# If I offered to give you \$100, you would probably

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 File C5-96 June Understanding the Time Value of Money If I offered to give you \$100, you would probably say yes. Then, if I asked you if you wanted the \$100 today or one year from today, you would probably say today. This is a rational decision because you could spend the money now and get the satisfaction from your purchase now rather than waiting a year. Even if you decided to save the money, you would rather receive it today because you could deposit the money in a bank and earn interest on it over the coming year. So there is a time value to money. Next, let s discuss the size of the time value of money. If I offered you \$100 today or \$105 dollars a year from now, which would you take? What if I offered you \$110, \$115, or \$120 a year from today? Which would you take? The time value of money is the value at which you are indifferent to receiving the money today or one year from today. If the amount is \$115, then the time value of money over the coming year is \$15. If the amount is \$110, then the time value is \$10. In other words, if you will receive an additional \$10 a year from today, you are indifferent to receiving the money today or a year from today. When discussing the time value of money, it is important to understand the concept of a time line. Time lines are used to identify when cash inflows and outflows will occur so that an accurate financial assessment can be made. A time line is shown in the next column with five time periods. The time periods may represent years, months, days, or any length of time so long as each time period is the same length of time. Let s assume they represent years. The zero tick mark represents today. The one tick mark represents a year from today. Any time during the next 365 days is represented on the time line from the zero tick mark to the one tick mark. At the one tick mark, a full year has been completed. When the second tick mark is reached, two full years have been completed, and it represents two years from today. You can move on to the five tick mark, which represents five years from today. Time Line Because money has a time value, it gives rise to the concept of interest. Interest can be thought of as rent for the use of money. If you want to use my money for a year, I will require that you pay me a fee for the use of the money. The size of the rental rate or user fee is the interest rate. If the interest rate is 10 percent, then the rental rate for using \$100 for the year is \$10. Compounding Compounding is the impact of the time value of money (e.g., interest rate) over multiple periods into the future, where the interest is added to the original amount. For example, if you have \$1,000 and invest it at 10 percent per year for 20 years, its value after 20 years is \$6,727. This assumes that you leave the interest amount earned each year with the investment rather than withdrawing it. If you remove the interest amount every year, at the end of 20 years the \$1,000 will still be worth only \$1,000. But if you leave it with the investment, the size of the investment will grow exponentially. This is because you are earning interest on your interest. This process is called compounding. And, as the amount grows, the size of the interest amount will also grow. As shown in Table 1, during the first year of a \$1,000 investment, you will earn \$100 of interest if the interest rate is 10 percent. When the \$100 interest is added to the \$1,000 investment it becomes \$1,100 and 10 percent of \$1,100 in year two is \$110. This process continues until year 20, when the amount of interest is 10 percent of \$6,116 or \$ The amount of the investment is \$6,727 at the end of 20 years. The impact of compounding outlined in Table 1 is Don Hofstrand retired extension agriculture specialist

2 Page 2 File C5-96 shown graphically in Figure 1. The increase in the size of the cash amount over the 20-year period does not increase in a straight line but rather exponentially. Because the slope of the line increases over time it means that each year the size of the increase is greater than the previous year. If the time period is extended to 30 or 40 years, the slope of the line would continue to increase. Over the long-term, compounding is a very powerful financial concept. The effect of compounding is also greatly impacted by the size of the interest rate. Essentially, the larger the interest rate the greater the impact of compounding. In addition to the compounding impact of a 10 percent interest rate, Figure 2 shows the impact of a 15 percent interest rate (5 percent higher rate) and 5 percent (5 percent lower rate). Over the 20-year period, the 15 percent rate yields almost \$10,000 more than the 10 percent rate, while the 5 percent rate results in about \$4,000 less. By examining the last 10 years of the 20-year period you can see that increasing the number of time periods and the size of the interest rate greatly increases the power of compounding. Table 1. Compounding computation of \$1,000 over 20 years at an annual interest rate of 10 percent. Year Amount Computation 0 \$1,000 1 \$1,100 \$1,000 x 10% = \$100 + \$1,000 = \$1,100 2 \$1,210 \$1,100 x 10% = \$110 + \$1,100 = \$1,210 3 \$1,331 \$1,210 x 10% = \$121 + \$1,210 = \$1,331 4 \$1,464 \$1,331 x 10% = \$133 + \$1,331 = \$1,464 5 \$1,611 \$1,464 x 10% = \$146 + \$1,464 = \$1,611 6 \$1,772 \$1,611 x 10% = \$161 + \$1,611 = \$1,772 7 \$1,949 \$1,772 x 10% = \$177 + \$1,772 = \$1,949 8 \$2,144 \$1,949 x 10% = \$195 + \$1,949 = \$2,144 9 \$2,358 \$2,144 x 10% = \$214 + \$2,144 = \$2, \$2,594 \$2,358 x 10% = \$236 + \$2,358 = \$2, \$2,853 \$2,594 x 10% = \$259 + \$2,594 = \$2, \$3,138 \$2,853 x 10% = \$285 + \$2,853 = \$3, \$3,452 \$3,138 x 10% = \$314 + \$3,138 = \$3, \$3,797 \$3,452 x 10% = \$345 + \$3,452 = \$3, \$4,177 \$3,797 x 10% = \$380 + \$3,797 = \$4, \$4,959 \$4,177 x 10% = \$418 + \$4,177 = \$4, \$5,054 \$4,595 x 10% = \$456 + \$4,595 = \$5, \$5,560 \$5,054 x 10% = \$505 + \$5,054 = \$5, \$6,116 \$5,560 x 10% = \$556 + \$5,560 = \$6, \$6,727 \$6,116 x 10% = \$612 + \$6,116 = \$6,727

