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1. Engineering Economy

   Chapter 1: Introduction to Engineering Economy
2. The purpose of this course is to develop and illustrate the principles and methodology required to answer the basic economic question of any design: Do its benefits exceed its cost?
3. Engineering Economy is Problem Solving Engineering is a profession devoted to problem solving and design of alternative courses of action. Engineering economy is a subset of engineering devoted to deciding which course of action best meets technical performance criteria while using capital in a prudent manner.
4. WHAT IS ECONOMICS ? The study of how limited resources is used to satisfy unlimited human wants The study of how individuals and societies choose to use scarce resources that nature and previous generations have provided
5. Pioneer: Arthur M. Wellington, civil engineer latter part of nineteenth century; addressed role of economic analysis in engineering projects; area of interest: railroad building Followed by other contributions which emphasized techniques depending on financial and actuarial mathematics. Origins of Engineering Economy
6. Engineering economy… involves the systematic evaluation of the economic merits of proposed solutions to engineering problems.
7. Why Engineering Economy is Important to Engineers Engineers design and create Designing involves economic decisions Engineers must be able to incorporate economic analysis into their creative efforts Often engineers must select and implement from multiple alternatives Understanding and applying time value of money, economic equivalence, and cost estimation are vital for engineers A proper economic analysis for selection and execution is a fundamental task of engineering
8. Engineering Economy Engineering Economy involves Formulating Estimating, and Evaluating expected economic outcomes of alternatives designed to accomplish a defined purpose Easy-to-use math techniques simplify the evaluation Estimates of economic outcomes can be deterministic or stochastic in nature
9. Solutions to engineering problems must promote the well-being and survival of an organization, embody creative and innovative technology and ideas, permit identification and scrutiny of their estimated outcomes, and translate profitability to the “bottom line” through a valid and acceptable measure of merit.
10. Engineering economic analysis can play a role in many types of situations. Choosing the best design for a high-efficiency gas furnace. Selecting the most suitable robot for a welding operation on an automotive assembly line. Making a recommendation about whether jet airplanes for an overnight delivery service should be purchased or leased. Determining the optimal staffing plan for a computer help desk.
11. There are seven fundamental principles of engineering economy. Develop the alternatives Focus on the differences Use a consistent viewpoint Use a common unit of measure Consider all relevant criteria Make uncertainty explicit Revisit your decisions
12. The final choice (decision) is among alternatives. The alternatives need to be identified and then defined for subsequent analysis. DEVELOP THE ALTERNATIVES
13. Only the differences in expected future outcomes among the alternatives are relevant to their comparison and should be considered in the decision. FOCUS ON THE DIFFERENCES
14. The prospective outcomes of the alternatives, economic and other, should be consistently developed from a defined viewpoint (perspective). USE A CONSISTENT VIEWPOINT
15. 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. USE A COMMON UNIT OF MEASURE
16. Selection of a preferred alternative (decision making) 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. CONSIDER ALL RELEVANT CRITERIA
17. Uncertainty is inherent in projecting (or estimating) the future outcomes of the alternatives and should be recognized in their analysis and comparison. MAKE UNCERTAINTY EXPLICIT
18. 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. REVISIT YOUR DECISIONS
19. Engineering economic analysis procedure Problem definition Development of alternatives Development of prospective outcomes Selection of a decision criterion Analysis and comparison of alternatives. Selection of the preferred alternative. Performance monitoring and postevaluation of results.
