Foundation 3 slides - Time Value of Money Question You are offered two options to receive a cash payment Option A $100 today Option B O i B $107 i

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1 Time Value of Money Question ± You are offered two options to receive a cash payment. ² Option A: $100 today Prof. Q. Ma HADM 2222: Time Value of Money 0 ² Option B: $107 in future year t ± Which one is more valuable to you? General Question Earlier time Later time Prof. Q. Ma HADM 2222: Time Value of Money 1 Time Line $$$$ (PV) $$$$$$ (FV) Learning Objectives ± Be able to compute ² The FV of a cash payment made today ² The PV of cash at some future date ² The return (r) on an investment ² The number of periods (T) that equates a PV Prof. Q. Ma HADM 2222: Time Value of Money 2 The number of periods (T) that equates a PV and an FV given an interest rate (r) ± Be able to use a financial calculator to solve TVM problems
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2 Future Value ± Suppose you invest $100 for one year at 6% per year. What do you have in one year? ² Interest = 100 * .06 = 6 ² Value in one year = principal + interest = 100 + 6 ² Future Value (FV) = 100 * (1 + .06) Prof. Q. Ma HADM 2222: Time Value of Money 3 ± Suppose you leave the money in for another year. How much will you have two years from now? ² FV = 106 + 106 * .06 = 106 * (1+.06) ² FV = 100 * (1+.06) 2 Future Value – General Formula FV = PV (1 + r) T ± FV = future value Prof. Q. Ma HADM 2222: Time Value of Money 4 ± PV = present value ± r = period interest rate, expressed as a decimal ± T = number of periods Definitions Earlier time Later time Time Line PV FV Prof. Q. Ma HADM 2222: Time Value of Money 5 ± Present Value – earlier money on a time line ± Future Value – later money on a time line ± Interest rate – “exchange rate” between earlier money and later money ² Discount rate; required return ² Cost of capital; opportunity cost of capital
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3 Effect of Compounding ± Simple interest ± Compound interest ± = simple interest + interest on interest ± Consider the previous example (two years) Prof. Q. Ma HADM 2222: Time Value of Money 6 ² FV with simple interest = 100 + 6 + 6 = 112 ² FV with compound interest = 112.36 ² The extra $.36 comes from the interest of the first interest payment. ± .06(6) = .36 FV Interest Factor ± FVIF = (1 + r) T ± FVIF Increases with time (T). ± FVIF increases with interest rate (r). Prof. Q. Ma HADM 2222: Time Value of Money 7 FVIF = (1 + r) T 400 5.00 6.00 7.00 1 5% 10% 20% Prof. Q. Ma HADM 2222: Time Value of Money 8 0.00 1.00 2.00 3.00 4.00 01234567891 0 Year FV of $1
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4 FV of $1 at 5% for 100 years 80 100 120 140 Prof. Q. Ma HADM 2222: Time Value of Money 9 0 20 40 60 1 1 12 13 14 15 16 17 18 19 11 0 1 Present Value – One Period Suppose you need $10,000 in one year for the down payment on a new sports car. If you can earn 7% annually, how much do you need to invest today? Prof. Q. Ma HADM 2222: Time Value of Money 10 Present Value – General Formula ± PV = FV / (1 + r) T ± PV = present value ± FV = future value Prof. Q. Ma HADM 2222: Time Value of Money 11 ± r = period interest rate, expressed as a decimal ± T = number of periods
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5 PVIF = 1/(1+r) T 0.8 1 1.2 1 5% 10% 20% Prof. Q. Ma HADM 2222: Time Value of Money 12 0 0.2 0.4 0.6 01234567891 0 Year PV of $ PV & FV: Their Relation ± PV = FV / (1 + r) T ± FV = PV (1 + r) T ± There are four parts in these equations ² PV, FV, r and T Prof. Q. Ma HADM 2222: Time Value of Money 13 ² From any three, we can get the fourth ± Sign convention when using financial calculator to solve for r or T.
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This note was uploaded on 10/09/2009 for the course H ADM 211 at Cornell University (Engineering School).

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Foundation 3 slides - Time Value of Money Question You are offered two options to receive a cash payment Option A $100 today Option B O i B $107 i

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