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Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,The McGraw-Hill Companies, Inc.,2001,3-,35,Irwin/McGraw-Hill,Irwin/McGraw-Hill,Chapter 3,Fundamentals of Corporate Finance,Third Edition,The Time Value of Money,Brealey Myers Marcus,slides by Matthew Will,Irwin/McGraw-Hill,The McGraw-Hill Companies, Inc.,2001,Topics Covered,Future Values,Present Values,Multiple Cash Flows,Perpetuities and Annuities,Inflation & Time Value,Effective Annual Interest Rate,Future Values,Future 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 investment.,Future Values,Future Value of $100 = FV,Future Values,Example - FV,What is the future value of $100 if interest is compounded annually at a rate of 6% for five years?,Future Values,Example - FV,What is the future value of $100 if interest is compounded annually at a rate of 6% for five years?,Future Values with Compounding,Interest Rates,Manhattan Island Sale,Peter 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 Values,Present Value,Value today of a future cash flow.,Discount Rate,Interest rate used to compute present values of future cash flows.,Discount Factor,Present value of a $1 future payment.,Present Values,Present Values,Example,You just bought a new computer for $3,000. The payment terms are 2 years same as cash. If you can earn 8% on your money, how much money should you set aside today in order to make the payment when due in two years?,Present Values,Discount Factor = DF = PV of $1,Discount Factors can be used to compute the present value of any cash flow.,The PV formula has many applications. Given any variables in the equation, you can solve for the remaining variable.,Time Value of Money,(applications),Value of Free Credit,Implied Interest Rates,Internal Rate of Return,Time necessary to accumulate funds,Time Value of Money,(applications),PV of Multiple Cash Flows,Example,Your auto dealer gives you the choice to pay $15,500 cash 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 Flows,PVs can be added together to evaluate multiple cash flows.,Perpetuities & Annuities,Perpetuity,A stream of level cash payments that never ends.,Annuity,Equally spaced level stream of cash flows for a limited period of time.,Perpetuities & Annuities,PV of Perpetuity Formula,C = cash payment,r = interest rate,Perpetuities & Annuities,Example - Perpetuity,In order to create an endowment, which pays $100,000 per year, forever, how much money must be set aside today in the rate of interest is 10%?,Perpetuities & Annuities,Example - continued,If the first perpetuity payment will not be received until three years from today, how much money needs to be set aside today?,Perpetuities & Annuities,PV of Annuity Formula,C = cash payment,r = interest rate,t = Number of years cash payment is received,Perpetuities & Annuities,PV Annuity Factor (PVAF),- The present value of $1 a year for each of t years.,Perpetuities & Annuities,Example - Annuity,You are purchasing a car. You are scheduled to make 3 annual installments of $4,000 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 & Annuities,Applications,Value of payments,Implied interest rate for an annuity,Calculation of periodic payments,Mortgage payment,Annual income from an investment payout,Future Value of annual payments,Perpetuities & Annuities,Example - Future Value of annual payments,You 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?,Inflation,Inflation,- Rate at which prices as a whole are increasing.,Nominal Interest Rate,- Rate at which money invested grows.,Real Interest Rate,- Rate at which the purchasing power of an investment increases.,Inflation,approximation formula,Inflation,Example,If the interest rate on one year govt. bonds is 5.0% and the inflation rate is 2.2%, what is the real interest rate?,Savings,Bond,Effective Interest Rates,Annual Percentage Rate,- Interest rate that is annualized using simple interest.,Effective Annual Interest Rate,- Interest rate that is annualized using compound interest.,Effective Interest Rates,example,Given a monthly rate of 1%, what is the Effective Annual Rate(EAR)? What is the Annual Percentage Rate (APR)?,基本財務數學摘要,現值與未來值,年金（,Annuity）的未來值和現值,貸款常數,（,mortgage constant）,與沉入基金因子,（sinking fund factor）,現值與未來值,現值與未來值之關係,FV,n,=PV(1+r),n,FV,n,=PV(1+r/m),nm,Effective Annual Yield (EAY),EAY=(1+r/m),m,-1,未來值因子：FV(r/m,nm)=(1+r/m),nm,現值因子：,PV(r/m,nm)=1/(1+r/m),nm,年金的未來值和現值（,I）,永久年金(,Annuity)的現值：,年金現值因子(,Annuity Present Value Factor),為：,年金的未來值和現值（,II）,年金未來值因子為,貸款常數,(,mortgage constant),與,沉入基金因子,(,sinking fund factor),貸款常數,PV=APVA(r,n) A=PV1/PVA(r,n,MC=11/PVA(r,n,沉入基金因子,FV=AFVA(r,n) A=FV1/FVA(r,n,SFF,=11/FVA(r,n,
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