Instructional Materials For Engineering Economy PDF

POLYTECHNIC UNIVERSITY OF THE PHILIPPINES SANTA MARIA, BULACAN CAMPUS Km. 38, Sitio Gulod, Pulong Buhangin, Santa Maria, Bulacan INSTRUCTIONAL MATERIALS FOR ENGINEERING ECONOMY Bachelor of Science in Computer Engineering Asst. Prof. JENNILYN S. AVANCEÑA,...

POLYTECHNIC UNIVERSITY OF THE PHILIPPINES SANTA MARIA, BULACAN CAMPUS Km. 38, Sitio Gulod, Pulong Buhangin, Santa Maria, Bulacan INSTRUCTIONAL MATERIALS FOR ENGINEERING ECONOMY Bachelor of Science in Computer Engineering Asst. Prof. JENNILYN S. AVANCEÑA, MIT FIRST TERM ACADEMIC YEAR 2024 – 2025  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES SANTA MARIA, BULACAN CAMPUS Km. 38, Sitio Gulod, Pulong Buhangin, Santa Maria, Bulacan CHAPTER 1: INTRODUCTION TO ENGINEERING ECONOMICS OVERVIEW Engineering Economics is a discipline that integrates engineering principles with economic analysis to evaluate and guide decision-making in technical projects. It involves the systematic comparison of costs, benefits, and alternatives to optimize project outcomes, ensuring resource-efficient solutions. By applying economic concepts such as supply and demand, cost analysis, and investment evaluation, engineers can assess project feasibility, manage resources, and maximize returns. Key principles include developing alternatives, focusing on differences, using consistent viewpoints, measuring outcomes with common units, and accounting for risks and uncertainties, all while revisiting decisions for continuous improvement. DESIRE LEARNING OUTCOMES 1. Apply the fundamental concepts and processes for decision-making in engineering economics -------------------------------------------------------------------------------------------------- What is Engineering Economics? Engineering is the profession in which the knowledge gained in physics, chemistry, life sciences, and mathematics is applied to make products on a large scale that increase the prosperity of man. (ABET - Accreditation for Engineering and Technology) Economics deals with the production, distribution, and consumption of goods and services. Engineering Economics is the discipline concerned with the economic aspects of engineering. It involves the systematic evaluation of the cost and benefits of proposed technical projects. (Eugene Grant) Principles of Engineering Economics Principle 1: Develop the Alternatives The alternates can be developed using a brainstorming session. The more creative and resourceful the team members are, the better the selection of alternates available for a go/no-go decision would be. Principle 2: Focus on the Difference The future outcomes from the alternates are set as a higher priority. Based on differences among alternates, a future course of action is selected. Analysis, projection, and comparison are used to differentiate alternates. Principle 3: Use a Consistent Viewpoint The prospective outcomes of the alternatives should be consistently developed from a defined point of view. Goal-setting mode. 2|Page  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES SANTA MARIA, BULACAN CAMPUS Km. 38, Sitio Gulod, Pulong Buhangin, Santa Maria, Bulacan The perspective of the decision-maker, which is often that of the owners of the form, would be normally used. Principle 4: Use a Common Unit of Measure Using a common unit of measurement to enumerate as many of the prospective outcomes as possible will make easier the analysis and comparison of alternatives. A common unit of measure (such as pesos versus units) totals costs or total profits that can be generated from the alternate considered. Principle 5: Consider All Relevant Criteria The selection of a preferred alternative requires the use of a criterion or several criteria. The decision process should consider the outcomes enumerated in the monetary unit and those expressed in some other unit of measurement or made explicit in a descriptive manner. Principle 6: Make Uncertainty Explicit Risk and uncertainty are inherent in projecting (or estimating) the future outcomes of the alternatives and should be recognized with the firm’s analysis, comparison projection, and probability. Principle 7: Revisit Your Decisions Learning from and adapting based on our experience are essential and are indicators of a good organization. The initial projected outcomes of the selected alternate should be subsequently compared with the actual results achieved. Economic Concepts Studying economics gives insights into the general environment of resource allocation decisions, opportunity costs, and project evaluation, which are crucial in many areas. Economics studies economic activities. Economics does not deal with all of them, but humans spend the maximum time on economic activities. Study of wants > efforts > wealth > satisfaction: Every human being has some wants, and these wants are unlimited. To fulfill these wants, a person makes efforts; by doing efforts, he gets wealth, and with this earned wealth, he satisfies his wants. 