Problem and Solution: In 2005, total debit (credit cards, auto loans, home mortgages, etc.) amounted to more than 100% of total disposable income for the average U.S household. If your total disposable income is $50,000, how much sum can you expect to pay at the end of one year period when the average interest rate on your debit is 12% per year? SI = (P).(i).(n) = $50,000*X(0.12)*1 Therefore, SI = $ 6,000 MGTS 301 (ENGINEERING ECONOMY), Kathmandu University By Punya Ram Sujakhu (9841395153) Page 1 of 16  CHAPTER-3: TIME VALUE OF MONEY 2 COMPOUND INTEREST Compound interest is the interest which is calculated on the both of initial principal and on any interest earned. It considers all of the accumulated interest of previous periods of a deposit or loan while calculating interest. The equation to find the compound interest is n Interest = P (1+i) – P Where, P = Principal or Present Value i = Interest rate n = No. of Periods (years) Let, Assume the Principal amount be $1,000 on which interest charge at10%. (1) (2)=(1)x10% (3)=(1)+(2) Period Amount owed at beginning of Interest amount for period Amount owed at end of period period 1 $1,000 $100 $1,100 2 $1,100 $110 $1,210 3 $1,210 $121 $1,331 3.1.3 CONCEPT OF EQUIVALENCE In general, compounding is the process of finding future value of a cash flow or a series of cash flow. The compounded amount equals to the present value plus the interest earned. The interest rate and time period is known compounding rate and compounding period which is used to convert the present value into future value. Whereas, discounting is the process to findings present value of a cash flow or a series of cash flow. Discounting is the reciprocal or reverse of compounding. The interest rate is called discounts rate and time period is called discounts period which is used to convert the future value into present value. An annuity is a series of equal amount of payment made of each year. It is popularly known as installment.If equal amount of payment is made at the end of the year it is called simply annuity or ordinary annuity. If equal amount of payment is made at the beginning of each year then it is called annuity due. An annuity whose payments occur forever is called perpetuity. 3.1.4 CASH FLOW DIAGRAM (CFD) 1. CASH FLOW Cash flows are described as the inflows and outflows of money. Every person or company has cash receipts- revenue and income (inflows); and cash disbursements expenses, and costs (outflows). These receipts and disbursements are the cash flows, with a plus sign representing cash inflows and a minus sign representing cash outflows. The cash flow is fundamental to every economic study. 1. Cash inflows, or receipts, may be comprised of the following 1. Revenues (usually incremental resulting from an alternative). 2. Operating cost reductions (resulting from an alternative). 3. Asset salvages value. 4. Receipt of loan principal. 5. Income tax savings. 6. Receipts from stock and bond sales. 7. Construction and facility cost savings. 8. Saving or return of corporate capital funds. MGTS 301 (ENGINEERING ECONOMY), Kathmandu University By Punya Ram Sujakhu (9841395153) Page 2 of 16  CHAPTER-3: TIME VALUE OF MONEY 2. Cash outflows, or disbursements, may be comprised of the following, 1. First cost of assets. 2. Engineering design costs. 3. Operating costs (annual and incremental). 4. Periodic maintenance and rebuild costs. 5. Loan interest and principal payments. 6. Major expected/unexpected upgrade costs. 