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REAL4000 Aug 24 Chap 14

REAL4000 Aug 24 Chap 14 - The Time Value of Money A...

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4 The Time Value of Money A. Terminology 1. Compounding a. Compound interest b. Simple interest 2. Discounting 3. Annuity A series of fixed-sum payments for a specific number of payments. a. Ordinary annuity b. Annuity due 4. Components of TVM Problems a. Present Value (PV) A single cash flow (lump sum) at time period 0. b. Future Amounts Future Value (FV) - A single cash flow at any future time point Annuity Payment (PMT) - series of fixed-sum payments Cash Flows (CFi) – uneven series of payments c. rate of return ( i ) interest rate, discount rate, yield or required rate d. length of time years (n) periods per year (m)
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5 The Time Value of Money B. Future Value of Cash Flows 1. Future Value of a Lump Sum ( ) [ ] nm m i nm m i PV FVF PV FV + = = 1 , Q1: What is the value of one hundred dollars in one year if it is invested at an annual yield of 5%? Q2: What is the value of one hundred dollars in three years if it is invested at an annual yield of 5%? Q3: What is the value of one hundred dollars in three years if it is invested at an annual yield of 5% compounded monthly?
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6 The Time Value of Money B. Future Value of Cash Flows 2. Future Value of an Ordinary Annuity ( ) ( ) ( ) ( ) ( ) ( ) ( ) [ ] nm m i N m i N N t t N N N m i FVAF ANN ANN FVA i i ANN i ANN FVA ANN i ANN i ANN i ANN i ANN FVA , 1 1 2 2 1 1 1 1 1 1 1 1 1 1 = = + = + = + = + + + + + + + + + = K What is the future value of a $100 ordinary annuity which will be received for 3 years at 12%? 3. Future Value of an Annuity Due ( ) m i nm m i FVAF ANN FVAD + 1 = , What is the future value of a $100 annuity due which will be received for 3 years at 12%?
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7 The Time Value of Money C. Present Value of Cash Flows 1. Present Value of a Lump Sum ( ) + = = nm m i nm m i FV PVF FV PV 1 1 , Q1: What is the value today of one hundred and five dollars that will be received at the end of one year? Assume a 5% interest rate compounded annually. Q2: If you are going to receive $100 three years from today, what is it worth to you today? Assume a 5% interest rate compounded annually.
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8 The Time Value of Money C. Present Value of Cash Flows 2. Present Value of an Ordinary Annuity ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) [ ] nm m i nm m i i N t t N N m i t PVAF ANN ANN PVA i ANN i ANN PVA i i i i ANN PVA i ANN i ANN i ANN i ANN PVA , 1 1 1 3 2 1 3 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 =
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