3|Page  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES SANTA MARIA, BULACAN CAMPUS Km. 38, Sitio Gulod, Pulong Buhangin, Santa Maria, Bulacan Study of human behavior with relation to ends and scarce means: If a person is alive, his wants go on increasing, but the person cannot fulfill all the wants. The reason is that the resources required to fulfill these wants are limited. Economics studies the problem of choice: Scarcity and choice go together. If things were available in abundance, then there would have been no problem of choice; the point is that “problems of choice” arise because of scarcity. Basic Economic Activities An economic activity is a systematic endeavor to satisfy a material need. Material needs are the needs for goods and services. Production is a process of creation of utility or value in goods or services (or both). “Production may be defined as the creation of utilities.” (Anatol Murad) Factors of Production: Factors of production are essential elements that cooperate in the process of production. Land: It is the factor of production which is available to humankind as a gift of nature. Labor: It is the physical or mental effort of human beings in the process of production. The services of a doctor, lawyer, teacher, worker in the factory all constitute labor. Capital: Capital is a man-made material and is a source of production. It consists of the part of production which is used for further production. Entrepreneurship: Entrepreneurship refers to the skills of the entrepreneur: (a) to organize business (b) to undertake risks of business Consumption has a special meaning in economics; it means the use of or utility of goods and services for the direct satisfaction of individual and collective wants. o Individual Consumption: It is that consumption that leads to the final satisfaction of the wants of an individual. o Collective consumption: It is that consumption that leads to the final satisfaction of collective wants, for example, Uses of roads, dams, bridges, or parks. Investment: “Investment is that part of production during a year which is not consumed but saved as a capital formation for further production.” Distribution refers to the way total output, income, or wealth is distributed among individuals or among the factors of production. The excess of production over consumption in an accounting year is called capital formation or investment. The circular flow of production, income, and expenditure never stops. Supply and Demand Concepts What is the Theory of Demand? 4|Page  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES SANTA MARIA, BULACAN CAMPUS Km. 38, Sitio Gulod, Pulong Buhangin, Santa Maria, Bulacan In economics, demand is regarded as the lifeline of a business enterprise. The demand for a particular good is the amount that will be purchased at a given time and a given price. (Vera Anstey) 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. (Charles Ferguson) Demand is the want of a person, which will become demand when he is ready to buy the goods at a given price and at a given point in time. What is the Law of Demand? The law of demand states that other things being equal, the demand for a good extends with a fall in price and contracts with a rise in price. There is an inverse relationship with a price, and the quantity demanded. The Law of Demand states that people will buy more at lower prices and buy less at higher prices, ceteris paribus, or the other things remaining the same. (Paul Samuelson) The Law of Demand states that the amount demanded increases with a fall in price and diminishes when price raises, other things being equal. (Alfred Marshall) What is the Theory of Supply? The theory of supply is as much necessary as the theory of demand for the