3 File C5-96 Page 3 Table 2. Compounding computation of \$1,000 over 20 years at an annual interest rate of 10 percent. Year Amount Computation 0 \$1,000 1 \$1,100 \$1,000 x 1.10 = \$1,100 2 \$1,210 \$1,100 x 1.10 = \$1,210 3 \$1,331 \$1,210 x 1.10 = \$1,331 4 \$1,464 \$1,331 x 1.10 = \$1,464 5 \$1,611 \$1,464 x 1.10 = \$1,611 6 \$1,772 \$1,611 x 1.10 = \$1,772 7 \$1,949 \$1,772 x 1.10 = \$1,949 8 \$2,144 \$1,949 x 1.10 = \$2,144 9 \$2,358 \$2,144 x 1.10 = \$2, \$2,594 \$2,358 x 1.10 = \$2, \$2,853 \$2,594 x 1.10 = \$2, \$3,138 \$2,853 x 1.10 = \$3, \$3,452 \$3,138 x 1.10 = \$3, \$3,797 \$3,452 x 1.10 = \$3, \$4,177 \$3,797 x 1.10 = \$4, \$4,595 \$4,177 x 1.10 = \$4, \$5,054 \$4,595 x 1.10 = \$5, \$5,560 \$5,054 x 1.10 = \$5, \$6,116 \$5,560 x 1.10 = \$6, \$6,727 \$6,116 x 1.10 = \$6,727 Table 2 shows the same compounding impact as Table 1 but with a different computational process. An easier way to compute the amount of compound interest is to multiply the investment by one plus the interest rate. Multiplying by one maintains the cash amount at its current level and.10 adds the interest amount to the original cash amount. For example, multiplying \$1,000 by 1.10 yields \$1,100 at the end of the year, which is the \$1,000 original amount plus the interest amount of \$100 (\$1,000 x.10 = \$100). Another dimension of the impact of compounding is the number of compounding periods within a year. Table 3 shows the impact of 10 percent annual compounding of \$1,000 over 10 years. It also shows the same \$1,000 compounded semiannually over the 10-year period. Semiannual compounding means a 10 percent annual interest rate is converted to a 5 percent interest rate and charged for half of the year. The interest amount is then added to the original amount, and the interest during the last half of the year is 5 percent of this larger amount. As shown in Table 3, semiannual compounding will result in 20 compounding periods over a 10-year period, while annual compounding results in only 10 compounding period. A shorter compounding period means a larger number of compounding periods over a given time period and

4 Page 4 File C5-96 Table 3. A comparison of \$1,000 compounding annually versus semiannually (20 years, 10 percent interest) Compounding Annually Compounding Semiannually Year Amount Computation Amount Computation 0 \$1,000 \$1, \$1,050 \$1,000 x 1.05 = \$1,050 1 \$1,100 \$1,000 x 1.10 = \$1,100 \$1,103 \$1,050 x 1.05 = \$1, \$1,158 \$1,103 x 1.05 = \$1,158 2 \$1,210 \$1,100 x 1.10 = \$1,210 \$1,216 \$1,158 x 1.05 = \$1, \$1,276 \$1,216 x 1.05 = \$1,276 3 \$1,331 \$1,210 x 1.10 = \$1,331 \$1,340 \$1,276 x 1.05 = \$1, \$1,407 \$1,276 x 1.05 = \$1,407 4 \$1,464 \$1,331 x 1.10 = \$1,464 \$1,477 \$1,407 x 1.05 = \$1, \$1,551 \$1,477 x 1.05 = \$1,551 5 \$1,611 \$1,464 x 1.10 = \$1,611 \$1,629 \$1,551 x 1.05 = \$1, \$1,710 \$1,629 x 1.05 = \$1,710 6 \$1,772 \$1,611 x 1.10 = \$1,772 \$1,796 \$1,710 x 1.05 = \$1, \$1,886 \$1,710 x 1.05 = \$1,886 7 \$1,949 \$1,772 x 1.10 = \$1,949 \$1,980 \$1,886 x 1.05 = \$1, \$2,079 \$1,980 x 1.05 = \$2,079 8 \$2,144 \$1,949 x 1.10 = \$2,144 \$2,183 \$2,079 x 1.05 = \$2, \$2,292 \$2,183 x 1.05 = \$2,292 9 \$2,358 \$2,144 x 1.10 = \$2,358 \$2,407 \$2,292 x 1.05 = \$2, \$2,527 \$2,407 x 1.05 = \$2, \$2,594 \$2,358 x 1.10 = \$2,594 \$2,653 \$2,527 x 1.05 = \$2,653 a greater compounding impact. If the compounding period is shortened to monthly or daily periods, the compounding impact will be even greater. Discounting Although the concept of compounding is straight forward and relatively easy to understand, the concept of discounting is more difficult. However, the important fact to remember is that discounting is the opposite of compounding. As shown below, if we start with a future value of \$6,727 at the end of 20 years in the future and discount it back to today at an interest rate of 10 percent, the present value is \$1,000

5 File C5-96 Page 5 Table 4. Discounting computation of \$6,727 over 20 years at an annual discount rate of 10 percent. Year Amount Computation 20 \$6, \$6,116 \$6,727 x.91 = \$6, \$5,560 \$6,115 x.91 = \$5, \$5,054 \$5,560 x.91 = \$5, \$4,595 \$5,054 x.91 = \$4, \$4,177 \$4,595 x.91 = \$4, \$3,797 \$4,117 x.91 = \$3, \$3,452 \$3,797 x.91 = \$3, \$3,138 \$3,452 x.91 = \$3, \$2,853 \$3,138 x.91 = \$2, \$2,594 \$2,853 x.91 = \$2,594 9 \$2,358 \$2,594 x.91 = \$2,358 8 \$2,144 \$2,358 x.91 = \$2,144 7 \$1,949 \$2,144 x.91 = \$1,949 6 \$1,772 \$1,949 x.91 = \$1,772 5 \$1,611 \$1,772 x.91 = \$1,611 4 \$1,464 \$1,661 x.91 = \$1,464 3 \$1,331 \$1,464 x.91 = \$1,331 2 \$1,210 \$1,331 x.91 = \$1,210 1 \$1,100 \$1,210 x.91 = \$1,100 0 \$1,000 \$1,100 x.91 = \$1,000 As shown in Table 2, the compounding factor of annually compounding at an interest rate of 10 percent is 1.10 or 1.10/1.00. If discounting is the opposite of compounding, then the discounting factor is 1.00 / 1.10 = or.91. As shown in Table 4, the discounted amount becomes smaller as the time period moves closer to the current time period. When we compounded \$1,000 over 20 years at a 10 percent interest rate, the value at the end of the period is \$6,727 (Table 2). When we discount \$6,727 over 20 years at a 10 percent interest rate, the present value or value today is \$1,000. The discounting impact is shown in Figure 3. Note that the curve is the opposite of the compounding curve in Figure 1. The impact of discounting using interest rates of 5 percent, 10 percent, and 15 percent is shown in Figure 4. The 15 percent interest rate results in a larger discounting impact than the 10 percent rate, just as the 15 percent interest rate results in a larger compounding impact as shown in Figure 2.