7. Income taxes. 8. Expenditure of corporate capital funds. 2. CASH FLOW DIAGRAM (CFD) A cash flow diagram is a very important tool for clarifying and visualizing a series of cash flows. The costs and benefits of engineering projects occur over time. It means, Engineering projects generally have cash inflow (receipts) or cash outflow (disbursements) at different points in time. Specifically, a CFD illustrates the size, sign, and timing of individual cash flows. Components to show in a CFD 1. A CFD is created by first drawing a segmented time-based horizontal line, divided into appropriate time unit. 2. Each time when there is a cash flow, a vertical arrow is added - pointing down for costs and up for revenues or benefits. The cost flows are drawn to relative scale. An Example of Cash Flow Diagram: A man borrowed $1,000 from a bank at 8% interest. Two end-of-year payments: at the end of the first year, he will repay half of the $1000 principal plus the interest that is due. At the end of the second year, he will repay the remaining half plus the interest for the second year. Cash flow for this problem is: End of year (EOY) Cash flow (CF) 0 +$1000 1 -$580 (-$500 - $80) 2 -$540 (-$500 - $40) 3. TYPES OF CASH FLOW The cash flow is fundamental to every economic analysis. Cash flows occur in many configurations and amounts isolated single values, series that are uniform, and series that increase or decrease by constant amounts or constant percentages. There are no any rules to classify the cash flow but we can find the following types of cash flow in engineering economy. 1. Single payment Cash flow 2. Uniform payment cash flow 3. Linear (Arithmetic) gradient cash flow 4. Geometric gradient cash flow 5. Irregular (random) cash flow MGTS 301 (ENGINEERING ECONOMY), Kathmandu University By Punya Ram Sujakhu (9841395153) Page 3 of 16  CHAPTER-3: TIME VALUE OF MONEY 14 1. SINGLE PAYMENT or ONE TIME CASH FLOW or SINGLE CASH FLOWS If an investment offers only one lump sum cash flow at the given time period then it is called single cash flow. It may be the case to find future value (F) or may be to find Present Value (P). For example, today you deposited Rs. 1000 in saving account for 10 years at the interest rate of 12%. How much money will you have after 10 year? Formula for single payment 1. Single Payment Compound Amount Factor i. F/P factor = (F/P,i%,n) = 1 + i ii. Future Value (F)= P (F/P,i%,n) 2. Single Payment Present Worth Factor   i. P/F factor = (P/F,i%,n)=   or 1 + i or /, %, ii. Present Value (P)= F(P/F,i%,n) MGTS 301 (ENGINEERING ECONOMY), Kathmandu University By Punya Ram Sujakhu (9841395153) Page 4 of 16  CHAPTER-3: TIME VALUE OF MONEY NUMERICAL EXAMPLE ON SINGLE CASH FLOW 1. Find F when given P (Annually) 2. Find F when given P (Quarterly) 3. Find P when given F (Annually) 4. Find P when given F (uneven) 5. Decision on F and P 6. Decision on F and P Which amount is worth more at 14 percent; Rs 1000 in Lottery officials offer the choice of following hand today or Rs 2000 due in 6 years?