analysis of prices. Supply means the amount offered for sale at a given price during a certain period of time. The supply of goods is the quantity offered for sale in a given market at a given time at various prices. (Thomas Robert Malthus) What is the Law of Supply? The law of supply expresses the relation between the price of a commodity and its supply. In other words, the law of supply states that “other things being equal, when the price rises, supply extends and when the price falls, supply contracts.” The law of supply states that other things being equal, the higher the price, the greater the quantity supplied or, the lower the price, the smaller the quantity supplied. (Peter Dooley) 5|Page  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES SANTA MARIA, BULACAN CAMPUS Km. 38, Sitio Gulod, Pulong Buhangin, Santa Maria, Bulacan Necessities vs. Luxuries Necessity is a good that is vital to the function of the enterprise. Example: Cash supply for the snack factory to pay its employees their wages. Luxury is an item that is in surplus of need. Luxury is an item that is not needed for the survival of the enterprise. Example: Luxury tax. A fur coat is an example of luxury. It has been observed that for most goods and services, there exists a relationship between the price that must be paid and the quantity that will be demanded or purchased. Consumer and Producer Goods and Services The goods and services that are produced and utilized may be categorized into two groups. Consumer goods and services are those products or services that are directly used by consumers to satisfy their desire. Food, clothing, homes, air conditioners, fast-moving consumer goods, telephones, mobile phones, and banking services are examples of consumer goods and services. Producer goods and services are those products or services that are used to produce consumer goods and services or other producer goods. Manufacturing infrastructure that includes building, machinery, instruments and control systems, locomotives, and land transport used for the transportation of manufactured goods are some examples. Cost Concepts The following are different types of cost that are involved in engineering and managerial problems: Fixed costs associated with a new or existing project are those costs that do not change over a wide range of activities of the project. These are the inevitable costs that must be paid regardless of the level of output and the resources used. o For example, interest on borrowed capital, the rental cost of a warehouse, administrative salaries, license fees, property insurance, and taxes are fixed costs. Variable costs are costs that vary to changes in the activity level of a new or existing project. o Examples of variable costs include raw material cost, direct labor cost, power cost, shipping charges, utility, etc. Incremental costs are additional costs that result from increasing the output by one or more units. o For example, if the cost of manufacturing 10 pieces is 2,000 and that of 11 pieces is 2,200, then the incremental cost is 200. 6|Page  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES SANTA MARIA, BULACAN CAMPUS Km. 38, Sitio Gulod, Pulong Buhangin, Santa Maria, Bulacan Standard costs are the planned costs per unit of output, anticipated labor hours, materials, and overhead categories. Direct costs can be measured and attributed to a specific activity or output. Indirect costs cannot be attributed to a single activity. Cash Costs are transactions that involve payment of cash. Book Costs are a noncash cost such as depreciation on machinery, etc. Sunk cost refers to the cost that has occurred in the past and does not have any impact on the future course of action. o For example, a car enthusiast had made a down payment of 5,000 to an 80,000 secondhand vehicle. If the enthusiast decided not to buy the car, it would not give back the 5,000. The 5,000 is a sunk cost. Opportunity cost or implicit cost refers to the value of the resources owned and used by a firm in its own production activity. o Example: Investing capital in the most rewarding alternative use or renting its land and buildings to the highest bidder rather than using them itself. Investment cost, or first cost, refers to the capital required to start a project. It may be either a single lump sum or a series of cash inputs that must be made at the beginning of