6 Page 6 File C5-96 Discounting Example An example of discounting is to determine the present value of a bond. A bond provides a future stream of income. It provides a cash return at a future time period, often called the value at maturity. It may also provide a stream of annual cash flows until the maturity of the bond. Table 5 shows an example of a \$10,000 bond with a 10-year maturity. In other Table year bond with 10 percent annual annuity and \$10,000 payout at the end of 10 years. Year Annuity Value at Maturity Total 0 1 \$1,000 \$1,000 2 \$1,000 \$1,000 3 \$1,000 \$1,000 4 \$1,000 \$1,000 5 \$1,000 \$1,000 6 \$1,000 \$1,000 7 \$1,000 \$1,000 8 \$1,000 \$1,000 9 \$1,000 \$1, \$1,000 \$10,000 \$11,000 Total \$10,000 \$10,000 \$20,000 words, the bond will yield \$10,000 at maturity, which is received at the end of 10 years. The bond also has an annual annuity (an annuity is a stream of equal cash payments at regular time intervals for a fixed period of time) equity to 10 percent of the value at maturity. So, the bond yields 10 \$1,000 (10% x \$10,000) annual payments over the 10-year period. Adding together the 10 \$1,000 payments plus the \$10,000 value at maturity, the future cash return from the bond is \$20,000. To compute the current value of the bond, we must discount the future cash flows back to the time when the bond is purchased. To do this we must select an interest rate (called the discount rate when we are discounting). In Table 6, we have calculated the present value of the bond using discount rates of 5 percent, 10 percent, and 15 percent. First, let s examine the computation using a 5 percent rate. Each of the \$1,000 annuity payments is discounted to the present value. Note that the one year \$1,000 annuity payment has a present value of \$952 and the 10-year payment has a present value of \$614. This is because the first-year payment is only discounted one time and the tenth-year payment is discounted 10 times over 10 years. The present value of all 10 annuity payments is \$7,722. The present value of the

7 File C5-96 Page 7 \$10,000 at maturity (after 10 years) is \$6,139. Note that the present value of the \$10,000 of annual annuity payments is greater than the \$10,000 payment received at maturity because most of the annuity payments are discounted over time periods less than 10 years. The total present value of the annuity and the value at maturity is \$13,861. So, the \$20,000 of future cash payments has a value at the time of purchase of \$13,861. Looking at it from a different perspective, if you paid \$13,861 for this bond you would receive a 5 percent annual rate of return (called the internal rate of return) over the 10-year period. Table 6. Computing the Present Value of the Bond Shown in Table 5. Discount Rate = 5 Percent Year Annuity Value at Maturity Total 0 1 \$952 \$952 2 \$907 \$907 3 \$864 \$864 4 \$823 \$823 5 \$784 \$784 6 \$746 \$746 7 \$711 \$711 8 \$677 \$677 9 \$645 \$ \$614 \$6,139 \$6,753 Total \$7,722 \$6,139 \$13,861 If we increase the discount rate from 5 percent to 10 percent, the discounting power becomes greater. The present value of the bond drops from \$13,861 to \$10,000. In other words, if you want a 10 percent rate of return you can only pay \$10,000 for the bond that will generate \$20,000 in future cash payments. Note that the value at maturity dropped over \$2,000 from \$6,139 to \$3,855. Conversely, the value of the annuity dropped from \$7,722 to \$6,145, a reduction of about \$1,600. Year Discount Rate = 10 Percent Annuity Value at Maturity Total 0 1 \$909 \$909 2 \$826 \$826 3 \$751 \$751 4 \$683 \$683 5 \$621 \$621 6 \$564 \$564 7 \$513 \$513 8 \$467 \$467 9 \$424 \$ \$386 \$3,855 \$4,241 Total \$6,145 \$3,855 \$10,000 If we increase the discount rate to 15 percent, the discounting power becomes even greater. The present value of the bond drops to \$7,491. In other words, if you want a 15 percent rate of return you can only pay \$7,491 for the bond that will generate \$20,000 in future cash payments. Note that the value at maturity dropped from \$6,139 (5 percent) to \$3,855 (10 percent) to \$2,472 (15 percent). The value of the annuity dropped in smaller increments from \$7,722 (5 percent) to \$6,145 (10 percent) to \$5,019 (15 percent). Year Discount Rate = 15 Percent Annuity Value at Maturity Total 0 1 \$870 \$870 2 \$756 \$756 3 \$658 \$658 4 \$572 \$572 5 \$497 \$497 6 \$432 \$432 7 \$376 \$376 8 \$327 \$327 9 \$284 \$ \$247 \$2,472 \$2,719 Total \$5,019 \$2,472 \$7,491 A bond is a simple example of computing the present value of an asset with an annual cash income stream and a terminal value at the end of the time period. This methodology can be used to analyze any investment that has an annual cash payment and a terminal or salvage value at the end of the time period.

