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(2020)
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To apply the rate of return on an incremental basis for a group of independent projects, it is rst necessary to rank the projects in ascending order of their total Iw) Then Eq (2020) is employed to investment, xed plus working capital (I yield the incremental rates of return
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EVALUATING INVESTMENTS USING THE TIME VALUE OF MONEY
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Since many economic feasibility studies extend over a long period of time or deal with projects having long useful lives, it is necessary to recognize that future cash ows or pro ts generated by these projects will decrease in value over time because of in ation As stated earlier, today s dollar will have less purchasing power next year and even less the year after, and so on This section concerns itself with methods of comparing cash ows or pro ts at various points in time These take into account the time value of money, which is interest The basic and most important methods are 1 Maximum payback time (PTM) 2 Discounted-cash- ow analysis (DCF) 3 Bene t / cost analysis (B / C) The most widely used of these methods is DCF; however, since no single method is best for all cases, the engineer or technologist should understand the basic concepts involved in each method and be able to choose the one best suited to the needs of the particular situation
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CHAPTER TWENTY
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Before proceeding to the methods listed above, it is necessary to de ne interest and to present the mathematical relationships which permit conversion of money at a given point in time to an equivalent amount at some other point in time
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1 Interest and the Time Value of Money Interest is de ned as the compensation paid for the use of borrowed money Since most rms have to borrow capital in order to expand, interest expense plays a signi cant role in an economic analysis The rate at which the interest is to be repaid is usually determined at the time the capital is borrowed, along with a scheduled time of repayment To the lender, interest represents compensation for not being able to use the money elsewhere right now That is, interest in most respects is the compensation for the decrease in value of the money between now and when the loan is repaid, this decrease being due to in ation The borrower, on the other hand, must invest the borrowed capital in an activity that will yield a return higher than the penalty (interest) for borrowing the capital 2 Interest Formulas and Interest Tables In economic terms, principal is de ned as capital on which interest is paid, while interest rate is de ned as the cost per unit of time of borrowing a unit of principal The time unit most commonly taken is 1 year
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Interest Formula Symbols PW i n m S R principal, or present worth interest rate per period number of interest periods interest periods per year principal plus interest due, or future worth uniform periodic payment
Compound Interest Compound interest can be de ned as interest earned on interest, that is, interest is earned, not only on the principal, but also on all previously accumulated interest If a payment is not made, the interest due is added to the principal and interest is charged on this converted principal during the following year Annuities An annuity is a series of equal payments occurring at equal time intervals Payments of this type are used to pay off debt or depreciation In the case of depreciation, the decrease in the value of equipment with time is accounted for by an annuity plan For the uniform periodic payments made during n discrete periods at i percent interest to accumulate an amount S, S R (1 i)n i 1 (2021) i)n / i is
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