ENGINEERING ECONOMICS Machinery's Handbook, 31st Edition
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ENGINEERING ECONOMICS Engineers, managers, purchasing agents, and others are often required to plan and evaluate project alternatives and make economic decisions that may greatly affect the success or failure of a project. In industry, equipment has to be justified before it can be put into use; multiple projects demand money. The topic of this section is how decisions are made on which projects to prefer over others, based on financial considerations. The goals of a project, such as reducing manufacturing cost or increasing production, selection of machine tool alternatives, or reduction of tooling, labor and other costs, deter mine which of the available alternatives may bring the most attractive economic return. Various cost analysis techniques that may be used to obtain the desired outcome are dis cussed in the material that follows. Interest Interest is money paid out or earned for the use of money that has been borrowed or lent (the principal ). Simple interest is interest paid only on the principal; compound interest is interest paid on the principal and any previous interest earned. Principal multiplied by annual inter- est rate, expressed as a decimal, gives accrued interest . Annual percentage rate (APR) is per- cent of principal charged or earned in a year, also referred to as nominal interest rate per year . An APR is stated when no intermediate compounding occurs within a year. Effective rate per year is calculated by considering multiple compoundings occurring in periods throughout a year, using the nominal interest rate. Thus, effective rate is higher than nominal rate, and the more compounding periods per year, the higher the interest paid over the duration of the loan. Most commercial financial dealings these days involve compound interest. For example, a nominal interest rate of 10% would be 10/100 = 0.1 as a decimal. Adding the principal to the interest that results from this calculation gives the total value of the ac- count after a year. This is the basis of the formulas for both simple and compound interest. An example illustrates the difference between simple and compound calculations: A per- son borrows $10,000 from a bank for 2 years at an annual rate of 10%. At the end of the first year, the net amount owed, using both the simple interest and the compound interest calcula- tion, is $10,000 + ($10,000 × 0.1) = $11,000. Hence, the interest paid for the first year is $1,000, for both ways of calculating. In the second year, if simple interest is applied, the interest owed is still calculated on just the amount borrowed, $10,000. So, at the end of the second year, the interest paid will be the principal of $10,000 plus $2,000 in interest, or a total of $12,000. But, if compound interest is applied, for the second year, the borrower pays an interest of $11,000 × 0.1 = $1,100. Hence, the total paid to pay the bank is $10,000, plus this first-year interest of $1,000, plus the second-year accrued interest of $1,100, for a total of $12,100. Variables.— The symbols used in the formulas to calculate various types of interest are: P = principal amount of money lent, invested, or borrowed; sometimes also present value ( PV ) I = nominal annual interest rate stated as a percentage, e.g., 10 percent per annum EIR = effective annual interest rate when interest is compounded more often than once a year i = nominal annual interest rate percent expressed as a decimal, e.g., if I = 12 per cent, then i = 12 ⁄ 100 = 0.12 n = number of annual interest periods (that is, number of years) m = number of interest compounding periods in one year F = future sum of money at the end of n interest periods from the present date that is equivalent to P with added interest i A = the payment at the end of each period in a uniform series of payments continu ing for n periods, the entire series equivalent to P at interest rate i
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