8 Page 8 File C5-96 Perpetuity A perpetuity is similar to an annuity except that an annuity has a limited life and a perpetuity is an even payment that has an unlimited life. The computation of a perpetuity is straight forward. The present value of a perpetuity is the payment divided by the discount rate. Present Value = Perpetuity Payment Discount Rate Payment = \$10,000 Discount Rate = 10 percent Present Value =? \$10,000 = \$100,000 10% Time Value of Money Formulas There are mathematical formulas for compounding and discounting that simplify the methodology. At right are the formulas, in which: PV represents the present value at the beginning of the time period. FV represents the future value at the end of the time period. N or Nper represents the number of compounding or discounting periods. It can represent a specific number of years, months, days, or other predetermined time periods. Rate or i represents the interest rate for the time period specified. For example, if N represents a specified number of years, then the interest rate represents an annual interest rate. If N represents a specific number of days, then the interest rate represents a daily interest rate. If we are computing the compounded value of a current amount of money into the future, we will use the following formula. The future value FV that we are solving for is the current amount of money PV multiplied by one plus the interest rate to the power of the number of compounding periods. We are solving for the future compounded value (FV), in which the present value (PV) is \$1,000, the annual interest rate (Rate) is 10 percent, and the number of time periods (Nper) is 20 years. This results in \$1,000 multiplied by and a future value of \$6,727. Note that this is the same result as shown in Tables 1 and 2. FV = PV (1 + Rate) Nper FV = \$1,000 (1 +.10) 20 FV = \$1,000 x FV = \$1,000 x FV = \$6,727 To compute the discounted value of an amount of money to be received in the future, we use the same formula but solve for the present value rather than the future value. To adjust our formula, we divided both sides by (1 + Rate) Nper and the following formula emerges. PV = FV (1 + Rate) Nper PV = \$6,727 (1 +.10) 20 PV = \$6, PV = \$6, PV = \$1,000 The present value (PV) of a future value (FV) of \$6,727 discounted over 20 years (Npers) at an annual discount interest rate (Rate) of 10 percent is \$1,000, the same as shown in Table 4.

9 File C5-96 Page 9 Time Value of Money Computation A financial calculator or an electronic spreadsheet on a personal computer is a useful tool for making time value of money computations. For compounding computations, you enter the present value, interest rate, and the number of time periods, and the calculator or personal computer will compute the future value. The future value for the example below is \$6,727, the same as the future value shown in Tables 1 and 2. Present Value (PV) = \$1,000 Interest Rate (Rate) = 10 percent Number of Periods (Nper) = 20 years Future Value (FV) =? Likewise, for discounting computations you enter the future value, interest rate, and the number of time periods, and the calculator or personal computer will compute the present value. The present value for the example below is \$1,000, the same as the present value shown in Table 4. If an annuity is involved, you can use the payment function (PMT). In the example below, the present value is \$10,000, the same as the present value of the bond example in Table 6. Future Value (FV) = \$10,000 Discount Interest Rate (Rate) = 10 percent Time Period (Nper) = 10 years Annuity (PMT) = \$1,000 Present Value (PV) =? By using a financial calculator or personal computer, you can compute any of the values in the examples above as long as you know the other values. For example, you can compute the interest rate if you know the future value, present value, and number of time periods. You can compute the number of time periods if you know the present value, future value, and interest rate. The same is true if an annuity is involved. Future Value (FV) = \$6,727 Discount Rate (Rate) = 10 percent Time Period (Nper) = 20 years Present Value (PV) =?... and justice for all The U.S. Department of Agriculture (USDA) prohibits discrimination in all its programs and activities on the basis of race, color, national origin, gender, religion, age, disability, political beliefs, sexual orientation, and marital or family status. (Not all prohibited bases apply to all programs.) Many materials can be made available in alternative formats for ADA clients. To file a complaint of discrimination, write USDA, Office of Civil Rights, Room 326-W, Whitten Building, 14th and Independence Avenue, SW, Washington, DC or call Issued in furtherance of Cooperative Extension work, Acts of May 8 and November 30, 1914, in cooperation with the U.S. Department of Agriculture. Cathann A. Kress, director, Cooperative Extension Service, Iowa State University of Science and Technology, Ames, Iowa.

### Capital Budgeting and Decision Making Capital budgeting can be used to analyze a

File C5-242 September 2013 www.extension.iastate.edu/agdm Capital Budgeting and Decision Making Capital budgeting can be used to analyze a wide variety of investments in capital assets (assets lasting

### Capital investments are long-term investments

Capital Budgeting Basics File C5-240 August 2013 www.extension.iastate.edu/agdm Capital investments are long-term investments in which the assets involved have useful lives of multiple years. For example,

### Farm families have traditionally used the single entry (often referred to as cash) method of accounting

File C6-33 July 2009 www.extension.iastate.edu/agdm Understanding Double Entry Accounting Farm families have traditionally used the single entry (often referred to as cash) method of accounting for their

### Price options for grain, when used in conjunction

File A2-67 December 2009 www.extension.iastate.edu/agdm Options Tools to Reduce Risk options for, when used in conjunction with cash sales, provide a set of marketing tools for farmers. Two of these tools

### The basic concepts of grain price options are

Grain Price Options Basics File A2-66 December 2009 www.extension.iastate.edu/agdm The basic concepts of grain price options are discussed below. Methods of using grain price options to market grain are

### Chapter 5 Time Value of Money 2: Analyzing Annuity Cash Flows

1. Future Value of Multiple Cash Flows 2. Future Value of an Annuity 3. Present Value of an Annuity 4. Perpetuities 5. Other Compounding Periods 6. Effective Annual Rates (EAR) 7. Amortized Loans Chapter

### Chapter 6. Learning Objectives Principles Used in This Chapter 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams

Chapter 6 Learning Objectives Principles Used in This Chapter 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams 1. Distinguish between an ordinary annuity and an annuity due, and calculate present

