1. Copyright ©2004 Pearson Education, Inc. All rights reserved. Chapter 3 Applying Time Value Concepts

2. Copyright ©2004 Pearson Education, Inc. All rights reserved.2-2 Chapter Objectives Calculate the future value of a dollar amount that you save today Calculate the present value of a dollar amount that will be received in the future Calculate the future value of an annuity Calculate the present value of an annuity

3. Copyright ©2004 Pearson Education, Inc. All rights reserved.2-3 Time Value of Money Can be applied to a single dollar amount — also called a lump sum Can also be applied to an annuity –Annuity: a series of equal cash flow payments that occur at the end of each period –An example would be a monthly deposit of $50 into your savings account

4. Copyright ©2004 Pearson Education, Inc. All rights reserved.2-4 Future Value of a Single Dollar Amount Compounding: the process by which money accumulates interest To determine the future value of an amount of money you deposit today, you must know: –The amount of your deposit today –The interest rate to be earned on the deposit –The number of years the money will be invested

5. Copyright ©2004 Pearson Education, Inc. All rights reserved.2-5 Future Value of a Single Dollar Amount Future value interest factor (FVIF): a factor multiplied by today’s savings to determine how the savings will accumulate over time Can be calculated using the future value table or a financial calculator –Future value table shows various interest rates (i) and time periods (n)

6. Copyright ©2004 Pearson Education, Inc. All rights reserved.2-6 Future Value of a Single Dollar Amount Suppose you want to know how much money you will have in five years if you invest $5,000 now and earn an annual return of 9 percent –The present value of money (PV) is the amount invested, or $5,000 –Find the interest rate of 9 percent and a time period of five years on the table

7. Copyright ©2004 Pearson Education, Inc. All rights reserved.2-7 Future Value of a Single Dollar Amount Exhibit 3.1: Future Value of $1 (FVIF)

8. Copyright ©2004 Pearson Education, Inc. All rights reserved.2-8 Future Value of a Single Dollar Amount Exhibit 3.1 (continued)

9. Copyright ©2004 Pearson Education, Inc. All rights reserved.2-9 Future Value of a Single Dollar Amount Using the information in the example and the table, we can determine that, in five years, your money will be worth: $5,000  1.539 = $7,695 This can also be determined using a financial calculator

10. Copyright ©2004 Pearson Education, Inc. All rights reserved.2-10 Future Value of a Single Dollar Amount Focus on ethics: delaying payments –Investing money while delaying payment obligations allows you to earn interest on your funds –However, delaying payments may result in late fees and penalties that may damage your credit rating –Make use of your money while you can, but always make obligatory payments

11. Copyright ©2004 Pearson Education, Inc. All rights reserved.2-11 Financial Planning Online: Paying Your Bills Online Go to: http://moneycentral.msn.comhttp://moneycentral.msn.com Click on: Bill pay, under the heading Banking This Web site provides an illustration of how you can pay your bills online.

12. Copyright ©2004 Pearson Education, Inc. All rights reserved.2-12 Present Value of a Dollar Amount Discounting: the process of obtaining present values Present values tell you the amount you must invest today to accumulate a certain amount at some future time This amount is based on some interest rate you could earn over that period

13. Copyright ©2004 Pearson Education, Inc. All rights reserved.2-13 Present Value of a Dollar Amount To determine present values, you need to know: –The amount of money to be received in the future –The interest rate to be earned on the deposit –The number of years the money will be invested

14. Copyright ©2004 Pearson Education, Inc. All rights reserved.2-14 Present Value of a Dollar Amount Using the Present Value Table –Present value interest factor (PVIF): a factor multiplied by a future value to determine the present value of that amount –Notice that PVIF is lower as the number of years increases and as the interest rate increases Can also be calculated using a financial calculator

15. Copyright ©2004 Pearson Education, Inc. All rights reserved.2-15 Present Value of a Dollar Amount You would like to accumulate $50,000 in five years by making a single investment today. You believe you can achieve a return from your investment of 8 percent annually. What is the dollar amount that you need to invest today to achieve your goal?