20. Time Value of Money (TVM) Description: TVM explains the change in the amount of money over time for funds owed by or owned by a corporation (or individual) Corporate investments are expected to earn a return Investment involves money Money has a ‘time value’ The time value of money is the most important concept in engineering economy
21. Interest and Interest Rate Interest – the manifestation of the time value of money Fee that one pays to use someone else’s money Difference between an ending amount of money and a beginning amount of money Interest = amount owed now – principal Interest rate – Interest paid over a time period expressed as a percentage of principal
22. Rate of Return Interest earned over a period of time is expressed as a percentage of the original amount (principal) Borrower’s perspective – interest rate paid Lender’s or investor’s perspective – rate of return earned
23. Interest paid Interest earned Interest rate Rate of return
24. Cash Flow Engineering projects generally have economic consequences that occur over an extended period of time For example, if an expensive piece of machinery is installed in a plant were brought on credit, the simple process of paying for it may take several years The resulting favorable consequences may last as long as the equipment performs its useful function Each project is described as cash receipts or disbursements (expenses) at different points in time
25. Categories of Cash Flows The expenses and receipts due to engineering projects usually fall into one of the following categories: First cost: expense to build or to buy and install Operations and maintenance (O&M): annual expense, such as electricity, labor, and minor repairs Salvage value: receipt at project termination for sale or transfer of the equipment (can be a salvage cost) Revenues: annual receipts due to sale of products or services Overhaul: major capital expenditure that occurs during the asset’s life
26. Cash Flow diagrams The costs and benefits of engineering projects over time are summarized on a cash flow diagram (CFD). Specifically, CFD illustrates the size, sign, and timing of individual cash flows, and forms the basis for engineering economic analysis A CFD is created by first drawing a segmented time-based horizontal line, divided into appropriate time unit. 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
27. Drawing a Cash Flow Diagram In a cash flow diagram (CFD) the end of period t is the same as the beginning of period (t+1) Beginning of period cash flows are: rent, lease, and insurance payments End-of-period cash flows are: O&M, salvages, revenues, overhauls The choice of time 0 is arbitrary. It can be when a project is analyzed, when funding is approved, or when construction begins One person’s cash outflow (represented as a negative value) is another person’s inflow (represented as a positive value) It is better to show two or more cash flows occurring in the same year individually so that there is a clear connection from the problem statement to each cash flow in the diagram
28. 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 Cash flow 0 +$1000 1 -$580 (-$500 - $80) 2 -$540 (-$500 - $40)
29. Cash Flow Diagram $1,000 1 2 0 $540 $580
30. Commonly used Symbols t = time, usually in periods such as years or months P = value or amount of money at a timet designated as present or time 0 F = value or amount of money at some future time, such as at t = n periods in the future A = series of consecutive, equal, end-of-period amounts of money n = number of interest periods; years, months i= interest rate or rate of return per time period; percent per year or month
31. Time Value of Money
32. Nature of Interest Interest Payment for the use of money. Excess cash received or repaid over the amount borrowed (principal). Variables involved in financing transaction: Principal (p) - Amount borrowed or invested. Interest Rate (i) – An annual percentage. Time (n) - The number of years or portion of a year that the principal is borrowed or invested. SO 1 Distinguish between simple and compound interest.
33. Nature of Interest Simple Interest Interest computed on the principal only. Illustration: Assume you borrow $5,000 for 2 years at a simple interest of 12% annually. Calculate the annual interest cost. Interest = p x i x n FULL YEAR = $5,000 x .12 x 2 = $1,200 SO 1 Distinguish between simple and compound interest.
34. Nature of Interest Compound Interest Computes interest on the principal and any interest earned that has not been paid or withdrawn. Most business situations use compound interest. SO 1 Distinguish between simple and compound interest.
35. Compound Interest Illustration: Assume that you deposit $1,000 in Bank Two, where it will earn simple interest of 9% per year, and you deposit another $1,000 in Citizens Bank, where it will earn compound interest of 9% per year compounded annually. Also assume that in both cases you will not withdraw any interest until three years from the date of deposit. Year 1 $1,000.00 x 9% $ 90.00 $ 1,090.00 Year 2 $1,090.00 x 9% $ 98.10 $ 1,188.10 Year 3 $1,188.10 x 9% $106.93 $ 1,295.03
36. Present Value Variables Present valueis the value now of a given amount to be paid or received in the future, assuming compound interest. Present value variables: Dollar amount to be received in the future, Length of time until amount is received, and Interest rate (the discount rate). SO 2 Identify the variables fundamental to solving present value problems.
37. Present Value of a Single Amount Present Value = Future Value / (1 + i )n p = principal (or present value) i = interest rate for one period n = number of periods SO 3 Solve for present value of a single amount.
38. Present Value of a Single Amount Illustration: If you want a 10% rate of return, you would compute the present value of $1,000 for one year as follows: SO 3 Solve for present value of a single amount.
39. Present Value of a Single Amount Illustration: If you want a 10% rate of return, you can also compute the present value of $1,000 for one year by using a present value table. What table do we use? SO 3 Solve for present value of a single amount.
40. Present Value of a Single Amount What factor do we use? $1,000 x .90909 = $909.09 Future Value Factor Present Value SO 3 Solve for present value of a single amount.
41. Present Value of a Single Amount Illustration: If you receive the single amount of $1,000 in two years, discounted at 10% [PV = $1,000 / 1.102], the present value of your $1,000 is $826.45. What table do we use? SO 3 Solve for present value of a single amount.
