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Chapter 5 The Time Value of Money Foundations of Finance Arthur J. KeownJohn D. Martin J. William PettyDavid F. Scott, Jr.

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Presentation on theme: "Chapter 5 The Time Value of Money Foundations of Finance Arthur J. KeownJohn D. Martin J. William PettyDavid F. Scott, Jr."— Presentation transcript:

1 Chapter 5 The Time Value of Money Foundations of Finance Arthur J. KeownJohn D. Martin J. William PettyDavid F. Scott, Jr.

2 Chapter 5 The Time Value of Money Pearson Prentice Hall Foundations of Finance Learning Objectives  Explain the mechanics of compounding, which is how money grows over a time when it is invested.  Be able to move money through time using time value of money tables, financial calculators, and spreadsheets.  Discuss the relationship between compounding and bringing money back to present.

3 Chapter 5 The Time Value of Money Pearson Prentice Hall Foundations of Finance Learning Objectives  Define an ordinary annuity and calculate its compound or future value.  Differentiate between an ordinary annuity and an annuity due and determine the future and present value of an annuity due.  Determine the future or present value of a sum when there are nonannual compounding periods.

4 Chapter 5 The Time Value of Money Pearson Prentice Hall Foundations of Finance Learning Objectives Determine the present value of an uneven stream of paymentsDetermine the present value of an uneven stream of payments Determine the present value of a perpetuity.Determine the present value of a perpetuity. Explain how the international setting complicates the time value of money.Explain how the international setting complicates the time value of money.

5 Chapter 5 The Time Value of Money Pearson Prentice Hall Foundations of Finance Principles Used in this Chapter Principle 2: The Time Value of Money – A Dollar Received Today Is Worth More Than a Dollar Received in The Future.Principle 2: The Time Value of Money – A Dollar Received Today Is Worth More Than a Dollar Received in The Future.

6 Chapter 5 The Time Value of Money Pearson Prentice Hall Foundations of Finance Simple Interest Interest is earned on principal $100 invested at 6% per year 1 st yearinterest is $ nd yearinterest is $ rd year interest is $6.00 Total interest earned: $18.00

7 Chapter 5 The Time Value of Money Pearson Prentice Hall Foundations of Finance Compound Interest When interest paid on an investment during the first period is added to the principal; then, during the second period, interest is earned on the new sum.When interest paid on an investment during the first period is added to the principal; then, during the second period, interest is earned on the new sum.

8 Chapter 5 The Time Value of Money Pearson Prentice Hall Foundations of Finance Compound Interest Interest is earned on previously earned interest $100 invested at 6% with annual compounding 1 st year interest is $6.00 Principal is $ nd year interest is $6.36 Principal is $ rd year interest is $6.74 Principal is $ Total interest earned: $19.11

9 Chapter 5 The Time Value of Money Pearson Prentice Hall Foundations of Finance Future Value - The amount a sum will grow in a certain number of years when compounded at a specific rate. - The amount a sum will grow in a certain number of years when compounded at a specific rate.

10 Chapter 5 The Time Value of Money Pearson Prentice Hall Foundations of Finance Future Value FV 1 = PV (1 + i) Where FV 1 = the future of the investment at the end of one year i= the annual interest (or discount) rate i= the annual interest (or discount) rate PV = the present value, or original amount invested at the beginning of the first year PV = the present value, or original amount invested at the beginning of the first year

11 Chapter 5 The Time Value of Money Pearson Prentice Hall Foundations of Finance Future Value What will an investment be worth in 2 years? $100 invested at 6% FV 2 = PV(1+i) 2 = $100 (1+.06) 2 $100 (1.06) 2 = $112.36

12 Chapter 5 The Time Value of Money Pearson Prentice Hall Foundations of Finance Future Value Future Value can be increased by:Future Value can be increased by: Increasing number of years of compoundingIncreasing number of years of compounding Increasing the interest or discount rateIncreasing the interest or discount rate

13 Chapter 5 The Time Value of Money Pearson Prentice Hall Foundations of Finance Future Value Using Tables FV n = PV (FVIF i,n ) Where FV n = the future of the investment at the end of n year PV = the present value, or original amount invested at the beginning of the first year PV = the present value, or original amount invested at the beginning of the first year FVIF = Future value interest factor or the compound sum of $1 i= the interest rate i= the interest rate n= number of compounding periods n= number of compounding periods