the project. o For example, if we want to purchase a new car, then the investment cost for acquiring it is the sum of the down payment, taxes, and other charges involved in obtaining the ownership of the car. o For a capital-intensive project such as a construction project which takes several years to complete, the investment cost is usually spread over time in the form of progressive payments. Operation and Maintenance costs are costs that can be incurred by hiring people, purchasing machines, materials, information, and energy. Working Capital are funds required for the day-to-day operation of the enterprise. Salvage Value is the trade-in value of the equipment after its full use. Engineering Economics Environment The success of engineers depends upon their ability to manipulate goods and services by acquiring and applying physical laws. However, the worth of these goods and services lies in their utility, which is measured in economic terms. Thus, knowledge of both physical laws and economics is required for making appropriate decisions. 7|Page  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES SANTA MARIA, BULACAN CAMPUS Km. 38, Sitio Gulod, Pulong Buhangin, Santa Maria, Bulacan CHAPTER 2: MONEY-TIME RELATIONSHIPS AND EQUIVALENCE OVERVIEW The Time Value of Money (TVM) emphasizes that money available now is worth more than the same amount in the future due to its earning potential through interest. This principle is fundamental in finance and economics, where capital, whether equity or debt, can be used to generate more wealth over time. Interest, which is the cost of borrowing money, is calculated based on the principal amount and can be either simple or compound. Simple interest grows linearly, while compound interest accumulates on both the principal and previously earned interest. The formulae provided help calculate interest and total amounts owed or earned over different periods, illustrating how the value of money changes over time. DESIRE LEARNING OUTCOMES 1. Explain the concept of the Time Value of Money (TVM) and its importance in financial decision-making, including the difference between simple and compound interest. 2. Calculate simple and compound interest using appropriate formulas for various time periods, demonstrating an understanding of how money grows over time. 3. Analyze real-life scenarios involving loans and investments by applying TVM principles to determine interest earned, total repayment amounts, and the financial impact of different interest rates and compounding periods. -------------------------------------------------------------------------------------------------- Money is used as a means to store value. Before countries had viable currencies, the value was stored using gold, silver, and other precious metals. Eventually, the governments of many countries started using paper money backed by gold rather than using precious metals as a means of exchange. Time Value of Money It accounts for the interest an investment earns, and it indicates that an amount of money with a certain value now will increase in value in the future due to the interest the money earns during the intervening time period. Capital is wealth in the form of money or property that can be used to produce more wealth. o Equity Capital is owned by individuals who have invested their money or property in a business project or venture o Debt Capital (Borrowed Capital) is obtained from lenders for investment. Interest o It is defined as a commodity such as rent on money borrowed or loaned from one individual to another, from one institution to another institution, or from an institution to an individual. o It is the manifestation of the time value of money. Interest Computationally, interest is the difference between an ending amount of money and the beginning amount. 