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ENGINEERING ECONOMICS
Engineering economics, previously known as engineering economy, is a subset of economics
for application to engineering projects. Engineers seek solutions to problems, and the economic
viability of each potential solution is normally considered along with the technical aspects. In
some U.S. undergraduate engineering curricula, engineering economics is often a required
course. It is a topic on the Fundamentals of Engineering examination, and q

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ENGINEERING ECONOMICS Engineering economics
, previously known as
engineering economy
, is a subset of economics for application to engineering projects. Engineers seek solutions to problems, and the economic viability of each potential solution is normally considered along with the technical aspects. In some U.S. undergraduate engineering curricula, engineering economics is often a required course. It is a topic on the Fundamentals of Engineering examination, and questions might also be asked on the Principles and Practice of Engineering examination; both are part of the Professional Engineering registration process. Engineering economics is the application of economic techniques to the evaluation of design and engineering alternatives. The role of engineering economics is to assess the appropriateness of a given project, estimate its value, and justify it from an engineering standpoint. Considering the time value of money is central to most engineering economic analyses. Cash
flows are
discounted
using an interest rate, i, except in the most basic economic studies. For
each problem, there are usually many possible
alternatives
. One option that must be considered in each analysis, and is often the
choice
, is the
do nothing alternative
. The
opportunity cost
of making one choice over another must also be considered. There are also noneconomic factors to be considered, like colour, style, public image, etc.; such factors are termed
attributes
Costs
as well as
revenues
are considered, for each alternative, for an
analysis period
that is either a fixed number of years or the estimated life of the project. The
salvage value
is often forgotten, but is important, and is either the net cost or revenue for decommissioning the project. Some other topics that may be addressed in engineering economics are inflation, uncertainty,
replacements, depreciation, resource depletion, taxes, tax credits, accounting, cost estimations,
or capital financing. All these topics are primary skills and knowledge areas in the field of cost
engineering. Since engineering is an important part of the manufacturing sector of the economy, engineering
industrial economics is an important part of industrial or business economics.
Major topics in engineering industrial economics are:
the economics of the management, operation, and growth and profitability of engineering firms;
macro-level engineering economic trends and issues;
engineering product markets and demand influences; and
the development, marketing, and financing of new engineering technologies and products. Benefit to cost ratio (B/C)
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The specific engineering economics topics cover
Breakeven Analysis
Benefit-Cost Analysis
Future Worth or Value
Present Worth
Valuation and Depreciation
Time Value of Money
The
time value of money
is the value of money figuring in a given amount of interest earned over a given amount of time. The time value of money is the central concept in
finance theory.
Time Value of Money (TVM) is an important concept in financial management. It can be used to compare investment alternatives and to solve problems involving loans, mortgages, leases, savings, and annuities. TVM is based on the concept that a dollar that you have today is worth more than the promise or expectation that you will receive a dollar in the future. Money that you hold today is worth more because you can invest it and earn interest. After all, you should receive some compensation for foregoing spending. For instance, you can invest your dollar for one year at a 6% annual interest rate and accumulate $1.06 at the end of the year. You can say that the
future value
of the dollar is $1.06 given a 6%
interest rate
and a one-year
period
. It follows that the
present value
of the $1.06 you expect to receive in one year is only $1. A key concept of TVM is that a single sum of money or a series of equal, evenly-spaced payments or receipts promised in the future can be converted to an equivalent value today. Conversely, you can determine the value to which a single sum or a series of future payments will grow to at some future date. You can calculate the fifth value if you are given any four of: Interest Rate, Number of Periods, Payments, Present Value, and Future Value. Each of these factors is very briefly defined in the right-hand column below. The left column has references to more detailed explanations, formulas, and examples. For example, $100 of today's money invested for one year and earning 5% interest will be worth $105 after one year. Therefore, $100 paid now or $105 paid exactly one year from now both have the same value to the recipient who assumes 5% interest; using
time value of money terminology
, $100 invested for one year at 5% interest has a
future value
of $105.
