Time Value Of Money: Determining Your Future Worth If you were offered $100 today or $100 a year from now, which would you choose? Would you rather have $100,000 today or $1,000 a month for the rest of your life? Net present value (NPV) provides a simple way to answer these types of financial questions. This calculation compares the money received r eceived in the future to an amount of money received today, while accounting for time and interest interest.. It's based on the principle of time of time value of money (TVM), which explains how time affects monetary value. (For background reading, see Understanding The Time Value Of Money .) The TVM calculation may look complicated, but with some understanding of NPV and how the calculation works, along with its basic variations: present value and future value,, we can start putting this formula to use in common application. value Time Value of Money If you were offered $100 today or $100 a year from now, which would be the better option and why? This question is the classic method in which the TVM concept is taught in virtually every business school in America. The majority of people asked this question choose to take the money today. But why? What are the advantages and, more importantly, disadvantages of this decision?
There are three basic reasons to support the TVM theory. First, a dollar can be invested and earn interest over time, giving it potential earning power. Also, money is subject to inflation,, eating away at the spending power of the currency over time, making it worth inflation less in the future. Finally, there is always the risk of not actually receiving the dollar in the future - if you hold the dollar now, there is no risk of this happening. Getting an accurate estimate of this last risk isn't easy and, therefore, it's harder to use in a precise manner. Illustrating the Net Present Value Would you rather have $100,000 today or $1,000 a month for the rest of your life? Most people have some vague idea of which they'd take, but a net present value calculation can tell you precisely which is better, from a financial standpoint, assuming you know how long you will live and what rate of interest you'd earn if you took the $100,000. Specific variations of time value of money calculations are:
Net Present Value (lets you value a stream of future payments into one lump sum today, as you see in many lottery payouts) Present Value (tells you the current worth of a future sum of money) Future Value (gives you the future value of cash that you have now ) Determining the Time Value of Your Money Which would you prefer: $100,000 today or $120,000 a year from now? •
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The $100,000 is the "present value" and the $120,000 is the "future value" of your money. In this case, if the interest rate used in the calculation is 20%, there is no difference between the two. Five Factors to a TVM Calculation. 1. Number of time periods involved (months, years) 2. Annual interest rate (or discount rate, depending on the calculation) 3. Present value (what do you have right now in your pocket) 4. Payments (if any exist. If not, payments equal zero) 5. Future value (the dollar amount you will receive in the future. A standard mortgage will have a zero future value, because it is paid off at the end of the term) Many people use financial calculators to quickly solve these TVM questions. By knowing how to use one, you could easily calculate a present sum of money into a future one, or vice versa. The same goes for determining the payment on a mortgage, or how much interest is being charged on that short-term Christmas expenses loan. With four of the five components in-hand, the financial calculator can easily determine the missing factor. To calculate this by hand, the formula would lo ok like this: FV = PV (1+i) N Or conversely PV =
FV (1+i)N
Net present value calculations can also help you discover answers to other questions. Retirement planning needs can be determined on an overall, monthly or annual basis, as can the amount to contribute for college funds. By using a net present value calculation, you can find out how much you need to invest each month to achieve your goal. For example, in order to save $1 million dollars to retire in 20 years, assuming an annual return of 12.2%, you must save $984 per month. Try the calculation and test it for yourself. (To learn more about how compounding contributes to retirement savings, see Young Investors: What Are You Waiting For? and Why is retirement easier to afford if you start early? ) Below is a list of the most common areas in which people use net present value calculations to help them make decisions and solve their financial problems. •
Mortgage payments
Student loans Savings Home, auto or other major purchases Credit cards Money management Retirement planning Investments Financial planning (both business and personal) Conclusion The net present value calculation and its variations are quick and easy ways to measure the effects of time and interest on a given sum of money, whether it is received now or in the future. The calculation is perfect for short- and- long-term planning, budgeting or reference. When plotting out your financial future, keep this formula in mind. • • • • • • • •
Present Value - PV What Does Present Value - PV Mean? The current worth of a future sum of money or stream of cash flows given a specified rate of return. Future cash flows are discounted at the discount rate, and the higher the discount rate, the lower the present value of the future cash flows. Determining the appropriate discount rate is the key to properly valuing future cash flows, whether they be earnings or obligations. Also referred to as "discounted value".
