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Personal Finance: An Integrated Planning Approach

Personal Finance: An Integrated Planning Approach. Winger and Frasca Chapter 2 The Time Value of Money: All Dollars Are Not Created Equal. Introduction. “All dollars are not created equal” refers to a concept known as the time value of money.

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Personal Finance: An Integrated Planning Approach

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  1. Personal Finance:An Integrated Planning Approach Winger and Frasca Chapter 2 The Time Value of Money: All Dollars Are Not Created Equal

  2. Introduction • “All dollars are not created equal” refers to a concept known as the time value of money. • The time value of money concept recognizes that money received/paid at some point in the future is not as valuable as money received/paid today. There is an opportunity cost to waiting for money. • A dollar received today can be invested to earn interest and thus will grow to a larger amount. • On the other hand, money paid out at a later date is more desirable than paying it now.

  3. Introduction (continued) • Time value of money techniques facilitate planning for future events. • Individuals desire to invest for many financial goals such as retirement, children’s education, etc. • The expenditures associated with these goals will occur in the future and will be impacted by inflation. • The amount invested will be impacted by the state of the economy, investment choices, etc. • With the use of the time value of money techniques, we will be able to estimate our future funds needs.

  4. Chapter Objectives • To gain a general understanding that monies received or paid out at different points in time have different values and that these values can change dramatically depending on interest rate levels and the points in time when they are received or paid • To understand the process of compounding and to be able to compute a future value of a single payment or of an annuity • To understand the process of discounting and to be able to compute the present value of a single payment or of an annuity

  5. Chapter Objectives (continued) • To be able to find approximate values for unknown interest rates or unknown holding periods when the values for other financial variables are known • To recognize the importance of planning in the effort to achieve future goals • To be able to compute a required annual savings amount to meet future goals • To be able to construct a savings plan designed to show how savings will grow over time and be used to meet future goals

  6. Topic Outline • Compounding (Finding Future Values) • Discounting (Finding Present Values) • Goal Planning for the Steeles

  7. COMPOUNDING (FINDING FUTURE VALUES) • Compounding refers to the process of accumulating value over time. In other words, investing money to earn interest will facilitate the growth of our investment. • A single amount (or payment) can accumulate value over time. • A series of equal payments (annuity) can accumulate value over time. • The amount that the investment grows to is referred to as the future value. It includes both the amount invested as well as the interest earned.

  8. Compounding Example: Suppose you invest $1,000 today, hold the investment for 3 years, and earn 8% each year. How much will you accumulate at the end of 3 years (the future value)? __________________________________________ Year Beginning-of- Interest End-of-Year Year Amount Earned Amount 1 $1,000 $80 $1,080 2 1,080 86.40 1,166.40 3 1,166.40 93.31 Answer $1,259.71

  9. Compound versus Simple Interest • Compound interest assumes that the interest on our initial investment also earns interest—that the investment accumulates by earning interest on interest. • In the previous example, the interest in year 2 is greater than the interest in year 1 due to compound interest. • Simple interest, on the other hand, does not assume that interest is earned on interest. • If the previous example had assumed simple interest, the interest earned in years 1, 2, and 3 would only be $80 each year. Therefore, the future value would be $1,240 (not $1,259.71).

  10. The Importance of Additional Yield and Time • The future value is impacted significantly by both time and yield as can be seen in Figure 2.1 on the next slide • The future value of an investment will be significantly greater with a longer investment period. For example: • If a 22-year old begins saving for retirement, he will have to save a lot less each year than someone who waits until the age of 40. From an investment perspective, the 22-year old has time on his side. • The same is true for yield. The future value of an investment for someone who is willing to assume a little more risk and earns 10% rather than 8% will be significantly greater.

  11. Future Value Calculations • Future value calculations can be done with any of the following: • A financial calculator • The financial functions in Excel • Financial calculators on the Internet • Use of financial formulas and a calculator • Use of financial tables • To facilitate calculations, tables have been created that assume an initial investment of $1. These tables then specify various time periods and interest rates. Detailed tables appear in the appendix of many financial textbooks.

  12. Sample of a Future Value Table that assumes an Initial Investment of $1 Number of Interest Rate ( i ) Periods (n) 6% 8% 10% 1 1.0600 1.0800 1.1000 3 1.1910 1.25971.3310 10 1.79082.15892.5937 20 3.2071 4.6610 6.7275 30 5.7435 10.0620 17.4490 40 10.2850 21.7240 45.2590

  13. Future Value Example: Use FV Table • The previous future value table can be used to find the FV of any amount. • Simply multiply the investment by the number from the table. • Example 1: What is the future value of $500 invested at 6% for 10 years? $895.40 • Answer: Find 6% and 10 years on the table (1.7908) • Multiply $500 × 1.7908 = $895.40 • Example 2: What is the future value of $4,000 invested at 8% for 30 years? $40,248 • Answer: $4,000 × 10.062 = $40,248

  14. The Rule of 72 • A technique that is quite popular in estimating the time that it takes for an investment to double is called the rule of 72 • If we know the interest rate for an investment, we can use the rule of 72 to estimate how long it will take for the money to double • Doubling Time (DT) = 72/interest rate • Example: if the interest rate percent is 12 • DT = 72/12 = 6 years • If an investment earns 12% per year, it will double in value in 6 years (How could you verify this?)