14 Chapter 5 The Time Value of Money Pearson Prentice Hall Foundations of Finance Future Value What is the future value of $500 invested at 8% for 7 years? (Assume annual compounding) Using the tables, look at 8% column, 7 time periods. What is the factor? FV n = PV (FVIF 8%,7yr ) = $500 (1.714) = $500 (1.714) = $857 = $857

15 Chapter 5 The Time Value of Money Pearson Prentice Hall Foundations of Finance Future Value Using Calculators Using any four inputs you will find the 5th. Set to P/YR = 1 and END mode. INPUTSOUTPUT NI/YR PMT PV FV

16 Chapter 5 The Time Value of Money Pearson Prentice Hall Foundations of Finance Future Value Using Spreadsheets

17 Chapter 5 The Time Value of Money Pearson Prentice Hall Foundations of Finance Present Value The current value of a future payment PV = FV n {1/(1+i) n } Where FV n = the future of the investment at the end of n years n= number of years until payment is received n= number of years until payment is received i= the interest rate i= the interest rate PV = the present value of the future sum of money PV = the present value of the future sum of money

18 Chapter 5 The Time Value of Money Pearson Prentice Hall Foundations of Finance Present Value What will be the present value of $500 to be received 10 years from today if the discount rate is 6%? PV = $500 {1/(1+.06) 10 } = $500 (1/1.791) = $500 (1/1.791) = $500 (.558) = $500 (.558) = $279 = $279

19 Chapter 5 The Time Value of Money Pearson Prentice Hall Foundations of Finance Present Value Using Tables PV n = FV (PVIF i,n ) Where PV n = the present value of a future sum of money FV = the future value of an investment at the end of an investment period FV = the future value of an investment at the end of an investment period PVIF = Present Value interest factor of $1 i= the interest rate i= the interest rate n= number of compounding periods n= number of compounding periods

20 Chapter 5 The Time Value of Money Pearson Prentice Hall Foundations of Finance Present Value What is the present value of $100 to be received in 10 years if the discount rate is 6%? PV n = FV (PVIF 6%,10yrs. ) PV n = FV (PVIF 6%,10yrs. ) = $100 (.558) = $100 (.558) = $55.80 = $55.80

21 Chapter 5 The Time Value of Money Pearson Prentice Hall Foundations of Finance Present Value Using Calculators Using any four inputs you will find the 5th. Set to P/YR = 1 and END mode. INPUTSOUTPUT N I/YR PMT PV FV

22 Chapter 5 The Time Value of Money Pearson Prentice Hall Foundations of Finance Annuity Series of equal dollar payments for a specified number of years.Series of equal dollar payments for a specified number of years. Ordinary annuity payments occur at the end of each periodOrdinary annuity payments occur at the end of each period

23 Chapter 5 The Time Value of Money Pearson Prentice Hall Foundations of Finance Compound Annuity Depositing or investing an equal sum of money at the end of each year for a certain number of years and allowing it to grow.Depositing or investing an equal sum of money at the end of each year for a certain number of years and allowing it to grow.

24 Chapter 5 The Time Value of Money Pearson Prentice Hall Foundations of Finance Compound Annuity FV 5 = $500 (1+.06) 4 + $500 (1+.06) 3 +$500(1+.06) 2 + $500 (1+.06) + $500 = $500 (1.262) + $500 (1.191) + $500 (1.124) + $500 (1.090) + $500 = $500 (1.262) + $500 (1.191) + $500 (1.124) + $500 (1.090) + $500 = $ $ $ = $ $ $ $ $500 $ $500 = $2, = $2,818.50

25 Chapter 5 The Time Value of Money Pearson Prentice Hall Foundations of Finance Illustration of a 5yr $500 Annuity Compounded at 6% %

26 Chapter 5 The Time Value of Money Pearson Prentice Hall Foundations of Finance Future Value of an Annuity FV = PMT {(FVIF i,n -1)/ i } Where FV n = the future of an annuity at the end of the nth years FVIF i,n = future-value interest factor or sum of annuity of $1 for n years FVIF i,n = future-value interest factor or sum of annuity of $1 for n years PMT= the annuity payment deposited or received at the end of each year PMT= the annuity payment deposited or received at the end of each year i= the annual interest (or discount) rate i= the annual interest (or discount) rate n = the number of years for which the annuity will last n = the number of years for which the annuity will last

27 Chapter 5 The Time Value of Money Pearson Prentice Hall Foundations of Finance Compounding Annuity What will $500 deposited in the bank every year for 5 years at 10% be worth? FV = PMT {(FVIF i,n -1)/ i } Simplified this equation is: FV 5 = PMT(FVIFA i,n ) = $500(5.637) = $500(5.637) = $2, = $2,818.50