Twelve Steps to Ag Decision Maker Cash Flow Budgeting File C3-15 How much financing will your farm business require this year? When will money be needed and from where will it come? A little advance planning

### The financial position and performance of a farm

Farm Financial Ag Decision Maker Statements File C3-56 The financial position and performance of a farm business can be summarized by four important financial statements. The relationship of these statements

Your Farm Ag Decision Maker Income Statement File C3-25 How much did your farm business earn last year? Was it profitabile? There are many ways to answer these questions. A farm income statement (sometimes

### Chapter 6. Discounted Cash Flow Valuation. Key Concepts and Skills. Multiple Cash Flows Future Value Example 6.1. Answer 6.1

Chapter 6 Key Concepts and Skills Be able to compute: the future value of multiple cash flows the present value of multiple cash flows the future and present value of annuities Discounted Cash Flow Valuation

### Chapter The Time Value of Money

Chapter The Time Value of Money PPT 9-2 Chapter 9 - Outline Time Value of Money Future Value and Present Value Annuities Time-Value-of-Money Formulas Adjusting for Non-Annual Compounding Compound Interest

### rate nper pmt pv Interest Number of Payment Present Future Rate Periods Amount Value Value 12.00% 1 0 \$100.00 \$112.00

In Excel language, if the initial cash flow is an inflow (positive), then the future value must be an outflow (negative). Therefore you must add a negative sign before the FV (and PV) function. The inputs

### Accounting Building Business Skills. Interest. Interest. Paul D. Kimmel. Appendix B: Time Value of Money

Accounting Building Business Skills Paul D. Kimmel Appendix B: Time Value of Money PowerPoint presentation by Kate Wynn-Williams University of Otago, Dunedin 2003 John Wiley & Sons Australia, Ltd 1 Interest

### Important Financial Concepts

Part 2 Important Financial Concepts Chapter 4 Time Value of Money Chapter 5 Risk and Return Chapter 6 Interest Rates and Bond Valuation Chapter 7 Stock Valuation 130 LG1 LG2 LG3 LG4 LG5 LG6 Chapter 4 Time

### NPV calculation. Academic Resource Center

NPV calculation Academic Resource Center 1 NPV calculation PV calculation a. Constant Annuity b. Growth Annuity c. Constant Perpetuity d. Growth Perpetuity NPV calculation a. Cash flow happens at year

### CHAPTER 4. The Time Value of Money. Chapter Synopsis

CHAPTER 4 The Time Value of Money Chapter Synopsis Many financial problems require the valuation of cash flows occurring at different times. However, money received in the future is worth less than money

### Farm Financial Management

Farm Financial Management Your Farm Income Statement How much did your farm business earn last year? There are many ways to answer this question. A farm income statement (sometimes called a profit and

### Discounted Cash Flow Valuation

Discounted Cash Flow Valuation Chapter 5 Key Concepts and Skills Be able to compute the future value of multiple cash flows Be able to compute the present value of multiple cash flows Be able to compute

### Ing. Tomáš Rábek, PhD Department of finance

Ing. Tomáš Rábek, PhD Department of finance For financial managers to have a clear understanding of the time value of money and its impact on stock prices. These concepts are discussed in this lesson,

### Would you like to know more about the

Your Net Worth Ag Decision Maker Statement File C3-20 Would you like to know more about the current financial situation of your farming operation? A simple listing of the property you own and the debts

### Lesson 1. Key Financial Concepts INTRODUCTION

Key Financial Concepts INTRODUCTION Welcome to Financial Management! One of the most important components of every business operation is financial decision making. Business decisions at all levels have

### 2. How would (a) a decrease in the interest rate or (b) an increase in the holding period of a deposit affect its future value? Why?

CHAPTER 3 CONCEPT REVIEW QUESTIONS 1. Will a deposit made into an account paying compound interest (assuming compounding occurs once per year) yield a higher future value after one period than an equal-sized

### Chapter 4. The Time Value of Money

Chapter 4 The Time Value of Money 4-2 Topics Covered Future Values and Compound Interest Present Values Multiple Cash Flows Perpetuities and Annuities Inflation and Time Value Effective Annual Interest

### Appendix C- 1. Time Value of Money. Appendix C- 2. Financial Accounting, Fifth Edition

C- 1 Time Value of Money C- 2 Financial Accounting, Fifth Edition Study Objectives 1. Distinguish between simple and compound interest. 2. Solve for future value of a single amount. 3. Solve for future

### Dick Schwanke Finite Math 111 Harford Community College Fall 2013

Annuities and Amortization Finite Mathematics 111 Dick Schwanke Session #3 1 In the Previous Two Sessions Calculating Simple Interest Finding the Amount Owed Computing Discounted Loans Quick Review of

### Chapter 6 Contents. Principles Used in Chapter 6 Principle 1: Money Has a Time Value.

Chapter 6 The Time Value of Money: Annuities and Other Topics Chapter 6 Contents Learning Objectives 1. Distinguish between an ordinary annuity and an annuity due, and calculate present and future values

### How to calculate present values

How to calculate present values Back to the future Chapter 3 Discounted Cash Flow Analysis (Time Value of Money) Discounted Cash Flow (DCF) analysis is the foundation of valuation in corporate finance

### CHAPTER 9 Time Value Analysis

Copyright 2008 by the Foundation of the American College of Healthcare Executives 6/11/07 Version 9-1 CHAPTER 9 Time Value Analysis Future and present values Lump sums Annuities Uneven cash flow streams

### Calculations for Time Value of Money

KEATMX01_p001-008.qxd 11/4/05 4:47 PM Page 1 Calculations for Time Value of Money In this appendix, a brief explanation of the computation of the time value of money is given for readers not familiar with

### TIME VALUE OF MONEY (TVM)

TIME VALUE OF MONEY (TVM) INTEREST Rate of Return When we know the Present Value (amount today), Future Value (amount to which the investment will grow), and Number of Periods, we can calculate the rate

