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<br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />I <br />II <br /> <br />r. 'I, ":i ~i. f) <br />. ,I , ~ . <br />n '. "'" "'c <br /> <br />benefits and costs that occur at different points in time. It is relevant <br /> <br /> <br />to the determination of PIA because the benefits and costs of an irrigation <br /> <br /> <br />project occur at different points in time. Typically, a large portion of <br /> <br /> <br />the cost of an irrigation project is incurred during the construction <br /> <br /> <br />period, while project benefits accrue throughout the project's life. The <br /> <br /> <br />use of discounting in benefit-cost analysis involves finding the net <br /> <br /> <br />present value (NPV) of a stream of costs and benefits over time. Since <br /> <br /> <br />money has different values in different time periods, a discount rate is <br /> <br /> <br />used to adjust the dollar value of a project's various costs and benefits <br /> <br /> <br />to put them on an equal basis. <br /> <br /> <br />In algebraic form, the net present value (NPV) of any stream of costs <br /> <br /> <br />and benefits can be represented as: <br /> <br />n <br />NPV = L: <br />t=1 <br /> <br />n <br />L: ct <br /> <br />t=1 (l+r)t <br /> <br />bt <br />(l+r)t <br /> <br />(2-1) <br /> <br />In this formula, r represents the discount rate, t represents the time <br />intervals of interest (usually years), and ct and bt represent streams of <br />costs and benefits across time, respectively. <br />A crucial element in any benefit-cost analysis is the choice of an <br />appropriate discount rate for computing the NPV of benefits and costs. The <br />choice of a discount rate is the subject of much debate among economists, <br />partially because there are differing interpretations of what a discount <br />rate means, and thus how it should be empirically measured. One <br />interpretation of a discount rate is as a measure of the time value of <br />money. For example, if given a choice between receiving one hundred <br />dollars today or one hundred dollars one year from now, most individuals <br /> <br />10 <br /> <br />.t.'. <br />