Pesonal finance 6th madura chapter 03 applying time value concepts

Personal Finance SIXTH EDITION Chapter 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 percent – The present value of money (PV) is the amount invested, or $5,000 – Find the interest rate of 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 1.217 = $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 years? Assuming the interest rate is still 4%: $5,000 x 2.191 = $10,955 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 percent annually How much will be in your account at the end of 20 years, assuming you 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 40.995 = $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 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 9.823 = $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 Calculate how much savings I will accumulate by various future points in time 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 Assume Annual Return = 6% Return = 7% years $28,185 $28,753 10 years 65,905 69,080 15 years 116,380 125,645 20 years 183,930 204,975 25 years 274,325 316,245 30 years 395,290 472,305 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 Goal Assume 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 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 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. .. 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. .. 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