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0 PV 1 2 3 t ... FV • • • • Consider the time line above: PV is the Present Value, that is, the value today. FV is the Future Value, or the value at a future date. The number of time periods between the Present Value and the Future Value is represented by “t” or “n”. • The rate of interest is called “r” or “i”. • All time value questions involve the four values above: PV, FV, r, and t. Given three of them, it is always possible to calculate the fourth. • Timing of cashflows: end of period unless otherwise specified. Future Value for a Lump Sum
• Assuming that the interest rate is 10%, how much will you get after one year, if you invest $100 today? • Notice that – 1. $110 = $100 × (1 + .10) – 2. $121 = $110 × (1 + .10) = $100 × 1.10 × 1.10 = $100 × 1.102 – 3. $133.10 = $121 × (1 + .10) = $100 × 1.10 × 1.10 × 1.10 = $100 × ________ Future Value for a Lump Sum • In general, the future value, FVt, of $P invested today at r% for t periods is FVt = $P × (1 + r)t = $P × FF(r,t)
• The expression (1 + r)t is the future value interest factor, denoted by FF(r,t). 3 Example: Simple Future Value • Suppose that you want to find the future value, as of 10 years from now, of $200 paid today. The interest rate r is 4%. Present Value for a Lump Sum
• In general, the present value, PVt, of $P to be received in t periods when the rate is r is PV = $P/(1 + r )t • The expression 1/(1 + r)t is the present value interest factor. Example: Simple Present Value • Suppose that the interest rate is r = 7% and you want to compare the following two plans: A: Receive $300 4 years from now B: Re...
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This note was uploaded on 01/17/2011 for the course MGMT 107 taught by Professor ? during the Winter '08 term at UC Irvine.
 Winter '08
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