This notion dates at least to Martín de Azpilcueta (1491
–
1586) of the School of Salamanca. The method also allows the valuation of a likely stream of income in the future, in such a way that the annual incomes are discounted and then added together, thus providing a lump-sum present value of the entire income stream. All of the standard calculations for time value of money derive from the most basic algebraic expression for the present value of a future sum, discounted to the present by an amount equal
to the time value of money. For example, a sum of
FV
to be received in one year is discounted (at the rate of interest
r
) to give a sum of
PV
at present: PV = FV − r
·
PV = FV/(1+r).
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Some standard calculations based on the time value of money are: Present value.
The current worth of a future sum of money or stream of cash flows given a specified rate of return. Future cash flows are discounted at the discount rate, and the higher the discount rate, the lower the present value of the future cash flows. Determining the appropriate discount rate is the key to properly valuing future cash flows, whether they be earnings or obligations.
Present value of an annuity.
An annuity is a series of equal payments or receipts that occur at evenly spaced intervals. Leases and rental payments are examples. The payments or receipts occur at the end of each period for an ordinary annuity while they occur at the beginning of each period for an annuity due.
Present value of a perpetuity
is an infinite and constant stream of identical cash flows.
Future value
is the value of an asset or cash at a specified date in the future that is equivalent in value to a specified sum today.
Future value of an annuity
(FVA) is the future value of a stream of payments (annuity), assuming the payments are invested at a given rate of interest.
Number of Periods
Periods are evenly-spaced intervals of time. They are intentionally not stated in years since each interval must correspond to a compounding period for a single amount or a payment period for an annuity.
Payments
Payments are a series of equal, evenly-spaced cash flows. In TVM applications, payments must represent all outflows (negative amount) or all inflows (positive amount).
Present Value
Single Amount
Annuity
Present Value
is an amount today that is equivalent to a future payment, or series of payments, that has been discounted by an appropriate interest rate. The future amount can be a single sum that will be received at the end of the last period, as a series of equally-spaced payments (an annuity), or both. Since money has time value, the present value of a promised future amount is worth less the longer you have to wait to receive it.
Future Value
Single Amount
Annuity
Future Value
is the amount of money that an investment with a fixed, compounded interest rate will grow to by some future date. The investment can be a single sum deposited at the beginning of the first period, a series of equally-spaced payments (an annuity), or both. Since money has time value, we naturally expect the future value to be greater than the present value. The difference
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between the two depends on the number of compounding periods involved and the going interest rate.
Loan Amortization
A method for repaying a loan in equal installments. Part of each payment goes toward interest and any remainder is used to reduce the principal. As the balance of the loan is gradually reduced, a progressively larger portion of each payment goes toward reducing principal.
Cash Flow Diagram
A cash flow diagram is a picture of a financial problem that shows all cash inflows and outflows along a time line. It can help you to visualize a problem and to determine if it can be solved by TVM methods.
Interest
Interest is a charge for borrowing money, usually stated as a percentage of the amount borrowed over a specific period of time. Interest is the cost of borrowing money. An interest rate is the cost stated as a percent of the amount borrowed per period of time, usually one year. The prevailing market rate is composed of: 1. The
Real Rate of Interest
that compensates lenders for postponing their own spending during the term of the loan. 2. An
Inflation Premium
to offset the possibility that inflation may erode the value of the money during the term of the loan. A unit of money (dollar, peso, etc) will purchase progressively fewer goods and services during a period of inflation, so the lender must increase the interest rate to compensate for that loss. 3. Various
Risk Premiums to
compensate the lender for risky loans such as those that are unsecured, made to borrowers with questionable credit ratings, or illiquid loans that the lender may not be able to readily resell. The first two components of the interest rate listed above, the real rate of interest and an inflation premium, collectively are referred to as the nominal risk-free rate. In the USA, the nominal risk-free rate can be approximated by the rate of US Treasury bills since they are generally considered to have a very small risk.
Simple Interest
Simple interest
is computed only on the srcinal amount borrowed. It is the return on that principal for one time period.

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