Kế toán, kiểm toán - Chapter 1: Time value of money

Chapter 11Time Value of MoneyCopyright © 2011 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin11-*What is the Difference between Return Of and Return On an Investment?Return OFReturn of the initial amount investedReturn ONAdditional amount returned in excess (or less than) the amount invested11-*What is Risk?RiskThe chance of an unfavorable outcomeInflation riskRisk of changing price levelsBusiness riskRisk of a particular company going out of businessLiquidity riskRisk that an investment cannot be converted into cash when needed11-*How are Risk and Return Related?Expected rate of returnEstimated rate of return on an investmentRisk premiumExpected rate of return adjusted for inflation, business, and liquidity riskNote: The greater the risk, the higher the expected rate of return.11-*What is the Difference between Simple and Compound Interest?SimpleInterest is calculated on principal onlyInterest (1) = Principal * Rate * TimeInterest (2) = Principal * Rate * TimeCompoundInterest is calculated on principal plus accumulated interestInterest (1) = Principal * Rate * TimeInterest (2) = (Principal + Interest [1]) * Rate * Time11-*What are the Time Value of Money Components?FV = future valuePV = present valuec = compoundings/payments per yearr = annual interest raten = total number of compoundings/payments ANN = annuity11-*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, therefore: Answer: FV = $2,971.8911-*Formula: FV of $1PV * ($1 + r/c)n = FV $2,000 * ($1 + 0.08/4)20 = FV $2,000 * 1.4859 = FV $2,971.89 = FV11-*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, therefore: Answer: PV = $1,345.9411-*Formula: PV of $1FV * 1/($1 + r/c)n = PV $2,000 * 1/($1 + 0.08/4)20 = PV $2,000 * 0.6730 = PV $1,345.94 = PV11-*What is an Annuity? A series of EQUAL cash payments made at EQUAL intervals.11-*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, therefore: Answer: FV = $23,003.87 11-*Formula: Future Value of an AnnuityANN * [($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 = FV11-*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, therefore: Answer: ANN = $531.1811-*Formula: Present Value of an AnnuityANN * [$1 - $1/($1 + r/c)n]/(r/c) = PVANN * [$1 - $1/($1 + 0.10/12)60]/(0.10/12) = $25,000ANN * 47.0654 = $25,000ANN = $531.18