### Problem Set: Annuities and Perpetuities (Solutions Below)

Problem Set: Annuities and Perpetuities (Solutions Below) 1. If you plan to save \$300 annually for 10 years and the discount rate is 15%, what is the future value? 2. If you want to buy a boat in 6 years

### CHAPTER 6 DISCOUNTED CASH FLOW VALUATION

CHAPTER 6 DISCOUNTED CASH FLOW VALUATION Answers to Concepts Review and Critical Thinking Questions 1. The four pieces are the present value (PV), the periodic cash flow (C), the discount rate (r), and

### Compounding Quarterly, Monthly, and Daily

126 Compounding Quarterly, Monthly, and Daily So far, you have been compounding interest annually, which means the interest is added once per year. However, you will want to add the interest quarterly,

### Multiple Peril Crop Insurance

Multiple Peril Crop Insurance Multiple Peril Crop Insurance (MPCI) is a broadbased crop insurance program regulated by the U.S. Department of Agriculture and subsidized by the Federal Crop Insurance Corporation

### Finding the Payment \$20,000 = C[1 1 / 1.0066667 48 ] /.0066667 C = \$488.26

Quick Quiz: Part 2 You know the payment amount for a loan and you want to know how much was borrowed. Do you compute a present value or a future value? You want to receive \$5,000 per month in retirement.

### How To Use Excel To Compute Compound Interest

Excel has several built in functions for working with compound interest and annuities. To use these functions, we ll start with a standard Excel worksheet. This worksheet contains the variables used throughout

### Appendix. Time Value of Money. Financial Accounting, IFRS Edition Weygandt Kimmel Kieso. Appendix C- 1

C Time Value of Money C- 1 Financial Accounting, IFRS Edition Weygandt Kimmel Kieso C- 2 Study Objectives 1. Distinguish between simple and compound interest. 2. Solve for future value of a single amount.

### Discounted Cash Flow Valuation

6 Formulas Discounted Cash Flow Valuation McGraw-Hill/Irwin Copyright 2008 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter Outline Future and Present Values of Multiple Cash Flows Valuing

### Chapter 2 Present Value

Chapter 2 Present Value Road Map Part A Introduction to finance. Financial decisions and financial markets. Present value. Part B Valuation of assets, given discount rates. Part C Determination of risk-adjusted

### The Time Value of Money

The Time Value of Money Future Value - Amount to which an investment will grow after earning interest. Compound Interest - Interest earned on interest. Simple Interest - Interest earned only on the original

### Bond valuation. Present value of a bond = present value of interest payments + present value of maturity value

Bond valuation A reading prepared by Pamela Peterson Drake O U T L I N E 1. Valuation of long-term debt securities 2. Issues 3. Summary 1. Valuation of long-term debt securities Debt securities are obligations

### Present Value Concepts

Present Value Concepts Present value concepts are widely used by accountants in the preparation of financial statements. In fact, under International Financial Reporting Standards (IFRS), these concepts

### Present Value (PV) Tutorial

EYK 15-1 Present Value (PV) Tutorial The concepts of present value are described and applied in Chapter 15. This supplement provides added explanations, illustrations, calculations, present value tables,

### CHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY

CHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY Answers to Concepts Review and Critical Thinking Questions 1. The four parts are the present value (PV), the future value (FV), the discount

### 9. Time Value of Money 1: Present and Future Value

9. Time Value of Money 1: Present and Future Value Introduction The language of finance has unique terms and concepts that are based on mathematics. It is critical that you understand this language, because

### Basic financial arithmetic

2 Basic financial arithmetic Simple interest Compound interest Nominal and effective rates Continuous discounting Conversions and comparisons Exercise Summary File: MFME2_02.xls 13 This chapter deals

### CHAPTER 6 Accounting and the Time Value of Money

CHAPTER 6 Accounting and the Time Value of Money 6-1 LECTURE OUTLINE This chapter can be covered in two to three class sessions. Most students have had previous exposure to single sum problems and ordinary

### PowerPoint. to accompany. Chapter 5. Interest Rates

PowerPoint to accompany Chapter 5 Interest Rates 5.1 Interest Rate Quotes and Adjustments To understand interest rates, it s important to think of interest rates as a price the price of using money. When

### Key Concepts and Skills. Multiple Cash Flows Future Value Example 6.1. Chapter Outline. Multiple Cash Flows Example 2 Continued

6 Calculators Discounted Cash Flow Valuation Key Concepts and Skills Be able to compute the future value of multiple cash flows Be able to compute the present value of multiple cash flows Be able to compute

### Chapter 4. The Time Value of Money

Chapter 4 The Time Value of Money 1 Learning Outcomes Chapter 4 Identify various types of cash flow patterns Compute the future value and the present value of different cash flow streams Compute the return

### Chapter 3. Understanding The Time Value of Money. Prentice-Hall, Inc. 1

Chapter 3 Understanding The Time Value of Money Prentice-Hall, Inc. 1 Time Value of Money A dollar received today is worth more than a dollar received in the future. The sooner your money can earn interest,

### Financial Markets and Valuation - Tutorial 1: SOLUTIONS. Present and Future Values, Annuities and Perpetuities

Financial Markets and Valuation - Tutorial 1: SOLUTIONS Present and Future Values, Annuities and Perpetuities (*) denotes those problems to be covered in detail during the tutorial session (*) Problem

### PRESENT VALUE ANALYSIS. Time value of money equal dollar amounts have different values at different points in time.

PRESENT VALUE ANALYSIS Time value of money equal dollar amounts have different values at different points in time. Present value analysis tool to convert CFs at different points in time to comparable values

### Chapter 8. 48 Financial Planning Handbook PDP

Chapter 8 48 Financial Planning Handbook PDP The Financial Planner's Toolkit As a financial planner, you will be doing a lot of mathematical calculations for your clients. Doing these calculations for