[1000 and alternative payments. Which would you choose if 911.16] the interest rate is 10 percent? [9091 & 12418.50] Alt. 1 Rs.10, 000 one year from now Alt. 2 Rs.20, 000 five years from now 7. Find i when given F & P 8. Find n when given F & P If Laurel can make an investment in a friend's business How long will it takes to grow from $5,000 to $8,500 of $3000 now in order to receive $5000 five years from at the interest rate of 9% quarterly? [5.96 years] now, determine the rate of return. [10.76%] 9. Find i when given F & P 10. Find n when given F & P What interest rate makes your money treble (3 times) How long will it take for an investment to double at in 10 years using (a) simple interest concept (b) 5% per year (a) simple interest and (b) compound interest? [a. 20 years b. 14.2 years] compound interest concept? [20% and11.61%] 2. UNIFORM SERIES or EVEN CASH FLOWS or ANNUITY An annuity is a special cash flow pattern in which equal payments or receipts occurring over a specified number of periods. For example, Equal monthly installment (EMI) and insurance premium are the example of annuity. It is popularly known as annuity and annuity is two types 1. Ordinary Annuities A series of equal amount of payments made at the end of specified number of periods. Then it is called ordinary annuity. 2. Deferred Annuities Deferred annuities are uniform series that do not begin until sometime in the future. If the annuity is deferred J periods then the first payment (cash flow) begins at the end of period J+1. MGTS 301 (ENGINEERING ECONOMY), Kathmandu University By Punya Ram Sujakhu (9841395153) Page 5 of 16  CHAPTER-3: TIME VALUE OF MONEY Formula for uniform series 1. Uniform Series Compound Amount Factor 1+in -1 i. F/A factor = (F/A,i%,n)= i ii. Future Value (F)= A(F/A,i%,n) 2. Uniform Series Sinking Fund Factor  i. A/F factor = (A/F,i%,n)=    ii. Annual Amount (A)= F(A/F,i%,n) 3. Uniform Series Present Worth Factor 1 1+in -1 1+in i. P/A factor = (P/A,i%,n)= or 1- i1+in i ii. Present Value (P)= A(P/A,i%,n) 4. Uniform Series Capital Recovery Factor i1+in i. A/P factor = (A/P,i%,n)= 1+in -1 ii. Annual Amount (A)= P(A/P,i%,n) NUMERICAL EXAMPLE ON UNIFORM SERIES 1. Find F when given A (Annually) 2. Find A when given F (Annually) 3. Find P when given A (Annually) 4. Find A when given P (Annually) 5. Find i when given F and A (Formula) 6. Find i when given P and A (Interpolation) MGTS 301 (ENGINEERING ECONOMY), Kathmandu University By Punya Ram Sujakhu (9841395153) Page 6 of 16  CHAPTER-3: TIME VALUE OF MONEY TR-LR HR-LR TR-LR = ∴TRi = LR+ (HR-LR) TRF-LRF HRF-LRF TRF-LRF 7. Find n when given P and A 8. Find i when given A and P (Interpolation) 9. Find n when given P and A 10. Find n when given P and A (Interpolation) You need to accumulate Rs 10,000. To do so, you plan While steve Bouchard was a student at the to make deposits of Rs 1750 per year, with the first University of Florida, he borrowed Rs.12, 000 in payment being made a year from today, in a bank student loans at an annual interest rate of 9 percent. account which pays 6 percent annual interest. How If Steve repays Rs.1500 per year, how long to the many years will it take out to reach your goal? [5years] nearest year, will it take you to repay the loan? [15 years] 3. ARITHMETIC GRADIENT SERIES or LINEAR GRADIENT CASH FLOW Cash flows that increase or decrease by a constant amount are considered arithmetic gradient series. The amount of increase (or decrease) is called the gradient. Sometimes cash flows change by a constant amount each period. Arithmetic gradient series is linear gradient cash flow in nature. The first cash flow in the arithmetic gradient series becomes zero (i.e. G=0 in year1). Since the gradient (G) series normally is used along with a uniform series (A). Formula for arithmetic gradient series 1. Arithmetic Gradient Present worth Factor 1+i n -in-1 1 1+in -1 or  - 1+in  n i. P/G factor = (P/G,i%,n)= i2 1+in i i1+in