8|Page  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES SANTA MARIA, BULACAN CAMPUS Km. 38, Sitio Gulod, Pulong Buhangin, Santa Maria, Bulacan From the perspective of the borrower, Interest paid on borrowed funds (a loan) is determined using the original amount, also called the principal. When interest paid over a specific time unit is expressed as a percentage of the principal, the result is called the interest rate. FORMULA Interest Paid = A – P Interest Rate (%) = 𝑰𝒏𝒕𝒆𝒓𝒆𝒔𝒕 𝑷𝒂𝒊𝒅 x 100% 𝑷𝒓𝒊𝒏𝒄𝒊𝒑𝒂𝒍 𝑨𝒎𝒐𝒖𝒏𝒕 Where: A = amount owed P = principal amount Example 1: An employee borrows ₱10,000 on May 1 and must repay a total of ₱10,700 exactly 1 year later. Determine the interest amount and the interest rate paid. Example 2: You borrow ₱11,000 today and must repay a total of ₱11,550 exactly 1 year later. What are the interest amount and the interest rate paid? 9|Page  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES SANTA MARIA, BULACAN CAMPUS Km. 38, Sitio Gulod, Pulong Buhangin, Santa Maria, Bulacan Simple and Compound Interest Simple interest is the total interest earned or charged is linearly proportional to the initial amount of the loan (principal), the interest rate, and the number of interest periods. Where: I - total interest I = Pni P - principal amount lent or borrowed n - number of interest periods (annually, semi- annually, monthly, weekly, daily, etc.) always convert to yearly i - interest rate per interest period Where: F - total amount to be paid 𝐅 = 𝐏(𝟏 + 𝐧𝐢) P - principal amount lent or borrowed n - number of interest periods (annually, semi- annually, monthly, weekly, daily, etc.) always convert to yearly i - interest rate per interest period Period must be in years Semi-annually – divided by 2 Quarterly – by 4 Bi-monthly – by 6 Months – by 12 Weekly – by 52 Daily – by 365 Example 3: You borrow ₱1,500 from your friend for three years at a simple interest rate of 8% per year. How much interest will you pay after three years, and what is the value of the total amount that you will pay? 10 | P a g e  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES SANTA MARIA, BULACAN CAMPUS Km. 38, Sitio Gulod, Pulong Buhangin, Santa Maria, Bulacan Example 4: A total of ₱1200 is invested at a simple interest rate of 6% for 4 months. How much interest is earned on this investment and total amount need to pay. Example 5: Find the interest rate and final amount due investing ₱50,000 at a simple interest rate of 15.4% for 1.5years. Compound Interest is the interest charge for any interest period, e.g., a year, based on the remaining principal amount plus any accumulated interest charges up to the beginning of that period. where: A - total amount to be paid 𝐀 = 𝐏(𝟏 + 𝐢)𝐧 P - principal amount lent or borrowed or n - number of interest periods (annually, 𝒊 semi-annually, monthly, weekly, daily, 𝐀 = 𝐏(𝟏 + 𝒏)𝐧t etc.) – compounded t – period ( in years) 𝐂𝐨𝐦𝐩𝐨𝐮𝐧𝐝 𝐈𝐧𝐭𝐞𝐫𝐞𝐬𝐭 = 𝐀 − 𝐏 i - interest rate per interest period 11 | P a g e  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES SANTA MARIA, BULACAN CAMPUS Km. 38, Sitio Gulod, Pulong Buhangin, Santa Maria, Bulacan Example 6: The City Bank has issued a loan of ₱1,000 to a sole proprietor for a period of 5-years. The interest rate for this loan is 5%, and the interest is compounded annually. Compute for the compound amount and interest. Example 7: Your local bank branch recently announced a new savings plan with an interest rate of 0.0274% compounded daily. What is the compound payment on ₱52,000 at the end of one year? Example 8: A deposit of ₱3000 earns 2% interest compounded semi-annually. How much money is in the bank after 4 years? Example 9: If you deposit ₱4000 into an account paying 6% annual interest quarterly, how much money will be in the account after 5 years? 12 | P a g e  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES SANTA MARIA, BULACAN CAMPUS Km. 38, Sitio Gulod, Pulong Buhangin, Santa Maria, Bulacan CHAPTER 3: APPLICATION OF MONEY-TIME RELATIONSHIP OVERVIEW The application of the money-time relationship is essential for evaluating the financial viability of projects. It helps engineers and decision-makers understand how the value of money changes over time due to factors such as inflation, interest rates, and investment opportunities. DESIRE LEARNING OUTCOMES 1. Perform computation that show cash flow and the time value of money -------------------------------------------------------------------------------------------------- CASH FLOW DIAGRAMS The cash flow diagram is a graphical representation of cash flows drawn on a time scale. The horizontal line is a time scale, with the progression of time moving from left to right. The period (e.g., year, quarter, and month) can be applied to intervals of time. Cash flow diagram time t = 0 is the present, and the end of interval 1 is the end of time period 1. The arrows signify cash flows and are placed at the end of the period when the end- of-period