3-2a[1].- Time Value of Money &amp; NPV

# 3-2a[1].- Time Value of Money & NPV - The Time Value of...

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The Time Value of Money The Time Value of Money Ramesh Rao 1

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Chapter Organization A. Preliminary Concepts A1. Single v. Multi-period period Cash Flows A2. Generalization to Multiple periods B. Annuities B1. PV of an Ordinary Annuity B2. Annuity Due B3. Growing Annuity B4. PV of a Perpetuity B5. Growing Perpetuity Example C. Summary of Formulas D. Compounding Periods D1. Infrequent Annuity D2. Stated v. Effective Interest Rates D3. Continuous Compounding E. A Prototypical example to illustrate several ideas F. When is Wealth Created? Ramesh Rao 2
A. Preliminary Concepts The first principle of Finance: Money has a “time” dimension There can be two “values” of a cash flow: It’s value today: Present Value It’s value at some point in the future: Future Value Methods of determining the “value” of a cash flow: Discounting: Finding the present value of future cash flows Compounding: Finding the future value of today’s cash flow Ramesh Rao 3

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Why do interest rates exist? The concept of Opportunity Cost What is the difference between hiding money under the pillow and investing it? Money can be invested in a security for a certain rate of return in the market. If the money is not invested, it loses value at the rate of the opportunity cost of not investing it. Ramesh Rao 4
A1. Single v. Multi-Period Cash Flows Ramesh Rao 5 \$105 \$100(1.05) = 1 C \$100(1.05) = 1 1 0 C r) (1 C FV = = + 0 1 r) (1 C C PV 1 0 + = = ) 1.05 1 \$105( \$100 = \$100 \$105 r =5%

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Simple vs. Compound Interest Ramesh Rao 6 Number of compounding periods Future value \$140 \$135 \$130 \$125 \$120 \$115 \$110 \$105 \$100 1 2 3 4 5 6
A2. Generalizing to n periods Ramesh Rao 7 0 1 2 3 4 \$200 r = 5% FV 4 = C 0 (1+r) 4 FV = \$200(1+0.05) 4 = \$243.10 Generalizing for n periods FV n = C 0 (1+r) n OR C 0 (FVF r, n ) Future Value: Formula Tables ?

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Ramesh Rao 8 Present Value: r = 5% PV = C 4 / (1+r) 4 = PV = \$200 /(1+0.05) 4 = \$164.54 Generalizing for n periods PV = C n / (1+r) n OR C n (PVF r,n ) Formula Tables 1 3 \$200 0 2 4 ?
FV of a single Cash Flow What is the FV of a Cash Flow of \$100 today, with r = 5%, and T = 5 years Formula Method: ( 29 ( 29 ( 29 63 . 127 \$ 27628 . 1 100 \$ 05 . 0 1 * 100 \$ 1 5 0 = = + = + = T r C FV Ramesh Rao 9 Table A.3, pp 876 RWJ, (with r = 5%, T = 5yrs) = 1.2763 FV = \$100(1.2763) = \$127.63 Table Method: Look up the FV factor in the table

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PV of a Single Cash Flow What is the PV of a Cash Flow of \$100 in year 5, with r = 5%, and T = 5 years Formula Method: ( 29 ( 29 ( 29 35 . 78 \$ 7835 . 0 100 \$ 05 . 0 1 1 * 100 \$ 1 5 = = + = + = T T r C PV Ramesh Rao 10 Table A.1, pp 872 RWJ, (with r = 5%, T = 5 yrs) = 0.7835 PV = \$100(0.7835) = \$78.35 Table Method: Look up the PV factor in the table
Observations about Future Values Ramesh Rao 11 2 4 6 8 10 12 14 16 18 20 Number of compounding periods Future value of \$1 5.00 4.00 3.00 2.00 1.00 0.00 1. FVs are always larger than PVs 2. Longer the time period, larger the FV 3. Larger the value of r, larger will be the FV r = 0% r = 8% r = 12%

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## This note was uploaded on 01/15/2010 for the course FIN 357 taught by Professor Hadaway during the Fall '06 term at University of Texas.

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3-2a[1].- Time Value of Money & NPV - The Time Value of...

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