Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendix 4A The Time Value of Money
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 4A-2 The Time Value of Money Time Value of Money: as long as an opportunity exists to earn interest, the value of money is affected by the point in time when the money is received –A dollar received today is worth more than a dollar received in the future –The sooner you receive money from an investment, the better –The sooner your money can begin earning interest, the faster it will grow
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 4A-3 Interest: The Basic Return to Savers Interest: the “rent” paid by a borrower for use of the lender’s money Simple Interest –Interest is paid only on the initial deposit Compound Interest –Interest is paid on the initial deposit and any interest accumulated from prior periods –Interest is earned on interest –More frequent compounding periods provide higher true rate of interest –Compounding periods range from annually to continuously
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 4A-4 Figure 4A.1 Financial Tables
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 4A-5 Figure 4A.2 Calculator Keys
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 4A-6 Calculating Time Value: Computers and Spreadsheets Built-in routines similar to financial calculators –Values for variables are entered in individual cells on spreadsheet –Cells are linked by equations programmed to calculate time values –Changes in variable values automatically update time values Provides flexibility to investors
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 4A-7 Future Value: An Extension of Compounding Future Value: the amount a current deposit will grow to over a period of time when it is placed in an account paying compound interest Future Value Example: How much will $1,000 deposited into an account earning 8% compounded annually be worth in two years?
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 4A-8 Future Value: Using an Excel Spreadsheet
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 4A-9 Future Value of an Annuity Annuity: a stream of equal cash flows that occur at equal intervals over time Ordinary Annuity: an annuity where cash flows occur at the end of each period Future Value of an Annuity Example: What is the future value of $1,000 deposited at the end of each year for 8 years in an account earning 6% compounded annually?
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 4A-10 Future Value of an Annuity: Using an Excel Spreadsheet
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 4A-11 Present Value: An Extension of Future Value Present Value: the value today of a sum to be received at some future date Present Value Example: How much would need to be deposited today into an accounting earning 6% compounded annually to grow to $500 in 7 years?
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 4A-12 Present Value: Using an Excel Spreadsheet
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 4A-13 Present Value of a Mixed Stream of Returns Mixed Stream of Returns: series of returns that have no special pattern Present Value of an Annuity Example: What is the present value of the following stream of returns discounted at 9%? Table 4A.4 Mixed and Annuity Return Streams
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 4A-14 Table 4A.5 Mixed-Stream Present-Value Calculation
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 4A-15 Present Value of a Mixed Stream of Returns: Using an Excel Spreadsheet
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 4A-16 Present Value of an Annuity Annuity: a stream of equal cash flows that occur at equal intervals over time Present Value of an Annuity Example: What is the present value of $50 deposited at the end of each year for 5 years in an account earning 9% compounded annually?
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 4A-17 Present Value of an Annuity: Using an Excel Spreadsheet
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Appendix 4A Additional Chapter Art
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 4A-19 Table 4A.1 Savings Account Balance Data (5% interest compounded annually)
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 4A-20 Table 4A.2 Savings Account Balance Data (5% interest compounded semiannually)
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 4A-21 Table 4A.3 True Rate of Interest for Various Compounding Frequencies (5% stated rate of interest)