Copyright © 2017, 2014, 2011 Pearson Education, Inc. All Rights Reserved Personal Finance SIXTH EDITION Chapter 3 Applying Time Value Concepts

Copyright © 2017, 2014, 2011 Pearson Education, Inc. All Rights Reserved Chapter Objectives (1 of 2) 3.1 Describe the importance of the time value of money 3.2 Calculate the future value of a dollar amount that you save today 3.3 Calculate the present value of a dollar amount that will be received in the future 3.4 Calculate the future value of an annuity

Copyright © 2017, 2014, 2011 Pearson Education, Inc. All Rights Reserved Chapter Objectives (2 of 2) 3.5 Calculate the present value of an annuity 3.6 Explain how time value can be used to estimate savings 3.7 Explain how time value fits within your financial plan

Copyright © 2017, 2014, 2011 Pearson Education, Inc. All Rights Reserved The Importance of the Time Value of Money (1 of 2) 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

Copyright © 2017, 2014, 2011 Pearson Education, Inc. All Rights Reserved The Importance of the Time Value of Money (2 of 2) 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

Copyright © 2017, 2014, 2011 Pearson Education, Inc. All Rights Reserved Future Value of a Single Dollar Amount (1 of 9) 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

Copyright © 2017, 2014, 2011 Pearson Education, Inc. All Rights Reserved Future Value of a Single Dollar Amount (2 of 9) 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)

Copyright © 2017, 2014, 2011 Pearson Education, Inc. All Rights Reserved Future Value of a Single Dollar Amount (3 of 9) 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

Copyright © 2017, 2014, 2011 Pearson Education, Inc. All Rights Reserved Future Value of a Single Dollar Amount (4 of 9) Using the information in the example and the table, we can determine that, in five years, your money will be worth: $5,000 x = $6,085 The future value can also be determined using a financial calculator with the following inputs; PV = -$5,000; N = 5; I/Y = 4; PMT = 0; CPT FV = $6,083.26* *Note there is a slight rounding error between the two values.

Copyright © 2017, 2014, 2011 Pearson Education, Inc. All Rights Reserved Future Value of a Single Dollar Amount (5 of 9) 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 = $10,955

Copyright © 2017, 2014, 2011 Pearson Education, Inc. All Rights Reserved Future Value of a Single Dollar Amount (6 of 9) 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 = $28,020

Copyright © 2017, 2014, 2011 Pearson Education, Inc. All Rights Reserved Future Value of a Single Dollar Amount (7 of 9)

Copyright © 2017, 2014, 2011 Pearson Education, Inc. All Rights Reserved Future Value of a Single Dollar Amount (8 of 9) 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

Copyright © 2017, 2014, 2011 Pearson Education, Inc. All Rights Reserved Future Value of a Single Dollar Amount (9 of 9) 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! –They fail to recognize how debt can accumulate over a long-term period

Copyright © 2017, 2014, 2011 Pearson Education, Inc. All Rights Reserved Financial Planning Online (1 of 2) Go to the banking section of About.com This Web site provides information on how you can pay your bills online.

Copyright © 2017, 2014, 2011 Pearson Education, Inc. All Rights Reserved Present Value of a Dollar Amount (1 of 5) 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

Copyright © 2017, 2014, 2011 Pearson Education, Inc. All Rights Reserved Present Value of a Dollar Amount (2 of 5) 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

Copyright © 2017, 2014, 2011 Pearson Education, Inc. All Rights Reserved Present Value of a Dollar Amount (3 of 5) 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

Copyright © 2017, 2014, 2011 Pearson Education, Inc. All Rights Reserved Present Value of a Dollar Amount (4 of 5) 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?

Copyright © 2017, 2014, 2011 Pearson Education, Inc. All Rights Reserved Present Value of a Dollar Amount (5 of 5) Using the information in the example and the table we can determine that in order to have $50,000 today: $50,000 x = $35,650 This can also be determined using a financial calculator with these inputs; FV = $50,000; N = 5; I/Y = 7; PMT = 0; CPT PV = $35,649.30* *Note there is a slight rounding error between the two methods.

Copyright © 2017, 2014, 2011 Pearson Education, Inc. All Rights Reserved Future Value of an Annuity (1 of 4) Annuity due: a series of equal cash flow payments that occur at the beginning of each period Ordinary annuity: a series of equal cash flows that occur at the end 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

Copyright © 2017, 2014, 2011 Pearson Education, Inc. All Rights Reserved Future Value of an Annuity (2 of 4) 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

Copyright © 2017, 2014, 2011 Pearson Education, Inc. All Rights Reserved Future Value of an Annuity (3 of 4) 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? Note that this is an ordinary annuity

Copyright © 2017, 2014, 2011 Pearson Education, Inc. All Rights Reserved Future Value of an Annuity (4 of 4) Using our example and the table, we can determine that, at the end of twenty years, you would have: $150,000 x = $6,149,250 This can also be determined using a financial calculator with these inputs; PMT = -$150,000; N = 20; I/Y = 7; PV = 0; CPT FV = $6,149,323.85* *Note there is a slight rounding error between these two methods.