Investopedia explains Present Value - PV This sounds a bit confusing, but it really isn't. The basis is that receiving $1,000 now is worth more than $1,000 five years from now, because if you got the money now, you could invest it and receive an additional return over the five years. The calculation of discounted or present value is extremely important in many financial calculations. For example, net present value, bond yields, spot rates, and pension obligations all rely on the principle of discounted or present value. Learning how to use a financial calculator to make present value calculations can help you decide whether
you should accept a cash rebate, 0% financing on the purchase of a car or to pay points on a mortgage
Future Value - FV What Does Future Value - FV Mean? The value of an asset or cash at a specified date in the future that is equivalent in value to a specified sum today. There are two ways to calculate FV: 1) For an asset with simple annual interest: = Original Investment x (1+(interest rate*number of years)) 2) For an asset with interest compounded annually: = Original Investment x ((1+interest rate)^number of years)
Investopedia explains Future Value - FV Consider the following examples: 1) $1000 invested for 5 years with simple annual interest of 10% would have a future value of $1,500.00. 2) $1000 invested for 5 years at 10%, compounded annually has a future value of $1,610.51.
Calculating The Present And Future Value Of Annuities by Shauna Carther (Contact Author | Biography) Email Article Print Feedback Reprints Share Filed Under:
Formulas, Personal Finance, Retirement, Savings
At some point in your life you may have had to make a series of fixed payments over a period of time - such as rent or car payments - or have received a series of payments
over a period of time, such as bond coupons. These are called annuities. If you understand the time value of money and have an understanding of future and present value you're ready to learn about annuities and how their present and future values are calculated. (To read more on this subject, see Understanding The Time Value Of Money and Continuously Compound Interest .)
What Are Annuities? Annuities are essentially series of fixed payments required from you or paid to you at a specified frequency over the course of a fixed period of time. The most common payment frequencies are yearly (once a year), semi-annually (twice a year), quarterly (four times a year) and monthly (once a month). There are two basic types of annuities: ordinary annuities and annuities due.
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Ordinary Annuity: Payments are required at the end of each period. For example, straight bonds usually pay coupon payments at the end of every six months until the bond's maturity date. Annuity Due: Payments are required at the beginning of each period. Rent is an example of annuity due. You are usually required to pay rent when you first move in at the beginning of the month, and then on the first of each month thereafter.
Since the present and future value calculations for ordinary annuities and annuities due are slightly different, we will first discuss the present and future value calculation for ordinary annuities. Calculating the Future Value of an Ordinary Annuity If you know how much you can invest per period for a certain time period, the future value of an ordinary annuity formula is useful for finding out how much you would have in the future by investing at your given interest rate. If you are making payments on a loan, the future value is useful for determining the total cost of the loan.
Let's now run through Example 1. Consider the following annuity cash flow schedule:
In order to calculate the future value of the annuity, we have to calculate the future value of each cash flow. Let's assume that you are receiving $1,000 every year for the next five years, and you invested each payment at 5%. The following diagram shows how much you would have at the end of the five-year period:
Since we have to add the future value of each payment, you may have noticed that, if you have an ordinary annuity with many cash flows, it would take a long time to calculate all the future values and then add them together. Fortunately, mathematics provides a formula that serves as a short cut for finding the accumulated value of all cash flows received from an ordinary annuity:
C = Cash flow per period i = interest rate n = number of payments
If we were to use the above formula for Example 1 above, this is the result:
= $1000*[5.53] = $5525.63 Note that the one cent difference between $5,525.64 and $5,525.63 is due to a rounding error in the first calculation. Each of the values of the first calculation must be rounded to the nearest penny - the more you have to round numbers in a calculation the more likely rounding errors will occur. So, the above formula not only provides a shortcut to finding FV of an ordinary annuity but also gives a more accurate result. (Now that you know how to do these on your own, check out our Future Value of an Annuity Calculator for the easy method.) Calculating the Present Value of an Ordinary Annuity If you would like to determine today's value of a series of future payments, you need to use the formula that calculates the present value of an ordinary annuity. This is the formula you would use as part of a bond pricing calculation. The PV of ordinary annuity calculates the present value of the coupon payments that you will receive in the future. For Example 2, we'll use the same annuity cash flow schedule as we did in Example 1. To obtain the total discounted value, we need to take the present value of each future payment and, as we did in Example 1, add the cash flows together.
