Fundamentals of Corporate Finance Chapter 3 The Time Value of Money

1、Fundamentals of Corporate Finance Chapter 3 The Time Value of MoneyIrwin/McGraw-HillChapter 3Fundamentals of Corporate FinanceThird EditionThe Time Value of MoneyBrealey Myers Marcusslides by Matthew WillIrwin/McGraw-HillThe McGraw-Hill Companies, Inc4.,2001Topics CoveredFuture ValuesPresent ValuesM

2、ultiple Cash FlowsPerpetuities and AnnuitiesInflation & Time ValueEffective Annual Interest RateFuture ValuesFuture Value - Amount to which an investment will grow after earning interest.Compound Interest - Interest earned on interest.Simple Interest - Interest earned only on the original invest

3、ment.Future ValuesFuture Value of $100 = FVFuture ValuesExample - FVWhat is the future value of $100 if interest is compounded annually at a rate of 6% for five years?Future ValuesExample - FVWhat is the future value of $100 if interest is compounded annually at a rate of 6% for five years?Future Va

4、lues with CompoundingInterest RatesManhattan Island SalePeter Minuit bought Manhattan Island for $24 in 1626. Was this a good deal? To answer, determine $24 is worth in the year 2000, compounded at 8%. FYI - The value of Manhattan Island land is well below this figure. Present ValuesPresent ValueVal

5、ue today of a future cash flow.Discount RateInterest rate used to compute present values of future cash flows.Discount FactorPresent value of a $1 future payment.Present ValuesPresent ValuesExampleYou just bought a new computer for $3,000. The payment terms are 2 years same as cash. If you can earn

6、8% on your money, how much money should you set aside today in order to make the payment when due in two years?Present ValuesDiscount Factor = DF = PV of $1Discount Factors can be used to compute the present value of any cash flow.Time Value of Money(applications)The PV formula has many applications

7、. Given any variables in the equation, you can solve for the remaining variable. Time Value of Money(applications)Value of Free CreditImplied Interest RatesInternal Rate of ReturnTime necessary to accumulate fundsPV of Multiple Cash FlowsExampleYour auto dealer gives you the choice to pay $15,500 ca

8、sh now, or make three payments: $8,000 now and $4,000 at the end of the following two years. If your cost of money is 8%, which do you prefer?PV of Multiple Cash FlowsPVs can be added together to evaluate multiple cash flows.Perpetuities & AnnuitiesPerpetuity A stream of level cash payments that

9、 never ends.Annuity Equally spaced level stream of cash flows for a limited period of time.Perpetuities & AnnuitiesPV of Perpetuity FormulaC = cash payment r = interest rate Perpetuities & AnnuitiesExample - PerpetuityIn order to create an endowment, which pays $100,000 per year, forever, ho

10、w much money must be set aside today in the rate of interest is 10%?Perpetuities & AnnuitiesExample - continuedIf the first perpetuity payment will not be received until three years from today, how much money needs to be set aside today?Perpetuities & AnnuitiesPV of Annuity FormulaC = cash p

11、ayment r = interest rate t = Number of years cash payment is receivedPerpetuities & AnnuitiesPV Annuity Factor (PVAF) - The present value of $1 a year for each of t years. Perpetuities & AnnuitiesExample - AnnuityYou are purchasing a car. You are scheduled to make 3 annual installments of $4

12、,000 per year. Given a rate of interest of 10%, what is the price you are paying for the car (i.e. what is the PV)?Perpetuities & AnnuitiesApplicationsValue of paymentsImplied interest rate for an annuityCalculation of periodic payments Mortgage paymentAnnual income from an investment payoutFutu

13、re Value of annual paymentsPerpetuities & AnnuitiesExample - Future Value of annual paymentsYou plan to save $4,000 every year for 20 years and then retire. Given a 10% rate of interest, what will be the FV of your retirement account? InflationInflation - Rate at which prices as a whole are incr

14、easing.Nominal Interest Rate - Rate at which money invested grows.Real Interest Rate - Rate at which the purchasing power of an investment increases.Inflationapproximation formulaInflationExampleIf the interest rate on one year govt. bonds is 5.0% and the inflation rate is 2.2%, what is the real int

15、erest rate?SavingsBondEffective Interest RatesAnnual Percentage Rate - Interest rate that is annualized using simple interest.Effective Annual Interest Rate - Interest rate that is annualized using compound interest.Effective Interest RatesexampleGiven a monthly rate of 1%, what is the Effective Ann

16、ual Rate(EAR)? What is the Annual Percentage Rate (APR)?基本财务数学摘要现值与未来值年金（Annuity）的未来值和现值贷款常数（mortgage constant） 与沉入基金因子（sinking fund factor）现值与未来值现值与未来值之关系FVn=PV(1+r)nFVn=PV(1+r/m)nmEffective Annual Yield (EAY)EAY=(1+r/m)m -1未来值因子：FV(r/m,nm)=(1+r/m)nm现值因子：PV(r/m,nm)=1/(1+r/m)nm年金的未来值和现值（I）永久年金(Annuity)的现值：年金现值因子