42. Present Value of a Single Amount What factor do we use? $1,000 x .82645 = $826.45 Future Value Factor Present Value SO 3 Solve for present value of a single amount.
43. Present Value of a Single Amount Illustration: Suppose you have a winning lottery ticket and the state gives you the option of taking $10,000 three years from now or taking the present value of $10,000 now. The state uses an 8% rate in discounting. How much will you receive if you accept your winnings now? $10,000 x .79383 = $7,938.30 Future Value Factor Present Value SO 3 Solve for present value of a single amount.
44. Present Value of a Single Amount Illustration: Determine the amount you must deposit now in a bond investment, paying 9% interest, in order to accumulate $5,000 for a down payment 4 years from now on a new Toyota Prius. $5,000 x .70843 = $3,542.15 Future Value Factor Present Value SO 3 Solve for present value of a single amount.
45. Present Value of an Annuity The value now of a series of future receipts or payments, discounted assuming compound interest. Present Value $100,000 100,000 100,000 100,000 100,000 100,000 . . . . . 0 1 2 3 4 19 20 SO 4 Solve for present value of an annuity.
46. Present Value of an Annuity Illustration: Assume that you will receive $1,000 cash annually for three years at a time when the discount rate is 10%. What table do we use? SO 4 Solve for present value of an annuity.
47. Present Value of an Annuity What factor do we use? $1,000 x 2.48685 = $2,486.85 Future Value Factor Present Value SO 4 Solve for present value of an annuity.
48. Present Value of an Annuity Illustration: Kildare Company has just signed a capitalizable lease contract for equipment that requires rental payments of $6,000 each, to be paid at the end of each of the next 5 years. The appropriate discount rate is 12%. What is the amount used to capitalize the leased equipment? $6,000 x 3.60478 = $21,628.68 SO 4 Solve for present value of an annuity.
49. Time Periods and Discounting Illustration: When the time frame is less than one year, you need to convert the annual interest rate to the applicable time frame. Assume that the investor received $500 semiannually for three years instead of $1,000 annually when the discount rate was 10%. $500 x 5.07569 = $2,537.85 SO 4
50. Present Value of a Long-term Note or Bond Two Cash Flows: Periodic interest payments (annuity). Principal paid at maturity (single-sum). 100,000 $5,000 5,000 5,000 5,000 5,000 5,000 . . . . . 0 1 2 3 4 9 10 SO 5 Compute the present value of notes and bonds.
51. Present Value of a Long-term Note or Bond Illustration: Assume a bond issue of 10%, five-year bonds with a face value of $100,000 with interest payable semiannually on January 1 and July 1. Calculate the present value of the principal and interest payments. 100,000 $5,000 5,000 5,000 5,000 5,000 5,000 . . . . . 0 1 2 3 4 9 10 SO 5 Compute the present value of notes and bonds.
52. Present Value of a Long-term Note or Bond PV of Principal $100,000 x .61391 = $61,391 Principal Factor Present Value SO 5 Compute the present value of notes and bonds.
53. Present Value of a Long-term Note or Bond PV of Interest $5,000 x 7.72173 = $38,609 Principal Factor Present Value SO 5 Compute the present value of notes and bonds.
54. Present Value of a Long-term Note or Bond Illustration: Assume a bond issue of 10%, five-year bonds with a face value of $100,000 with interest payable semiannually on January 1 and July 1. Present value of Principal $61,391 Present value of Interest 38,609 Bond current market value $100,000 SO 5 Compute the present value of notes and bonds.
55. Present Value of a Long-term Note or Bond Illustration: Now assume that the investor’s required rate of return is 12%, not 10%. The future amounts are again $100,000 and $5,000, respectively, but now a discount rate of 6% (12% / 2) must be used. Calculate the present value of the principal and interest payments. SO 5 Compute the present value of notes and bonds.
56. Present Value of a Long-term Note or Bond Illustration: Now assume that the investor’s required rate of return is 8%. The future amounts are again $100,000 and $5,000, respectively, but now a discount rate of 4% (8% / 2) must be used. Calculate the present value of the principal and interest payments. SO 5 Compute the present value of notes and bonds.
57. Tables… = i F3 = 50 000(F/P,10%,3) F3 = 50 000(F/P,10%,3) = 50 000(1.3310) F3 = 50 000(F/P,10%,3) = 50 000(1.3310) = $66 550
58. F3 = 50 000(F/P, 10%,3) = 50 000(1+.10)3 = 50 000(1.3310) = $66 550 Formulas…