台湾大学：《财务管理》（英文版） Chapter 3 Value of Money

Fundamentals of Corporate Finance Third edition Chapter 3 The Time Brealey Myers Marcus Value of Money ndamentals of Corporate Finan Brealey Myers Marcus slides by Matthew will IrwinMcGraw-Hill CThe McGraw-Hill Companies, Inc, 2001

©The McGraw-Hill Companies, Inc.,2001 3- 1 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

3-2 Topics Covered S Future values S Present values MTONEY MUltiple Cash Flows pErpetuities and Annuities INflation time value SEffective Annual Interest rate Irwin/McGraw-Hill CThe McGraw-Hill Commpanies, Inc, 2001

©The McGraw-Hill Companies, Inc.,2001 3- 2 Irwin/McGraw-Hill 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 Irwin/McGraw-Hill CThe McGraw-Hill Commpanies, Inc, 2001

©The McGraw-Hill Companies, Inc.,2001 3- 3 Irwin/McGraw-Hill 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

3-4 Future values Future Value of S100=FV FV=$100×(1+r) Irwin/McGraw-Hill CThe McGraw-Hill Commpanies, Inc, 2001

©The McGraw-Hill Companies, Inc.,2001 3- 4 Irwin/McGraw-Hill Future Values Future Value of $100 = FV F V r t = $100  (1+ )

3-5 Future values FV=$100×(1+r) Example- FV What is the future value of $100 if interest is compounded annually at a rate of 6%0 for five years? Irwin/McGraw-Hill CThe McGraw-Hill Commpanies, Inc, 2001

©The McGraw-Hill Companies, Inc.,2001 3- 5 Irwin/McGraw-Hill Future Values FV r t = $100  (1+ ) Example - FV What is the future value of $100 if interest is compounded annually at a rate of 6% for five years?

3-6 Future values FV=$100×(1+r) Example- FV What is the future value of $100 if interest is compounded annually at a rate of 6%0 for five years? FV=$100×(1+.06)=$133.82 Irwin/McGraw-Hill CThe McGraw-Hill Commpanies, Inc, 2001

©The McGraw-Hill Companies, Inc.,2001 3- 6 Irwin/McGraw-Hill Future Values FV r t = $100  (1+ ) Example - FV What is the future value of $100 if interest is compounded annually at a rate of 6% for five years? $100 (1 .06) $133.82 5 FV =  + =

3-7 Future Values with Compounding 70 Interest rates 60 0 5% 0 10% 40 15% 30 20 10 0 小心小少少少少少 Number of years Irwin/McGraw-Hill CThe McGraw-Hill Companies, Inc, 2001

©The McGraw-Hill Companies, Inc.,2001 3- 7 Irwin/McGraw-Hill 0 10 20 30 40 50 60 70 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 Number of Years FV of $1 0% 5% 10% 15% Future Values with Compounding Interest Rates

3-8 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 FV=$24x(1+08)374 75.979 trillion FOR SOLE FY- The value of manhattan island land is well below this figure Irwin/McGraw-Hill CThe McGraw-Hill Commpanies, Inc, 2001

©The McGraw-Hill Companies, Inc.,2001 3- 8 Irwin/McGraw-Hill Manhattan Island Sale Peter Minuit bought Manhattan Island for $24 in 1626. Was this a good deal? trillion FV $75.979 $24 (1 .08) 374 = =  + 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

3-9 Present Values Present value Discount factor alue today of a Present value of future cash a SI future flow payment Discount rate Interest rate used o compute present values of future cash flows Irwin/McGraw-Hill CThe McGraw-Hill Commpanies, Inc, 2001

©The McGraw-Hill Companies, Inc.,2001 3- 9 Irwin/McGraw-Hill 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

3-10 Present Values Present value= pv PV= Future Value after t periods Irwin/McGraw-Hill CThe McGraw-Hill Commpanies, Inc, 2001

©The McGraw-Hill Companies, Inc.,2001 3- 10 Irwin/McGraw-Hill Present Values Present Value = P V P V = Future Value after t periods (1+r)t