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What is Engineering Economics?. What is Engineering Economics?. Subset of General Economics Different from general economics situations - project driven Analysis performed by technical professionals (not economists) Requires advanced technical knowledge in some cases.
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What is Engineering Economics? • Subset of General Economics • Different from general economics situations - project driven • Analysis performed by technical professionals (not economists) • Requires advanced technical knowledge in some cases
Lots of Questions: Project/$ driven • Why do this at all? • Is there a need for the project? • Why do it now? • Can it be delayed? Can we afford it now? • Why do it this way? • Is this the best alternative? Is this the optimal solution? • Will the project pay? • Will we run a loss or make a profit?
Hydro: expensive initially far away from load centres (high transmission cost) no fuel required longer life no pollution Thermal less expensive initially can be near load centres require fuel shorter life can cause pollution Sample Engineering Project • Hydro vs. Thermal power
Other examples • Buy vs. rent (car, house, equipment) • Good quality (expensive) but longer life vs. poor quality (cheap) but shorter life • car, shoes, computers • Investments decisions - GIC, RRSP, Bonds, Stocks and Shares
Steps in Engineering Economics Study • Define alternatives in physical terms • Cost and revenue estimates • All money estimates placed on a comparable basis • appropriate interest rate used • time horizon (economic life) • Recommend choice among alternatives
Engineering Economics on the Web • The discipline that translates engineering technology into a form that permits evaluation by businesses or investors. • The application of economic principles to engineering problems, for example in comparing the comparative costs of two alternative capital projects or in determining the optimum engineering course from the cost aspect.
The Time Value of Money Would you prefer to have $1 millionnow or $1 million100 years from now? Of course, we would all prefer the money now! This illustrates that there is an inherent monetary value attached to time.
What is Time Value? • We say that money has a time value because that money can be invested with the expectation of earning a positive rate of return • In other words, “a dollar received today is worth more than a dollar to be received tomorrow” • That is because today’s dollar can be invested so that we have more than one dollar tomorrow
What is The Time Value of Money? • A dollar received today is worth more than a dollar received tomorrow • This is because a dollar received today can be invested to earn interest • The amount of interest earned depends on the rate of return that can be earned on the investment • Time value of money quantifies the value of a dollar through time
Uses of Time Value of Money • Time Value of Money, is a concept that is used in all aspects of finance including: • Stock valuation • Financial analysis of firms • Accept/reject decisions for project management • And many others!
The Terminology of Time Value • Present Value - An amount of money today, or the current value of a future cash flow • Future Value - An amount of money at some future time period • Period - A length of time (often a year, but can be a month, week, day, hour, etc.) • Interest Rate - The compensation paid to a lender (or saver) for the use of funds expressed as a percentage for a period (normally expressed as an annual rate)
Abbreviations • PV - Present value • FV - Future value • Pmt - Per period payment amount • i - The interest rate per period
0 1 2 3 4 5 Timelines • A timeline is a graphical device used to clarify the timing of the cash flows for an investment • Each tick represents one time period PV FV Today
0 1 2 3 4 5 Calculating the Future Value • Suppose that you have an extra $100 today that you wish to invest for one year. If you can earn 10% per year on your investment, how much will you have in one year? -100 ?
0 1 2 3 4 5 Calculating the Future Value • Suppose that at the end of year 1 you decide to extend the investment for a second year. How much will you have accumulated at the end of year 2? -110 ?
Generalizing the Future Value • Recognizing the pattern that is developing, we can generalize the future value calculations • If you extended the investment for a third year, you would have:
Compound Interest • Note from the example that the future value is increasing at an increasing rate • In other words, the amount of interest earned each year is increasing • Year 1: $10 • Year 2: $11 • Year 3: $12.10 • The reason for the increase is that each year you are earning interest on the interest that was earned in previous years in addition to the interest on the original principle amount
The Magic of Compounding • On Nov. 25, 1626 Peter Minuit, purchased Manhattan from the Indians for $24 worth of beads and other trinkets. Was this a good deal for the Indians? • This happened about 378 years ago, so if they could earn 5% per year they would in 2005 have • If they could have earned 10% per year, they would now have:
Calculating the Present Value • So far, we have seen how to calculate the future value of an investment • But we can turn this around to find the amount that needs to be invested to achieve some desired future value:
Present Value: An Example • Your five-year old daughter has just announced her desire to attend college. After some research, you determine that you will need about $100,000 on her 18th birthday to pay for four years of college. If you can earn 8% per year on your investments, how much do you need to invest today to achieve your goal?
Continuous Compounding • There is no reason why we need to stop increasing the compounding frequency at daily • We could compound every hour, minute, or second • We can also compound every instant (i.e., continuously): • Here, F is the future value, P is the present value, r is the annual rate of interest, t is the total number of years, and e is a constant equal to about 2.718
Continuous Compounding • Suppose that the Fourth National Bank is offering to pay 10% per year compounded continuously. What is the future value of your $1,000 investment? • This is even better than daily compounding • The basic rule of compounding is: The more frequently interest is compounded, the higher the future value
Continuous Compounding • Suppose that the Fourth National Bank is offering to pay 10% per year compounded continuously. If you plan to leave the money in the account for 5 years, what is the future value of your $1,000 investment?
Summary • Engineering Economics • The Time Value of Money • Calculating the Future/Present Value • Simple/Compound Interest • Self-Study: Simple Interest P+P*N*5% 1+1=2 • Required: Slides/Book Chapter 2.1 2.2 2.3 2.5 • Feedback: Quiz Review before Quiz • Feedback: Book Library: waiting for answer