Again, calculating and adding all these values will take a considerable amount of time, especially if we expect many future payments. As such, there is a mathematical shortcut
we can use for PV of ordinary annuity.
C = Cash flow per period i = interest rate n = number of payments The formula provides us with the PV in a few easy steps. Here is the calculation of the annuity represented in the diagram for Example 2:
= $1000*[4.33] = $4329.48 Not that you'd want to use it now that you know the long way to get present value of an annuity, but just in case, you can check out our Present Value of an Annuity Calculator . Calculating the Future Value of an Annuity Due When you are receiving or paying cash flows for an annuity due, your cash flow schedule would appear as follows:
Since each payment in the series is made one period sooner, we need to discount the formula one period back. A slight modification to the FV-of-an-ordinary-annuity formula accounts for payments occurring at the beginning of each period. In Example 3, let's illustrate why this modification is needed when each $1,000 payment is made at the beginning of the period rather than the end (interest rate is still 5%):
Notice that when payments are made at the beginning of the period, each amount is held for longer at the end of the period. For example, if the $1,000 was invested on January 1st rather than December 31st of each year, the last payment before we value our investment at the end of five years (on December 31st) would have been made a year prior (January 1st) rather than the same day on which it is valued. The future value of annuity formula would then read:
Therefore,
= $1000*5.53*1.05 = $5801.91 Check out our Future Value Annuity Due Calculator to save some time. Calculating the Present Value of an Annuity Due For the present value of an annuity due formula, we need to discount the formula one period forward as the payments are held for a lesser amount of time. When calculating the present value, we assume that the first payment was made today. We could use this formula for calculating the present value of your future rent payments as specified in a lease you sign with your landlord. Let's say for Example 4 that you make your first rent payment at the beginning of the month and are evaluating the present value of your five-month lease on that same day. Your present value calculation would work as follows:
Of course, we can use a formula shortcut to calculate the present value of an annuity due:
Therefore,
= $1000*4.33*1.05 = $4545.95 Recall that the present value of an ordinary annuity returned a value of $4,329.48. The present value of an ordinary annuity is less than that of an annuity due because the further back we discount a future payment, the lower its present value: each payment or cash flow in ordinary annuity occurs one period further into future. Check out our Present Value Annuity Due Calculator . Conclusion Now you can see how annuity affects how you calculate the present and future value of any amount of money. Remember that the payment frequencies, or number of payments, and the time at which these payments are made (whether at the beginning or end of each payment period) are all variables you need to account for in your calculations.
Nominal Interest Rate What Does Nominal Interest Rate Mean? Nominal interest rates refer to referes to the rate of interest prior to taking inflation into account. Depending on its application, an inflation and risk premium must be added to the real interest rate in order to obtain the nominal rate.
Investopedia explains
Nominal Interest Rate
Nominal Interest Rate = Real Interest Rate + Inflation Premium + Risk Premium In practice, the inflation premium is often assumed to be the expec ted inflation rate and the risk premium is ignored. Unless the economy is experiencing a deflationary period, the nominal rate will be higher than the real rate.
Effective Annual Interest Rate What Does Effective Annual Interest Rate Mean? An investment's annual rate of interest when compounding occurs more often than once a year. Calculated as the following:
Investopedia explains Effective Annual Interest Rate Consider a stated annual rate of 10%. Compounded yearly, this rate will turn $1000 into $1100. However, if compounding occurs monthly, $1000 would grow to $1104.70 by the end of the year, rendering an effective annual interest rate of 10.47%. Basically the
effective annual rate is the annual rate of interest that accounts for the effect of compounding