ii. Present Worth of Arithmetic Gradient (PG) = G (P/G,i%,n) iii. Total Present Worth of Arithmetic Gradient (P  =  ±  or [A(P/A,i%,n) + G(P/G,i%,n)] iv. Total Future Worth of Arithmetic Gradient (FT )=PT (F/P,i%,n) or AT (F/A,i%,n) v. Annual Amount of Arithmetic Gradient (A   = PT A⁄P,i%,n or # ± # 2. Arithmetic Gradient Uniform series Factor (Optional) A/G factor = (A/G,i%,n)= P⁄G ,i%,nA⁄P ,i%,n or - 1+in 1 n i. i -1 ii. Annual Amount of Arithmetic Gradient (A  = $A/G, i%, n iii. Total Annual Series of Arithmetic Gradient (A   = # ± # 3. Arithmetic Gradient Future worth Factor (Optional) 1 1+in -1 i. F/G factor = (F/G,i%,n)= P⁄G ,i%,nF⁄P ,i%,n or  -n i i ii. Future Worth of Arithmetic Gradient (FG) = G(F/G,i%,n) iii. Total Future Worth of Arithmetic Gradient (F   = ( ± ( MGTS 301 (ENGINEERING ECONOMY), Kathmandu University By Punya Ram Sujakhu (9841395153) Page 7 of 16  CHAPTER-3: TIME VALUE OF MONEY NUMERICAL EXAMPLE ON ARITHMATIC GRADIENT SERIES (LINEAR) 1. Find P when given G (+ve) Find A when given G (-ve) Suppose that certain EOY cash flows are expected to be $1,000 for the second year, $2,000 for the third year, and $3,000 for the fourth year and that, if interestis 15% per year, it is desired to find (a) present equivalent value at the beginning of the first year [P0 = G(P/G, 15%, 4) = $1,000(3.79) = $3,790.] (b) uniform annual equivalent value at the end of each of the four years.[ A = P0(A/P, 15%, 4) = $3,790(0.3503) = $1,326.30.] 4. GEOMETRIC GRADIENT SERIES or PERCENTAGE GRADIENT CASH FLOW Cash flow which changes by a constant percentage from one interest period to the next is called geometric gradients series. The arithmetic gradient is applicable where the period by- period change in a cash receipt or payment is a uniform amount but geometric gradient is applicable where the period-by-period change is a uniform rate, g. For example, if the maintenance costs for an automobile are $100 for the first year and it increases at a uniform rate (g) of 10% per year. 1. Geometric Gradient Present worth Factor +,-  )* +,. / 0 i. P/g factor =(P/A,g,i%,n)= 2ℎ45 6 ≠ 8 1 9 ii (P/A,g,i%,n)=   2ℎ45 6 = 8   2. Geometric Gradient Uniform series Factor    1 i. (F/g,i%,n)= #   2ℎ45 6 ≠ 8 1 ii (F/g,i%,n)= #. 51 + 8 9 2ℎ45 6 = 8 MGTS 301 (ENGINEERING ECONOMY), Kathmandu University By Punya Ram Sujakhu (9841395153) Page 8 of 16  CHAPTER-3: TIME VALUE OF MONEY NUMERICAL EXAMPLE ON GEOMETRIC GRADIENT SERIES (PERCENTAGE) 1. Find F when given g (+ve) 2. Find P when given g (-ve) Determine the P, A, and F equivalent values. The rate of increase is 20% per year after the first year, and the interest rate is 25% per year. Suppose the yearly interest rate is 10%. a. Find the present worth of a geometric gradient series with base amount 100 and gradient 10 assuming the first payment (base amount) occurs at the end of period 5 and the last payment is made at the end of period 25. b. What is the equivalent uniform series which has a total of 25 consecutive payments and starts in period 1? c. What is the equivalent annuity to the series in part (a) such that the annuity consists of 10 payments and its first payment occurs at the end of period 8? [(a) n=25 – 5 + 1=21 so P4 = 100(P/A,10%,21) + 10 (P/G, 10%, 21) & P = (P4) (P/F,10%,4) = 987.594] [(b) A = (987.594)(A/P,10%,25) = 108.80324] [(c) A = (987.594)(F/P,10%,7)(A/P,10%,10) = 313.21365] MGTS 301 (ENGINEERING ECONOMY), Kathmandu University By Punya Ram Sujakhu (9841395153) Page 9 of 16  CHAPTER-3: TIME VALUE