lecture2 - Lecture 2: Equivalence At the beginning of the...

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At the beginning of the recent film, Sense and Sensibility , Mr John Dashwood and his avaricious wife, Mrs John Dashwood, are debating how he can most cheaply discharge his obligations towards his half-sister, the recently widowed Mrs Henry Dashwood and her three daughters, Elinor, Marianne and Margaret. He first considers giving her a lump sum of $1,500; then, since $1,500 seems a lot to part with in one lump, he considers paying her an annual sum of $100 for as long as she lives. But, objects his wife, although Mrs Dashwood is old, such an arrangement will encourage her to cling to life for an unreasonable time; and, should she survive for more than 15 years, her half-brother will lose money by the arrangement. [Actually, Mrs Dashwood is only 40, but Jane Austen evidently considers this to be near senility; Mrs Dashwood herself says at one point in the novel that she can scarcely expect to survive another fifteen years.] It is clear from this episode that Mrs John Dashwood cannot have studied engineering economics; for in fact, Mr Dashwood would save money by the latter alternative, even if Mrs Henry Dashwood were to live considerably longer than 15 years. Mrs John Dashwood's error lies in comparing future and present sums of money. To make such a comparison valid, we must take into account the potential of money to earn interest. $100 in hand will always be worth more than $100 a year from now, by the amount of interest that the sum will earn over that year. To make sensible comparisons between present and future sums, then, we must bring all the sums being compared into the same moment of time. This moment can be either present or future. The value of present money increases as we move it into the future, while the value of future income falls as we move it back to the present. The central notion here is that of equivalence . A present and future sums of money are equivalent if a rational person would be indifferent as to which he or she received. Thus, for example, if the best available interest rate is 10%, I should be indifferent between receiving $100 now or $110 this time next year. (In this, and in the remainder of this lecture, we will assume an inflation rate of zero.) The calculations needed to establish equivalence are relatively straightforward, but, since these calculations will often be steps in more complex calculations, it is useful to establish a standard notation for the quantities involved. The four most needed concepts are P , the present worth; F , future worth (or `compound amount'); i , the interest rate per period; and N , the number of time periods we are considering. These quantities are related by the simple formula P=F(P/F,i%,N) and its inverse, F=P(F/P,i%,N) The conversion factor can be calculated from a simple formula, which you can readily deduce, but it is usually more convenient to look it up in compound interest tables, such as those found at the back of most engineering economics textbooks. We also need to consider the common case in which a series of equal payments are made at regular intervals.
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This note was uploaded on 04/16/2009 for the course ENSC 201 taught by Professor Dr.johnjones during the Fall '08 term at Simon Fraser.

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lecture2 - Lecture 2: Equivalence At the beginning of the...

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