  15. What is an Annuity? • An annuity is simply a series of equal payments. • Examples of annuities can be found everywhere: rent payments, mortgage payments, car payments, etc. • From an investment perspective, bonds will often involve interest payments that are annuities. • There are two types of annuities: • An ordinary annuity (OA) assumes the payments occur at the end of the period. Most future-value-of-$1-annuity tables show ordinary annuities. • An annuity due (AD) assumes the payments occur at the beginning of the period.

  16. Example: FV of an Ordinary Annuity Assume an investment of $3,500 is made at the end of each of the next 3 years and earns 6%. What is the future value of this investment at the end of year 3? __________________________________________ First investment of $3,500 earns interest for 2 years. (Remember that an ordinary annuity assumes payments are made at the end of the year.) Second investment of $3,500 earns interest for 1 year. Third investment of $3,500 earns no interest.

  17. Example (Continued) The following is a timeline showing the investments at each point in time. We want to find the future value at year 3. Now 1 2 3 $3,500 $3,500 $3,500 FV? - First payment: $3,500 × (1.06) × (1.06) = $3,932.60 - Second payment: $3,500 × (1.06) = $3,710 - Third payment: $3,500 × (1.00) = $3,500 - Total value (FV): $3,932.60 + $3,710 + $3,500 = $11,142.60

  18. Sample of a Future Value Table that Assumes Equal Periodic Investments of $1 Number of Interest Rate ( i ) Periods (n) 6% 8% 10% 1 1.0000 1.0000 1.0000 3 3.1836 3.24643.3100 10 13.1800 14.4860 15.9370 20 36.7850 45.7620 57.2750 30 79.0580 113.2800 164.4900 40 154.7600 259.0500 442.5900

  19. Converting an Ordinary Annuity (OA) Into an Annuity Due (AD) • The conversion formula is: FV(AD) = FV(OA) × (1 + i ) • This formula accounts for the fact that each payment earns interest for one extra period. • In the previous example, we calculated the FV of an OA of $11,142.60. If payments were made at the beginning of the period, then FV(AD) = $11,142.60 × (1.06) =$11,811.16

  20. DISCOUNTING (FINDING PRESENT VALUES) • In compounding, we are finding future values given an investment amount. This single payment or investment is called the present value. • As with compounding, finding present values is useful in setting financial goals. • As with compounding, we can find the present value of: • A single payment • An annuity (ordinary and due)

  21. Sample of a Present Value Table That Assumes a Future Value of $1 Number of Interest Rate ( i ) Periods (n) 6% 8% 10% 1 0.9434 0.9259 0.9091 3 0.8396 0.79380.7513 10 0.5584 0.4632 0.3855 20 0.3118 0.2145 0.1486 30 0.1741 0.0994 0.0573 40 0.0972 0.0460 0.0221

  22. Example: Finding Present Values • The easiest method is to use the PV tables. • Example: What is the present value of $1,500 to be received at the end of 10 years assuming an 8% discount rate? • Find the PV of $1 for n = 10 and i = 8%; it is .4632 • Multiply .4632 by $1,500 to find the PV of $694.80 • $694.80 is the present value of $1,500 to be received in 10 years assuming 8%. Another way to think of this, $694.80 is the amount that should be invested today in order to have $1,500 in 10 years assuming 8% interest.

  23. Sample of a Present Value Table That Assumes Equal Periodic Investments of $1 Number of Interest Rate ( i ) Periods (n) 6% 8% 10% 1 0.9434 0.9259 0.9091 3 2.6730 2.5571 2.4869 10 7.3601 6.7101 6.1446 20 11.4699 9.8181 8.5136 30 13.7648 11.2578 9.4268 40 15.0463 11.9246 9.7791

  24. Example: Finding Present Values of an Annuity • Once again, we will use the PV table. • Example: What is the present value of $500 to be received at the end of each of the next 20 years, assuming a 10% interest rate (ordinary annuity)? • Find the PV of $1 annuity for n = 20 and i = 10% ; it is 8.5136 • Multiply 8.5136 by $500 = $4,256.80 • If payments were made at the beginning of the period (annuity due): • PV(AD) = PV(OA) × (1 + i) = $4256.80 × 1.10 = $4,682.48

  25. More Applications of Future and Present Values • For all of the problems that we have solved, we have assumed an interest rate and a number of periods. • It is possible to find either the interest rate or the number of periods if both the present and future values are known. • If we express the relationships between PV and FV: • FV = (FV of $1 factor: n, i) × PV

  26. More Applications of Future and Present Values (Example) • If we want to have $100,000 in 30 years but we only have $10,000 to invest now, what interest rate would we need to earn to make this goal possible? • FV = (FV of $1 factor: n, i) × PV • 100,000 = (FV of $1 factor: n, i) × 10,000 • Solve for the unknown: (FV of $1 factor: n, i) = 10 • Look at the table for 30 years. The interest rate of 8% has a factor of 10.0620; therefore, i = 8%

  27. Goal Planning • Time value of money techniques are useful for estimating required funds to meet future goals. • The first step in planning is to identify specific goals. • What is the particular goal? • When do you plan to achieve the goal? • How much will need to be saved currently or each year? • Inflation must be considered since most goals are long-term. • Determine how much must be saved each year to achieve these goals.

  28. Discussion Questions • What is meant by the term future value? • What is the relationship between future values and present values? • How is an annuity different from a single payment? • How can the concepts covered in this chapter help an individual to achieve future financial goals? • What are some simple steps that individuals could take to begin increasing their annual savings?

  29. NEXT:Chapter 3Financial Statements and Budgets

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