16. Copyright ©2004 Pearson Education, Inc. All rights reserved.2-16 Present Value of a Dollar Amount Exhibit 3.2: Present Value of $1 (PVIF)

17. Copyright ©2004 Pearson Education, Inc. All rights reserved.2-17 Present Value of a Dollar Amount Exhibit 3.2 (continued)

18. Copyright ©2004 Pearson Education, Inc. All rights reserved.2-18 Present Value of a Dollar Amount Using the information in the example and the table we can determine that in order to have $50,000 today: $50,000  0.681 = $34,050 This can also be determined using a financial calculator

19. Copyright ©2004 Pearson Education, Inc. All rights reserved.2-19 Future Value of an Annuity Annuity due: a series of equal cash flow payments that occur at the beginning of each period Timelines: diagrams that show payments received or paid over time These values can also be calculated using a table or a financial calculator

20. Copyright ©2004 Pearson Education, Inc. All rights reserved.2-20 Future Value of an Annuity Future value interest factor for an annuity (FVIFA): a factor multiplied by the periodic savings level (annuity) to determine how the savings will accumulate over time –i is the periodic interest rate –n is the number of payments in the annuity

21. Copyright ©2004 Pearson Education, Inc. All rights reserved.2-21 Future Value of an Annuity Suppose that you have won the lottery and will receive $150,000 at the end of every year for the next 20 years. As soon as you receive the payments, you will invest them at your bank at an interest rate of 7 percent annually. How much will be in your account at the end of 20 years, assuming you do not make any withdrawals?

22. Copyright ©2004 Pearson Education, Inc. All rights reserved.2-22 Future Value of an Annuity Exhibit 3.3: Future Value of a $1 Ordinary Annuity (FVIFA)

23. Copyright ©2004 Pearson Education, Inc. All rights reserved.2-23 Future Value of an Annuity Exhibit 3.3 (continued)

24. Copyright ©2004 Pearson Education, Inc. All rights reserved.2-24 Future Value of an Annuity Using our example and the table, we can determine that, at the end of twenty years, you would have: $150,000  40.995 = $6,149,250 This can also be determined using a financial calculator

25. Copyright ©2004 Pearson Education, Inc. All rights reserved.2-25 Financial Planning Online: Estimating the Future Value of Your Savings Go to: http://moneycentral.msn.com/investor/c alcs/n_savapp/main.asp http://moneycentral.msn.com/investor/c alcs/n_savapp/main.asp Click on: Savings Calculator This Web site provides an estimate of the future value of your savings.

26. Copyright ©2004 Pearson Education, Inc. All rights reserved.2-26 Present Value of an Annuity The present value of an annuity is determined by discounting the individual cash flows of the annuity and adding them up This value also can be obtained by either using a present value of an annuity table or a financial calculator

27. Copyright ©2004 Pearson Education, Inc. All rights reserved.2-27 Present Value of an Annuity Present value interest factor for an annuity (PFIFA): a factor multiplied by a periodic savings level (annuity) to determine the present value of the annuity i represents various rates of interest n represents the time periods in the annuity

28. Copyright ©2004 Pearson Education, Inc. All rights reserved.2-28 Present Value of an Annuity Suppose you have just won the lottery. As a result of your luck, you will receive $82,000 at the end of every year for the next 25 years. Now, a financial firm offers you a lump sum of $700,000 in return for these payments. If you can invest your money at an annual interest rate of 9 percent, should you accept the offer?

29. Copyright ©2004 Pearson Education, Inc. All rights reserved.2-29 Present Value of an Annuity Exhibit 3.4: Present Value of a $1 Ordinary Annuity (PVIFA)

30. Copyright ©2004 Pearson Education, Inc. All rights reserved.2-30 Present Value of an Annuity Exhibit 3.4 (continued)

31. Copyright ©2004 Pearson Education, Inc. All rights reserved.2-31 Present Value of an Annuity Using our example and the previous table we can determine that the present value of the stream of $82,000 payments is: $82,000  9.823 = $805,486 Since this amount is less than the $700,000 offered, you would reject the offer

32. Copyright ©2004 Pearson Education, Inc. All rights reserved.2-32 Using Time Value to Estimate Savings Estimating the future value from savings –Provides motivation for regular saving Estimating the annual savings that will achieve a future amount –Helps set specific goals when saving for a large purchase

33. Copyright ©2004 Pearson Education, Inc. All rights reserved.2-33 How a Savings Plan Fits Within Your Financial Plan Key savings decisions for building your financial plan are: –How much should I attempt to accumulate in savings for a future point in time? –How much should I attempt to save every month or every year?

34. Copyright ©2004 Pearson Education, Inc. All rights reserved.2-34 Integrating Key Concepts

35. Copyright ©2004 Pearson Education, Inc. All rights reserved.2-35 Integrating Key Concepts Part 1: Financial Planning Tools –In Chapter 2 we learned about personal financial statements –In Chapter 3 we learned about time value of money –Chapter 4 teaches tax planning Part 2: Liquidity Management Part 3: Financing Part 4: Protecting Your Wealth Part 5: Investing Part 6: Retirement and Estate Planning