convention is used. The end-of-period convention means that all cash flows are assumed to occur at the end of an interest period. Downward arrows represent expenses (negative cash flows or cash outflows). o Negative cash flows: These can be the first cost of assets, engineering design cost, annual operating costs, periodic maintenance and rebuild costs, loan interest and principal payments, major expected/unexpected upgrade costs, income taxes, etc. Upward arrows represent receipts (positive cash flows or cash inflows). o Positive cash flows: These can be revenues, operating cost reductions, asset salvage value, receipt of loan principal, income tax savings, receipts from stock and bond sales, construction and facility costs savings, saving or return of corporate capital funds, etc. 13 | P a g e  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES SANTA MARIA, BULACAN CAMPUS Km. 38, Sitio Gulod, Pulong Buhangin, Santa Maria, Bulacan The cash flow diagram is dependent on the point of view. Your point of view when you borrowed from an entity. The entity’s perspective when lending money. Example 1: 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 ₱400,000 can be made that will produce uniform annual revenue of ₱210,000 for five years and then have a market (recovery) value of ₱80,000 at the end of year five. Annual expenses will be ₱120,000 at the end of each year for operating and maintaining the project. Draw the cash flow diagram for the five-year life of the project. Use the corporation’s viewpoint. Example 2: You plan to borrow ₱15,000 to help in buying a two-wheeler. You have arranged to repay the entire principal plus interest of 8.5% accumulated yearly after 5 years. What is the total amount owed after 5 years. Also, draw the cash flow diagram. 14 | P a g e  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES SANTA MARIA, BULACAN CAMPUS Km. 38, Sitio Gulod, Pulong Buhangin, Santa Maria, Bulacan Patterns of capital investments, revenue, and expense differ from one project to another. Because of that, there is no single method for conducting engineering economy analyses that is ideal for all cases. Present Worth Method The Present Worth (PW) method is based on the concept of equivalent worth of all cash flows relative to some base or beginning point in time called the present. The PW of an investment alternative is a measure of how much money an individual or a firm could afford to pay for the investment in excess of its cost. A positive PW for an investment project is an amount of profit over the minimum amount required by investors. Formula PW = PW of cash inflows – PW of cash outflows For Annuity (series or annual payment) For Future (worth of money in the future) Present Worth = A(P/A, i%, n) Present Worth = F(P/F, i%, n) (1+𝑖)𝑛 −1 P/F = PW = 𝐹(1 + 𝑖)−𝑛 P/A = PW = 𝐴[ ] 𝑖(1+𝑖)𝑛 Where: Where: P = present value P = present value A = annual value or series or annual F = future value payment or annual cash flow PW = present worth PW = present worth i = interest rate i = interest rate n = time period n = time period Example 3: The production head proposed an acquisition of new equipment that could increase the productivity of a certain manual welding operation. The investment cost is ₱25,000 and the equipment will have a market value of ₱5,000 at the end of a study period of 5 years. The increased productivity would bring in ₱8,000 per year after extra operating costs have been subtracted from the revenue generated by the additional production. If the firm gives an effective interest rate of 20% per year, what is the potential improvement of the project? Solution: 15 | P a g e  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES SANTA MARIA, BULACAN CAMPUS Km. 38, Sitio Gulod, Pulong Buhangin, Santa Maria, Bulacan 1. Given: 2. Draw the cash flow diagram 3. Formula for PW PW = PW of cash inflows – PW of cash outflows PW (20%) = A(P/A,20%,5) + F(P/F, 20%,5) – P 16 | P a g e  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES SANTA MARIA, BULACAN CAMPUS Km. 38, Sitio Gulod, Pulong Buhangin, Santa Maria, Bulacan Example 4: A special purpose machine is to be acquired by paying a ₱15,000 initial cash payment plus a debt assumption of ₱135,000. The machine will generate additional net annual cash inflow of ₱40,000 for the firm throughout the 10 years of useful life of the asset. At the end of its life, a