Copyright © 2017, 2014, 2011 Pearson Education, Inc. All Rights Reserved Financial Planning Online (2 of 2) Go to the calculators in the personal finance section of Yahoo.com This Web site provides several tools that, among other things, will help you estimate of the future value of your savings

Copyright © 2017, 2014, 2011 Pearson Education, Inc. All Rights Reserved Present Value of an Annuity (1 of 4) 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

Copyright © 2017, 2014, 2011 Pearson Education, Inc. All Rights Reserved Present Value of an Annuity (2 of 4) 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

Copyright © 2017, 2014, 2011 Pearson Education, Inc. All Rights Reserved Present Value of an Annuity (3 of 4) 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?

Copyright © 2017, 2014, 2011 Pearson Education, Inc. All Rights Reserved Present Value of an Annuity (4 of 4) 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 = $805,486 Since this amount is more than the $700,000 offered, you would reject the offer

Copyright © 2017, 2014, 2011 Pearson Education, Inc. All Rights Reserved Using Time Value to Estimate Savings (1 of 2) 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

Copyright © 2017, 2014, 2011 Pearson Education, Inc. All Rights Reserved Using Time Value to Estimate Savings (2 of 2) 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

Copyright © 2017, 2014, 2011 Pearson Education, Inc. All Rights Reserved 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?

Copyright © 2017, 2014, 2011 Pearson Education, Inc. All Rights Reserved How a Savings Plan Fits Within Stephanie’s Financial Plan In the next two slides you can see how Stephanie Spratt can use the time value concepts to help her devise a savings plan that fits her budget

Copyright © 2017, 2014, 2011 Pearson Education, Inc. All Rights Reserved Using Time Value to Estimate Stephanie’s Savings (1 of 4) EXHIBIT 3.2 How Time Value of Money Decisions Fit Within Stephanie Spratt’s Financial Plan GOALS FOR A SAVINGS PLAN 1. Calculate how much savings I will accumulate by various future points in time. 2. Determine how much I need to save each year to ensure a comfortable living upon retirement. ANALYSIS Present Situation: Expected Savings per Year = $5,000 Expected Annual Rate of Return = 6% or 7% Estimated Amount of Savings to Be Accumulated: Savings Accumulated over: Assume Annual Return = 6% Assume Annual Return = 7% 5 years $28,185 $28, years 65,905 69, years 116, , years 183, , years 274, , years 395, ,305

Copyright © 2017, 2014, 2011 Pearson Education, Inc. All Rights Reserved Using Time Value to Estimate Stephanie’s Savings (2 of 4) EXHIBIT 3.2 How Time Value of Money Decisions Fit Within Stephanie Spratt’s Financial Plan Annual Savings Needed to Achieve a Specific Savings Goal: Savings Goal = $80,000 in 10 years, $200,000 in 20 years, $600,000 in 30 years Expected Annual Rate of Return = 6% or 7% Savings GoalAssume Annual Return = 6%Assume Annual Return = 7% $80,000 in 10 years $6,069 $5,790 $200,000 in 20 years 5,437 4,879 $600,000 in 30 years 7,589 6,352 To achieve a savings goal of $80,000 in 10 years, I would need to save $6,069 per year (assuming an annual return of 6% on my money). To achieve a goal of $200,000 in 20 years, I would need to save $5,437 per year (assuming a 6% annual return).

Copyright © 2017, 2014, 2011 Pearson Education, Inc. All Rights Reserved Using Time Value to Estimate Stephanie’s Savings (3 of 4) EXHIBIT 3.2 How Time Value of Money Decisions Fit Within Stephanie Spratt’s Financial Plan DECISIONS Decision on My Savings Goal in the Future: If I can save $5,000 a year, I should accumulate $28,185 in 5 years and $65,905 in 10 years. These estimates are based on an assumed annual return of 6%. If my annual return is higher, I should accumulate even more than that. The estimated savings for longer time periods are much higher. A comparison of the third column with the second column in the table shows how much more savings I could accumulate if I can earn an annual return of 7% instead of 6%.

Copyright © 2017, 2014, 2011 Pearson Education, Inc. All Rights Reserved Using Time Value to Estimate Stephanie’s Savings (4 of 4) EXHIBIT 3.2 How Time Value of Money Decisions Fit Within Stephanie Spratt’s Financial Plan Decision on My Savings Goal per Year: Although my initial plan was to develop a budget for saving about $5,000 a year, I will try to save more so that I can achieve my savings goals. I will use a minimum savings goal of $5,000, but will try to save about $6,000 per year.