copyright ©2004 pearson education, inc. all rights reserved. chapter 3 applying time value concepts

Copyright ©2004 Pearson Education, Inc. All rights reserved.

Chapter 3

Applying Time Value Concepts

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


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


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


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)



• 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



Exhibit 3.1: Future Value of $1 (FVIF)



Exhibit 3.1 (continued)



• 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


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


Financial Planning Online:Paying Your Bills Online

• Go to: http://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.

http://moneycentral.msn.com/




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



• 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



• 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



• 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?



Exhibit 3.2: Present Value of $1 (PVIF)



• 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



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



• 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



• 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?



Exhibit 3.3: Future Value of a $1 Ordinary Annuity (FVIFA)



• 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



Financial Planning Online: Estimating the Future Value of Your Savings

• Go to: http://moneycentral.msn.com/investor/calcs/n_savapp/main.asp

• Click on: Savings Calculator

• This Web site provides an estimate of the future value of your savings.

http://moneycentral.msn.com/investor/calcs/n_savapp/main.asp








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



• 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



• 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?



Exhibit 3.4: Present Value of a $1 Ordinary Annuity (PVIFA)



• 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


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


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?


Integrating Key Concepts


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

copyright ©2004 pearson education, inc. all rights reserved. chapter 3 applying time value concepts

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