### CHAPTER 6. Accounting and the Time Value of Money. 2. Use of tables. 13, 14 8 1. a. Unknown future amount. 7, 19 1, 5, 13 2, 3, 4, 6

CHAPTER 6 Accounting and the Time Value of Money ASSIGNMENT CLASSIFICATION TABLE (BY TOPIC) Topics Questions Brief Exercises Exercises Problems 1. Present value concepts. 1, 2, 3, 4, 5, 9, 17, 19 2. Use

### Integrated Case. 5-42 First National Bank Time Value of Money Analysis

Integrated Case 5-42 First National Bank Time Value of Money Analysis You have applied for a job with a local bank. As part of its evaluation process, you must take an examination on time value of money

### Creating a Mission Statement, Developing Strategies and Setting Goals A

File C5-09 October 2009 www.extension.iastate.edu/agdm Creating a Mission Statement, Developing Strategies and Setting Goals A mission statement is a guiding light for a business and the individuals who

### Chapter 7 SOLUTIONS TO END-OF-CHAPTER PROBLEMS

Chapter 7 SOLUTIONS TO END-OF-CHAPTER PROBLEMS 7-1 0 1 2 3 4 5 10% PV 10,000 FV 5? FV 5 \$10,000(1.10) 5 \$10,000(FVIF 10%, 5 ) \$10,000(1.6105) \$16,105. Alternatively, with a financial calculator enter the

### Dick Schwanke Finite Math 111 Harford Community College Fall 2015

Using Technology to Assist in Financial Calculations Calculators: TI-83 and HP-12C Software: Microsoft Excel 2007/2010 Session #4 of Finite Mathematics 1 TI-83 / 84 Graphing Calculator Section 5.5 of textbook

### Solutions to Time value of money practice problems

Solutions to Time value of money practice problems Prepared by Pamela Peterson Drake 1. What is the balance in an account at the end of 10 years if \$2,500 is deposited today and the account earns 4% interest,

### Chapter 4 Time Value of Money ANSWERS TO END-OF-CHAPTER QUESTIONS

Chapter 4 Time Value of Money ANSWERS TO END-OF-CHAPTER QUESTIONS 4-1 a. PV (present value) is the value today of a future payment, or stream of payments, discounted at the appropriate rate of interest.

### TIME VALUE OF MONEY #6: TREASURY BOND. Professor Peter Harris Mathematics by Dr. Sharon Petrushka. Introduction

TIME VALUE OF MONEY #6: TREASURY BOND Professor Peter Harris Mathematics by Dr. Sharon Petrushka Introduction This problem assumes that you have mastered problems 1-5, which are prerequisites. In this

### Module 5: Interest concepts of future and present value

Page 1 of 23 Module 5: Interest concepts of future and present value Overview In this module, you learn about the fundamental concepts of interest and present and future values, as well as ordinary annuities

### UNDERSTANDING HEALTHCARE FINANCIAL MANAGEMENT, 5ed. Time Value Analysis

This is a sample of the instructor resources for Understanding Healthcare Financial Management, Fifth Edition, by Louis Gapenski. This sample contains the chapter models, end-of-chapter problems, and end-of-chapter

### Chapter 02 How to Calculate Present Values

Chapter 02 How to Calculate Present Values Multiple Choice Questions 1. The present value of \$100 expected in two years from today at a discount rate of 6% is: A. \$116.64 B. \$108.00 C. \$100.00 D. \$89.00

### TIME VALUE OF MONEY PROBLEM #4: PRESENT VALUE OF AN ANNUITY

TIME VALUE OF MONEY PROBLEM #4: PRESENT VALUE OF AN ANNUITY Professor Peter Harris Mathematics by Dr. Sharon Petrushka Introduction In this assignment we will discuss how to calculate the Present Value

### Oklahoma State University Spears School of Business. Time Value of Money

Oklahoma State University Spears School of Business Time Value of Money Slide 2 Time Value of Money Which would you rather receive as a sign-in bonus for your new job? 1. \$15,000 cash upon signing the

### CHAPTER 4 DISCOUNTED CASH FLOW VALUATION

CHAPTER 4 DISCOUNTED CASH FLOW VALUATION Answers to Concepts Review and Critical Thinking Questions 1. Assuming positive cash flows and interest rates, the future value increases and the present value

### Time Value of Money. Reading 5. IFT Notes for the 2015 Level 1 CFA exam

Time Value of Money Reading 5 IFT Notes for the 2015 Level 1 CFA exam Contents 1. Introduction... 2 2. Interest Rates: Interpretation... 2 3. The Future Value of a Single Cash Flow... 4 4. The Future Value

### CHAPTER 4 DISCOUNTED CASH FLOW VALUATION

CHAPTER 4 DISCOUNTED CASH FLOW VALUATION Solutions to Questions and Problems NOTE: All-end-of chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability

### TIME VALUE OF MONEY PROBLEM #5: ZERO COUPON BOND

TIME VALUE OF MONEY PROBLEM #5: ZERO COUPON BOND Professor Peter Harris Mathematics by Dr. Sharon Petrushka Introduction This assignment will focus on using the TI - 83 to calculate the price of a Zero

### I. Personal and Family Information... 2. II. Current Estate Plan Information... 5. III. Advanced Directives... 6. IV. Assets... 7. a. Real Estate...