28 Chapter 5 The Time Value of Money Pearson Prentice Hall Foundations of Finance Future Value of an Annuity Using Calculators Using any four inputs you will find the 5th. Set to P/YR = 1 and END mode. INPUTSOUTPUT N I/YR PMT PV FV ,818.55

29 Chapter 5 The Time Value of Money Pearson Prentice Hall Foundations of Finance Present Value of an Annuity Pensions, insurance obligations, and interest received from bonds are all annuities. These items all have a present value.Pensions, insurance obligations, and interest received from bonds are all annuities. These items all have a present value. Calculate the present value of an annuity using the present value of annuity table.Calculate the present value of an annuity using the present value of annuity table.

30 Chapter 5 The Time Value of Money Pearson Prentice Hall Foundations of Finance Present Value of an Annuity Calculate the present value of a $500 annuity received at the end of the year annually for five years when the discount rate is 6%. PV = PMT(PVIFA i,n ) = $500(4.212) = $500(4.212) = $2,106 = $2,106

31 Chapter 5 The Time Value of Money Pearson Prentice Hall Foundations of Finance Annuities Due Ordinary annuities in which all payments have been shifted forward by one time period.Ordinary annuities in which all payments have been shifted forward by one time period.

32 Chapter 5 The Time Value of Money Pearson Prentice Hall Foundations of Finance Amortized Loans Loans paid off in equal installments over timeLoans paid off in equal installments over time –Typically Home Mortgages –Auto Loans

33 Chapter 5 The Time Value of Money Pearson Prentice Hall Foundations of Finance Payments and Annuities If you want to finance a new machinery with a purchase price of $6,000 at an interest rate of 15% over 4 years, what will your payments be?

34 Chapter 5 The Time Value of Money Pearson Prentice Hall Foundations of Finance Future Value Using Calculators Using any four inputs you will find the 5th. Set to P/YR = 1 and END mode. INPUTSOUTPUT N I/YR PMT PV FV , ,101.59

35 Chapter 5 The Time Value of Money Pearson Prentice Hall Foundations of Finance Amortization of a Loan Reducing the balance of a loan via annuity payments is called amortizing.Reducing the balance of a loan via annuity payments is called amortizing. A typical amortization schedule looks at payment, interest, principal payment and balance.A typical amortization schedule looks at payment, interest, principal payment and balance.

36 Chapter 5 The Time Value of Money Pearson Prentice Hall Foundations of Finance Amortization Schedule Yr.AnnuityInterestPrincipalBalance 1$2,101.58$900.00$1,201.58$4, $2, , , , , $2, , , , , $2, , ,827.51

37 Chapter 5 The Time Value of Money Pearson Prentice Hall Foundations of Finance Compounding Interest with Non-annual periods If using the tables, divide the percentage by the number of compounding periods in a year, and multiply the time periods by the number of compounding periods in a year. Example: 8% a year, with semiannual compounding for 5 years. 8% / 2 = 4% column on the tables N = 5 years, with semiannual compounding or 10 Use 10 for number of periods, 4% each

38 Chapter 5 The Time Value of Money Pearson Prentice Hall Foundations of Finance Perpetuity An annuity that continues forever is called perpetuityAn annuity that continues forever is called perpetuity The present value of a perpetuity isThe present value of a perpetuity is PV = PP/i PV = PP/i PV = present value of the perpetuity PV = present value of the perpetuity PP = constant dollar amount provided by the of perpetuity PP = constant dollar amount provided by the of perpetuity i = annuity interest (or discount rate) i = annuity interest (or discount rate)

39 Chapter 5 The Time Value of Money Pearson Prentice Hall Foundations of Finance The Multinational Firm Principle 1- The Risk Return Tradeoff – We Won ’ t Take on Additional Risk Unless We Expect to Be Compensated with Additional ReturnPrinciple 1- The Risk Return Tradeoff – We Won ’ t Take on Additional Risk Unless We Expect to Be Compensated with Additional Return The discount rate is reflected in the rate of inflation.The discount rate is reflected in the rate of inflation. Inflation rate outside US difficult to predictInflation rate outside US difficult to predict Inflation rate in Argentina in 1989 was 4,924%, in 1990 dropped to 1,344%, and in 1991 it was only 84%.Inflation rate in Argentina in 1989 was 4,924%, in 1990 dropped to 1,344%, and in 1991 it was only 84%.


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