IEMS 326 Notes02NPVandInflation

IEMS 326 Notes02NPVandInflation - Net Present Value and...

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Net Present Value and Inflation IEMS 326 Lecture 2
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Review: Discount Rate m periods in a year d = annual discount rate r = discount rate per period The 1-year discount factor 1/(1+d) = 1/(1+r) m , i.e. d = (1+r) m - 1 and r = (1+d) 1/m – 1 The present value of a cashflow y arriving in n periods, i.e. at time t = n/m (in years) is y(1+r) -n = y(1+d) -n/m = y(1+d) -t
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Present Value: Multiple Payments For a small number of multiple payments, compute the PV of each and add. For a perpetuity of C received every period, starting in 1 period, PV is C/r. For an annuity of C received at periods 1, 2, …, n, PV is (C/r)(1 - (1+r) -n ).
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Present Value Examples Use discount rate 12% for all examples. Present value of $100 received in 1.5 years. PV of $1 per month forever. PV of $1 per month for 8 months. Present value formulae: y(1+d) -t for y in t yrs C/r for C every period (C/r)(1 - (1+r) -t ) for C at each of t periods
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Present Value Examples Present value of $100 discounted at 12% over 1.5 years. ($100)(1.12) -1.5 = $84.37 PV of $1 per month forever at 12%: r = (1.12) 1/12 – 1 = 0.95% ($1)/0.0095 = $105.39 PV of $1 per month for 8 months at 12%. ($1/.0095)(1 – (1.12) -8/12 ) = $7.67 ($1/.0095)(1 – (1.0095) -8 ) = $7.67
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Net Present Value (NPV) The present value (PV) of a cashflow stream is the sum of the PVs of all cashflows.
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