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McGraw-Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter 11 The Time Value of Money

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11-2 What is the Difference between Return Of and Return On an Investment? Return OF Return of the initial amount invested Return ON Additional amount returned in excess (or less than) the amount invested

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11-3 What is Risk? Risk The chance of an unfavorable outcome Inflation risk Risk of changing price levels Business risk Risk of a particular company going out of business Liquidity risk Risk that an investment cannot be converted into cash when needed

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11-4 How are Risk and Return Related? Expected rate of return Estimated rate of return on an investment Risk premium Expected rate of return adjusted for inflation, business, and liquidity risk Note: The greater the risk, the higher the expected rate of return.

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11-5 What is the Difference between Simple and Compound Interest? Simple Interest is calculated on principal only Interest (1) = Principal * Rate * Time Interest (2) = Principal * Rate * Time Compound Interest is calculated on principal plus accumulated interest Interest (1) = Principal * Rate * Time Interest (2) = (Principal + Interest [1]) * Rate * Time

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11-6 What are the Time Value of Money Components? FV = future value PV = present value c = compoundings/payments per year r = annual interest rate n = total number of compoundings/payments ANN = annuity

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11-7 What is the Future Value of $1? Answers the question: What amount will $1 grow to at some point in the future? Example: If we invest $2,000 today, what will it be worth in 5 years, if we earn 8 percent interest compounded quarterly? PV = 2,000, r = 8, c = 4, n = 20, ANN = 0, FV = $2,971.89

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11-8 Formula: FV of $1 PV * ($1 + r/c) n = FV $2,000 * ($1 + 0.08/4) 20 = FV $2,000 * 1.4859 = FV $2,971.89 = FV

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11-9 What is the Present Value of $1? Answers the question: What is $1 at some point in the future worth today? Example: If we receive $2,000 in 5 years, what is it worth today if we could invest it at 8 percent interest compounded quarterly? FV = 2,000, r = 8, c = 4, n = 20, ANN = 0, PV = $1,345.94

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11-10 Formula: PV of $1 FV * 1/($1 + r/c) n = PV $2,000 * 1/($1 + 0.08/4) 20 = PV $2,000 * 0.6730 = PV $1,345.94 = PV

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11-11 What is an Annuity? A series of EQUAL cash payments made at EQUAL intervals.

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11-12 What is the Future Value of an Annuity? Answers the question: What is a series of payments going to be worth at some point in the future? Example: If we invest $100 every month for 10 years and earn 12 percent interest, how much money will we have in 10 years? ANN = 100, PV = 0, r = 12, c = 12, n = 120, FV = $23,003.87

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11-13 Formula: Future Value of an Annuity ANN * [($1 + r/c) n - $1]/(r/c) = FV $100 * [$1 + 0.12/12) 120 - $1]/(0.12/12) = FV $100 * 230.0387 = FV $23,003.87 = FV

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11-14 What is the Present Value of an Annuity? Answers the question: How much must be received today to generate a series of equal payments in the future? Example: We want to buy a car for $25,000. The dealer will finance us at 10 percent annual interest for 5 years, how much will the monthly payments be? PV = 25,000, FV = 0, r = 10, c = 12, n = 60, ANN = $531.18

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11-15 Formula: Present Value of an Annuity ANN * [$1 - $1/($1 + r/c) n ]/(r/c) = PV ANN * [$1 - $1/($1 + 0.10/12) 60 ]/(0.10/12) = $25,000 ANN * 47.0654 = $25,000 ANN = $531.18

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Math 1320 Chapter 2: The Mathematics of Finance 2.2 Compound Interest.

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