OF MONEY 5. IRREGULAR PAYMENT SERIES or UNEQUAL SERIES Irregular cash flows are series of received or payment which provides different from year to year. They are unexpected by the project and thus not taken into account in their predictions. NUMERICAL EXAMPLE ON IRREGULAR SERIES 1. Find F when given A (Uneven) 2. Find P when given F (Uneven) An engineering company in Wyoming that owns 50 hectares of valuable land has decided to lease the mineral rights to a mining company. The primary objective is to obtain longterm income to finance ongoing projects 6 and 16 years from the present time. The engineering company makes a proposal to the mining company that it pay $20,000 per year for 20 years beginning 1 year from now, plus $ 10,000 six years from now and $ 15,000 sixteen years from now. If the mining company wants to payoff its lease immediately, how much should it pay now if the investment should make 16% per year? [124,075] MGTS 301 (ENGINEERING ECONOMY), Kathmandu University By Punya Ram Sujakhu (9841395153) Page 10 of 16  CHAPTER-3: TIME VALUE OF MONEY FORMULA ON INTEREST FACTORS for DISCRET COMPOUNDING FOR SINGLE PAYMENT CASH FLOW 1. Single Payment Compound Amount Factor i. F/P factor = (F/P,i%,n) = 1 + i ii. Present Value (P)= F (F/P,i%,n) 2. Single Payment Present Worth Factor  i. P/F factor = (P/F,i%,n)=   ii. Future Value (F)= P(F/P,i%,n) FOR UNIFORM CASH FLOW 1. Uniform Series Compound Amount Factor 1+in -1 i. F/A factor = (F/A,i%,n)= i ii. Future Value (F)= A(F/A,i%,n) 2. Uniform Series Sinking Fund Factor  i. A/F factor = (A/F,i%,n)=    ii. Annual Amount (A)= F(A/F,i%,n) 3. Uniform Series Present Worth Factor 1 1+in -1 1+in i. P/A factor = (P/A,i%,n)= or 1- i1+in i ii. Present Value (P)= A(P/A,i%,n) 4. Uniform Series Capital Recovery Factor i1+in i. A/P factor = (A/P,i%,n)= 1+in -1 ii. Annual Amount (A)= P(A/P,i%,n) FOR ARITHMETIC GRADIENT CASH FLOW 1. Arithmetic Gradient Present worth Factor 1+i n -in-1 1 1+in -1 or  - 1+in  n i. P/G factor = (P/G,i%,n)= i2 1+in i i1+in ii. Present Worth of Arithmetic Gradient (P) = G (P/G,i%,n) iii. Total Present Worth of Arithmetic Gradient (P  =  ±  2. Arithmetic Gradient Uniform series Factor A/G factor = (A/G,i%,n)= P⁄G ,i%,nA⁄P ,i%,n or - 1+in 1 n i. i -1 ii. Annual amount of Arithmetic Gradient (A  = $A/G, i%, n iii. Total Annual Series of Arithmetic Gradient (A   = # ± # ;< A  = PT A⁄P,i%,n 3. Arithmetic Gradient Future worth Factor 1 1+in -1 i. F/G factor = (F/G,i%,n)= P⁄G ,i%,nF⁄P ,i%,n or  -n i i ii. Future Worth of Arithmetic Gradient (F) = G(F/G,i%,n) iii. Total Future Worth of Arithmetic Gradient (P  =  ±  MGTS 301 (ENGINEERING ECONOMY), Kathmandu University By Punya Ram Sujakhu (9841395153) Page 11 of 16  CHAPTER-3: TIME VALUE OF MONEY FOR GEOMETRIC GRADIENT CASH FLOW 1. Geometric Gradient Present worth Factor =,> @ )=* =,? / 0 i. P/g factor =(P/A,g,i%,n)= ABC@ > ≠ ? ?> @ ii (P/A,g,i%,n)=   ABC@ > = ? = ? 2. Geometric Gradient Uniform series Factor = ?@== >@ i. (F/g,i%,n)= D=   ABC@ > ≠ ? => ii (F/g,i%,n)= D=. @= + ?@= ABC@ > = ? RELATIONSHIP BETWEEN INTEREST FACTORS  1. P/F, i%, n = /, %,  2. A/P, i%, n = /E, %, 3. F/A, i%, n = P/A, i%, nF/P, i%, n 4. A/P, i%, n = A/F, i%, n + i% 5. F/G, i%, n = P/G, i%, nF/P, i%, n CONTINUOUS COMPOUNDING INTEREST FACTORS 1. Single Payment Compound Amount Factor (F/P,r%,N) = 4 FG 2. Single Payment Present Worth Factor  (P/F,r%,N)= H IJ 3. Uniform Series Compound Amount Factor H IJ  (F/A,r%,N)= H I  4. Uniform Series Present Worth Factor H IJ  (P/A,r%,N)= H IJ H I   MGTS 301 (ENGINEERING ECONOMY), Kathmandu University By Punya Ram Sujakhu (9841395153) Page 12 of 16  CHAPTER-3: TIME VALUE OF MONEY I. Construct the CASH FLOW DIAGRAM from the given data. 1. Where P = $10,000 is borrowed at 8% per year and F is sought after 5 years. Construct the cash flow diagram. 