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Economics Dynamics Problems 125

# Economics Dynamics Problems 125 - Discrete dynamic...

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Discrete dynamic systems 109 (a) FV = A (1 + r ) n 1 r = 1000 (1 + 0 . 065) 10 1 0 . 065 = £ 13494 . 40 (b) PV = A 1 (1 + r ) n r = 1000 1 (1 + 0 . 065) 10 0 . 065 = £ 7188 . 83 Discounting is readily used in investment appraisal and cost–benefit analysis. Suppose B t and C t denote the benefits and costs, respectively, at time t . Then the present value of such ﬂows are B t / (1 + r ) t and C t / (1 + r ) t , respectively. It follows, then, that the net present value , NPV , of a project with financial ﬂows over n -periods is NPV = n t = 0 B t (1 + r ) t n t = 0 C t (1 + r ) t = n t = 0 B t C t (1 + r ) t Notice that for t = 0 the benefits B 0 and the costs C 0 involve no discounting. In many projects no benefits accrue in early years only costs. If NPV > 0 then a project (or investment) should be undertaken. Example 3.9 Bramwell plc is considering buying a new welding machine to increase its output. The machine would cost £ 40,000 but would lead to increased revenue of £ 7,500 each year for the next ten years. Half way through the machine’s lifespan, in year 5, there is a one-off maintenance expense of £ 5,000. Bramwell plc consider that the appropriate discount rate is 8%. Should they buy the machine? NPV = − 40000 + 10 t = 1 7500 (1 + r ) t 5000 (1 +
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