Applying Time Value Concepts Chapter 3 Applying Time Value Concepts

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

The Importance of the Time Value of Money The value of money is influenced by the time it is received The value of a given amount of money is generally greater the earlier it is received The earlier you start saving, the more quickly your money can earn interest and grow

The Importance of the Time Value of Money (cont’d) 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 are received or paid at equal intervals in time An example would be a monthly deposit of $50 into your savings account

Future Value of a Single Dollar Amount Compounding: the process of earning interest on 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 (cont’d) 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)

Future Value of a Single Dollar Amount (cont’d) 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 4 percent The present value of money (PV) is the amount invested, or $5,000 Find the interest rate of 4 percent and a time period of five years on the table

Future Value of a Single Dollar Amount (cont’d) Using the information in the example and the table, we can determine that, in five years, your money will be worth: $5,000 x 1.217 = $6,085 This can also be determined using a financial calculator

Future Value of a Single Dollar Amount (cont’d) Impact of a longer period As the number of years increases, the FVIF increases What if you invested your $5,000 for 20 years instead of 5 years? Assuming the interest rate is still 4%: $5,000 x 2.191 = $10,955

Future Value of a Single Dollar Amount (cont’d) Impact of a higher interest rate The higher the interest rate, the more your money will grow What if you invested your $5,000 at an interest rate of 9% instead of 4%? Assuming a period of 20 years: $5,000 x 5.604 = $28,020

Future Value of a Single Dollar Amount (cont’d) The power of compounding An amount of savings can grow substantially due to compounding Compounding can also expand your debt Not only do you pay interest on your debt, you also pay interest on the interest on your debt

Future Value of a Single Dollar Amount (cont’d) The future value of debt Compounding can also expand your debt Not only do you pay interest on your debt, you also pay interest on the interest on your debt

Future Value of a Single Dollar Amount (cont’d) Twisted logic about long-term debt Some people believe that it is to their advantage to postpone payment of debt as long as possible More enjoyable to spend than to pay! Don’t recognize how debt can accumulate over a long-term period

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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

Present Value of a Dollar Amount (cont’d) 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

Present Value of a Dollar Amount (cont’d) 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

Present Value of a Dollar Amount (cont’d) 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 7 percent annually. What is the dollar amount that you need to invest today to achieve your goal?

Present Value of a Dollar Amount (cont’d) Using the information in the example and the table we can determine that in order to have $50,000 today: $50,000 x 0.713 = $35,650 This can also be determined using a financial calculator

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 of an Annuity (cont’d) 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

Future Value of an Annuity (cont’d) 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?

Future Value of an Annuity (cont’d) Using our example and the table, we can determine that, at the end of twenty years, you would have: $150,000 x 40.995 = $6,149,250 This can also be determined using a financial calculator

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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 of an Annuity (cont’d) Present value interest factor for an annuity (PVIFA): a factor multiplied by a periodic savings level (annuity) to determine the present value of the annuity

Present Value of an Annuity (cont’d) 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?

Present Value of an Annuity (cont’d) Using our example and the previous table we can determine that the present value of the stream of $82,000 payments is: $82,000 x 9.823 = $805,486 Since this amount is more 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

Using Time Value to Estimate Savings How time value can motivate saving Money can grow substantially over time when you invest periodically and earn interest May be more motivated to save because you can see the reward of your effort

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?

Using Time Value to Estimate Savings (cont’d)

Using Time Value to Estimate Savings (cont’d) Exhibit 3.2 How Time Value of Money Decisions Fit Within Stephanie Spratt’s Financial Plan (cont’d)