salvage value of 10% of its initial cost will be realized. Assuming the effective interest rate is 13.2% per annum, show whether the project is desirable by using the PW method. Solution: 1. Given: 2. Draw the cash flow diagram 3. Formula for PW PW = PW of cash inflows – PW of cash outflows PW (13.2%) = A(P/A,13.2%,10) + F(P/F, 13.2%,10) – P 17 | P a g e  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES SANTA MARIA, BULACAN CAMPUS Km. 38, Sitio Gulod, Pulong Buhangin, Santa Maria, Bulacan Example 5: A university lab is a research contractor to NASA for in-space fuel cell systems that are hydrogen and methanol based. During lab research, three equal-service machines need to be evaluated economically. Perform the present worth analysis with the costs show below with effective interest rate of 10% per annum. Electric-Powered Gas-Powered Solar-Powered First cost ₱4,500 ₱3,500 ₱6,000 Annual operating ₱900 ₱700 ₱50 cost Salvage value ₱200 ₱350 ₱100 Life, years 8 8 8 1. Given: 2. Draw the cash flow diagram 3. Formula for PW PW = PW of cash inflows – PW of cash outflows PW (10%) = A(P/A,10%,8) + F(P/F, 10%,8) – P 18 | P a g e  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES SANTA MARIA, BULACAN CAMPUS Km. 38, Sitio Gulod, Pulong Buhangin, Santa Maria, Bulacan Example 6: Your boss wants to buy an equipment for ₱30,000. It is believed that this equipment will bring an additional ₱8,500 income per year. The equipment’s value after 5 years will be ₱4,500. Your boss asks you if his idea is economically viable. Perform a present worth analysis with effective interest rate of 15% per annum. 1. Given: 2. Draw the cash flow diagram 3. Formula for PW PW = PW of cash inflows – PW of cash outflows PW (15%) = A(P/A,15%,5) + F(P/F, 15%,5) – P 19 | P a g e  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES SANTA MARIA, BULACAN CAMPUS Km. 38, Sitio Gulod, Pulong Buhangin, Santa Maria, Bulacan Example 7: Product “A” has a first cost of ₱20,000, an operating cost of ₱9,000 per year, and a ₱5,000 salvage value after 5 years, while the Product “B” will cost a ₱35,000 with an operating cost of ₱4,000 per year with a salvage value of ₱7,000 after 5 years. Perform a present worth analysis with effective interest rate of 12% per annum. Which should be selected? 1. Given: 2. Draw the cash flow diagram 3. Formula for PW PW = PW of cash inflows – PW of cash outflows PW (12%) = A(P/A,12%,5) + F(P/F, 12%,5) – P 20 | P a g e  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES SANTA MARIA, BULACAN CAMPUS Km. 38, Sitio Gulod, Pulong Buhangin, Santa Maria, Bulacan Future Worth Method The future worth method is useful in an investment situation where we need to compute the equivalent worth of a project at the end of its investment period rather than at its beginning. The Future Worth (FW) is based on the equivalent worth of all cash inflows and outflows at the end of the study period at an interest rate. A positive FW would result to acceptance of the problem solution. Formula FW = FW of cash inflows – FW of cash outflows For Annuity (series or annual payment) For Present (worth of money in the present) Future Worth = A(F/A, i%, n) Future Worth = A(F/P, i%, n) (1+𝑖)𝑛 −1 F/P = FW = 𝐹(1 + 𝑖)𝑛 F/A = FW = 𝐴[ ] 𝑖 Where: Where: F = future value P = present value A = annual value or series or annual F = future value payment or annual cash flow FW = future worth FW = future worth n = time period i = interest rate i = interest rate n = time period Example 8: The production head proposed an acquisition of new equipment that could increase the productivity of a certain manual welding operation. The investment cost is ₱25,000 and the equipment will have a market value of ₱5,000 at the end of a study period of 5 years. The increased productivity would bring in ₱8,000 per year after extra operating costs have been subtracted from the revenue generated by the additional production. If the firm gives an effective interest rate of 20% per year, what is the potential improvement of the project? Solution: 21 | P a g e  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES SANTA MARIA, BULACAN CAMPUS Km. 38, Sitio Gulod, Pulong Buhangin, Santa Maria, Bulacan 1. Given: 2. Draw the cash flow diagram 3. Formula for FW FW = FW of cash inflows – FW of cash outflows FW (20%) = A(F/A,20%,5)- A(F/P, 20%,5) + P 22 | P a g e  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES SANTA MARIA, BULACAN CAMPUS Km. 38, Sitio Gulod, Pulong Buhangin, Santa Maria, Bulacan Example 9: Product “A” has a first cost of ₱20,000, an operating cost of ₱9,000 per year, and a ₱5,000 salvage value after 5 years, while the Product “B” will cost a ₱35,000 with an operating cost of ₱4,000 per year with a salvage value of ₱7,000 after 5 years. Perform a future worth analysis with effective interest rate of 12% per annum. Which should be selected? 