Evaluating Your Estate Plan: Ag Decision Maker Estate Planning Questionnaire File C4-57 Table of Contents * I. Personal and Family Information... 2 II. Current Estate Plan Information... 5 III. Advanced

Chapter 4 Time Value of Money Learning Goals 1. Discuss the role of time value in finance, the use of computational aids, and the basic patterns of cash flow. 2. Understand the concept of future value

### Chapter 4. Time Value of Money. Learning Goals. Learning Goals (cont.)

Chapter 4 Time Value of Money Learning Goals 1. Discuss the role of time value in finance, the use of computational aids, and the basic patterns of cash flow. 2. Understand the concept of future value

### The Time Value of Money C H A P T E R N I N E

The Time Value of Money C H A P T E R N I N E Figure 9-1 Relationship of present value and future value PPT 9-1 \$1,000 present value \$ 10% interest \$1,464.10 future value 0 1 2 3 4 Number of periods Figure

### Module 5: Interest concepts of future and present value

file:///f /Courses/2010-11/CGA/FA2/06course/m05intro.htm Module 5: Interest concepts of future and present value Overview In this module, you learn about the fundamental concepts of interest and present

### Solutions to Problems

Solutions to Problems P4-1. LG 1: Using a time line Basic a. b. and c. d. Financial managers rely more on present value than future value because they typically make decisions before the start of a project,

### F V P V = F V = P (1 + r) n. n 1. FV n = C (1 + r) i. i=0. = C 1 r. (1 + r) n 1 ]

1 Week 2 1.1 Recap Week 1 P V = F V (1 + r) n F V = P (1 + r) n 1.2 FV of Annuity: oncept 1.2.1 Multiple Payments: Annuities Multiple payments over time. A special case of multiple payments: annuities

### 1. If you wish to accumulate \$140,000 in 13 years, how much must you deposit today in an account that pays an annual interest rate of 14%?

Chapter 2 - Sample Problems 1. If you wish to accumulate \$140,000 in 13 years, how much must you deposit today in an account that pays an annual interest rate of 14%? 2. What will \$247,000 grow to be in

### Ordinary Annuities Chapter 10

Ordinary Annuities Chapter 10 Learning Objectives After completing this chapter, you will be able to: > Define and distinguish between ordinary simple annuities and ordinary general annuities. > Calculate

### CHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY

CHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY 1. The simple interest per year is: \$5,000.08 = \$400 So after 10 years you will have: \$400 10 = \$4,000 in interest. The total balance will be

### Solutions to Problems: Chapter 5

Solutions to Problems: Chapter 5 P5-1. Using a time line LG 1; Basic a, b, and c d. Financial managers rely more on present value than future value because they typically make decisions before the start

### Chapter 2 Applying Time Value Concepts

Chapter 2 Applying Time Value Concepts Chapter Overview Albert Einstein, the renowned physicist whose theories of relativity formed the theoretical base for the utilization of atomic energy, called the

### Chapter 3 Mathematics of Finance

Chapter 3 Mathematics of Finance Section 3 Future Value of an Annuity; Sinking Funds Learning Objectives for Section 3.3 Future Value of an Annuity; Sinking Funds The student will be able to compute the

### Financial Math on Spreadsheet and Calculator Version 4.0

Financial Math on Spreadsheet and Calculator Version 4.0 2002 Kent L. Womack and Andrew Brownell Tuck School of Business Dartmouth College Table of Contents INTRODUCTION...1 PERFORMING TVM CALCULATIONS

### Time Value of Money 1

Time Value of Money 1 This topic introduces you to the analysis of trade-offs over time. Financial decisions involve costs and benefits that are spread over time. Financial decision makers in households

### Goals. The Time Value of Money. First example. Compounding. Economics 71a Spring 2007 Mayo, Chapter 7 Lecture notes 3.1

Goals The Time Value of Money Economics 7a Spring 2007 Mayo, Chapter 7 Lecture notes 3. More applications Compounding PV = present or starting value FV = future value R = interest rate n = number of periods

### DISCOUNTED CASH FLOW VALUATION and MULTIPLE CASH FLOWS

Chapter 5 DISCOUNTED CASH FLOW VALUATION and MULTIPLE CASH FLOWS The basic PV and FV techniques can be extended to handle any number of cash flows. PV with multiple cash flows: Suppose you need \$500 one

### Excel Financial Functions

Excel Financial Functions PV() Effect() Nominal() FV() PMT() Payment Amortization Table Payment Array Table NPer() Rate() NPV() IRR() MIRR() Yield() Price() Accrint() Future Value How much will your money

### This is Time Value of Money: Multiple Flows, chapter 7 from the book Finance for Managers (index.html) (v. 0.1).

This is Time Value of Money: Multiple Flows, chapter 7 from the book Finance for Managers (index.html) (v. 0.1). This book is licensed under a Creative Commons by-nc-sa 3.0 (http://creativecommons.org/licenses/by-nc-sa/

### 5. Time value of money

1 Simple interest 2 5. Time value of money With simple interest, the amount earned each period is always the same: i = rp o We will review some tools for discounting cash flows. where i = interest earned

### Time Value of Money, Part 5 Present Value aueof An Annuity. Learning Outcomes. Present Value

Time Value of Money, Part 5 Present Value aueof An Annuity Intermediate Accounting II Dr. Chula King 1 Learning Outcomes The concept of present value Present value of an annuity Ordinary annuity versus

### Time Value of Money. 2014 Level I Quantitative Methods. IFT Notes for the CFA exam

Time Value of Money 2014 Level I Quantitative Methods IFT Notes for the CFA exam Contents 1. Introduction... 2 2. Interest Rates: Interpretation... 2 3. The Future Value of a Single Cash Flow... 4 4. The

### PV Tutorial Using Excel

EYK 15-3 PV Tutorial Using Excel TABLE OF CONTENTS Introduction Exercise 1: Exercise 2: Exercise 3: Exercise 4: Exercise 5: Exercise 6: Exercise 7: Exercise 8: Exercise 9: Exercise 10: Exercise 11: Exercise

### Main TVM functions of a BAII Plus Financial Calculator

Main TVM functions of a BAII Plus Financial Calculator The BAII Plus calculator can be used to perform calculations for problems involving compound interest and different types of annuities. (Note: there

### Time Value of Money Revisited: Part 1 Terminology. Learning Outcomes. Time Value of Money

Time Value of Money Revisited: Part 1 Terminology Intermediate Accounting II Dr. Chula King 1 Learning Outcomes Definition of Time Value of Money Components of Time Value of Money How to Answer the Question