2. A father wants to deposit an unknown lump-sum amount into an investment opportunity 2 years from now that is large enough to withdraw $4000 per year for state university tuition for 5 years starting 3 years from now. If the rate of return is estimated to be 15.5% per year, construct the cash flow diagram. 3. An electrical engineer wants to deposit an amount P now such that she can withdraw an equal annual amount of A I = $2000 per year for the first 5 years starting 1 year after the deposit, and a different annual withdrawal of A2 = $3000 per year for the following 3 years. How would the cash flow diagram appear if i = 8.5% per year? 4. Construct a cash flow diagram for the following cash flows: $10,000 outflow at time zero, $3000 per year outflow in years 1 through 3 and $9000 inflow in years 4 through 8 at an interest rate of 10% per year, and an unknown future amount in year 8. 5. Construct a cash flow diagram to find the present worth of a future outflow of $40,000 in year 5 at an interest rate of 15% per year. 6. A sports apparel company has initiated a logo-licensing program. It expects to realize revenue of $80,000 in fees next year from the sale of its logo. Fees are expected to increase uniformly to a level of $200,000 in 6 years. Determine the arithmetic gradient and construct the cash flow diagram. 7. Before evaluating the economic merits of a proposed investment, the XYZ Corporation insists that its engineers develop a cash-flow diagram of the proposal. An investment of $10,000 can be made that will produce uniform annual revenue of $ 5,310 for five years and then have a market (recovery) value of $ 2000 at the end of the year five. Annual expenses will be $3000 at the end of each year for operating and maintaining the project. Draw a cash-flow diagram for the five year life of the project. II. Problems on INTEREST FACTOR 1. Find the correct numerical value for the following factors from the interest tables. a. (F/P,8%,25) b. (P/A,3%,8) c. (P/G,9%,20) d. (F/A,15%,18) e. (A/P,30%,15) [a. (F/P,8%25) = 6.8485; b. (P/A,3%,8) = 7.0197; c. (P/G,9%,20) = 61.7770; d. (F/A,15%,18) = 75.8364; e. (A/P,30%,15) = 0.30598] 2. Find the correct numerical value for the following interest factors from applying formula. a. (P/A ,3%,8) b. (P/G,9%,20) c. (F/A , 15%,18) d. (A/P,30%,15) 3. Find the value of the (P/F,4%,48) factor. [0.1522] 4. Determine the value of the A/P factor for an interest rate of 7.3% and n of 10 years, that is, (A/P,7.3%,10). [0.1444] III. Problems on SINGLE PAYMENT 1. If you deposited Rs. 20,000 in a bank that pays 10 percent interest annually. How much money will be in your bank account after 5 years? [F=32,210] 2. You will require Rs. 700,000 in 5 years. If you earn 5 percent interest on your fund. How much will you to invest today in order to reach your goal? [P=548,460] 3. How long will it take for an investment to double at 5% per year (a) simple interest and (b) compound interest? [a. 20 years b. 14.2 years] MGTS 301 (ENGINEERING ECONOMY), Kathmandu University By Punya Ram Sujakhu (9841395153) Page 13 of 16  CHAPTER-3: TIME VALUE OF MONEY 4. Calculate the future sum of an initial sum of $100,