1. Given: 2. Draw the cash flow diagram 3. Formula for FW FW = FW of cash inflows – FW of cash outflows FW (12%) = A(F/A,12%,5) - A(F/P, 12%,5) + P 23 | P a g e  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES SANTA MARIA, BULACAN CAMPUS Km. 38, Sitio Gulod, Pulong Buhangin, Santa Maria, Bulacan Example 10: A ₱45,000 investment in a new conveyor system is projected to improve throughout and increasing revenue by ₱14,000 per year for 5 years. The market value of ₱4000 at the end of five years using future worth with 12% interest, is this good investment? 1. Given: 2. Draw the cash flow diagram 3. Formula for FW FW = FW of cash inflows – FW of cash outflows FW (12%) = A(F/A,12%,5) – A(F/P, 12%,5) + P 24 | P a g e  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES SANTA MARIA, BULACAN CAMPUS Km. 38, Sitio Gulod, Pulong Buhangin, Santa Maria, Bulacan Annual Worth Method Annual Worth (AW) is an equal annual series of amounts, for a stated study period, that is equivalent to the cash inflows and outflows at an interest rate. As long as the AW is greater than or equal to zero, the project is economically attractive; otherwise, it is not. An AW of zero means that an annual return exactly equal to the effective interest that has been earned. Formula AW= AW of cash inflows – AW of cash outflows For Present (worth of money in the present) For Future (worth of money in the future) Annual Worth = A (A/P), i%, n) Annual Worth = A(A/F, i%, n) 𝑖(1+𝑖)𝑛 𝑖 A/P = AW = 𝑃[ ] A/F = AW = 𝐹[ ] (1+𝑖 )𝑛 −1 (1+𝑖 )𝑛 −1 Where: Where: P = present value F = future value AW = annual worth AW = annual worth i = interest rate n = time period n = time period i = interest rate Example 11: The production head proposed an acquisition of new equipment that could increase the productivity of a certain manual welding operation. The investment cost is ₱25,000 and the equipment will have a market value of ₱5,000 at the end of a study period of 5 years. The increased productivity would bring in ₱8,000 per year after extra operating costs have been subtracted from the revenue generated by the additional production. If the firm gives an effective interest rate of 20% per year, what is the potential improvement of the project? Solution: 1. Given: 25 | P a g e  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES SANTA MARIA, BULACAN CAMPUS Km. 38, Sitio Gulod, Pulong Buhangin, Santa Maria, Bulacan 2. Draw the cash flow diagram 3. Formula for AW AW = AW of cash inflows – AW of cash outflows FW (20%) = -A(A/P,20%,5) +A(A/F, 20%,5) + A 26 | P a g e  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES SANTA MARIA, BULACAN CAMPUS Km. 38, Sitio Gulod, Pulong Buhangin, Santa Maria, Bulacan Example 12: A manufacturing process can be carried out by using a machine which can be acquired for ₱20,000. The annual receipt generated by the investment is ₱150,000 and the annual disbursement is ₱138,000. The asset will have a life of 10 years in which it will have a salvage value of ₱2,000 at the end of its life. Assume that i = 20%. Is the project acceptable using the AW method? Solution: 1. Given: 2. Draw the cash flow diagram 3. Formula for AW AW = AW of cash inflows – AW of cash outflows FW (20%) = -A(A/P,20%,10) +A(A/F, 20%,10) + A 27 | P a g e  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES SANTA MARIA, BULACAN CAMPUS Km. 38, Sitio Gulod, Pulong Buhangin, Santa Maria, Bulacan Example 13: Product “A” has a first cost of ₱20,000, an operating cost of ₱9,000 per year, and a ₱5,000 salvage value after 5 years, while the Product “B” will cost a ₱35,000 with an operating cost of ₱4,000 per year with a salvage value of ₱7,000 after 5 years. Perform a future worth analysis with effective interest rate of 12% per annum. Which should be selected? 1. Given: 2. Draw the cash flow diagram 3. Formula for AW AW = AW of cash inflows – AW of cash outflows FW (12%) = -A(A/P,12%,5) +A(A/F, 12%,15) - A 28 | P a g e