Business, Legal & Accounting Glossary
Any investor prefers to receive payment for a fixed amount of money immediately, rather than waiting for the future. The thought that prevails behind this is that necessity of money at the present time can be more than the future. This phenomenon is termed as time value of money in the study of economics. The main fact that prevails here is that earning interest on money is more fruitful.
Time value of money is the financial concept that deals with equating the future value of money or an investment with its present value. The time value of money explains how interest rates and time affect the value of money. The general time value of money equation is:
PV = FV/(1+r)^t
where
FV = future value
PV = present value
r = interest rate per period
t = period (e.g. years)
To illustrate the time value of money, suppose an investor expects to receive $100 three years from now and that the investor can invest at a constant 5% annual investment rate. Based on the time value of money equation, the $100 to be received three years from now has a present value of $100/(1+.05)^3 = $86.38. Time value of money then suggests that at a 5% annual rate, $100 three years from now is equivalent to $86.38 today. Thus, the time value of money concludes that, if there is an investment vehicle with a positive real rate of return, owning a dollar today is worth more than owning a dollar in the future. The time value of money concept has numerous applications in finance including but not limited to the valuation of annuities, bonds, and equities. The time value of money is also applied to solve calculations such as net present value and internal rate of return.
If an individual is given two options that he can take $10,000 now or in three years; the probability here is that the individual prefers to take $10,000 now. Waiting for three years is not a rational decision. Though the amount remains the same, the value of money increases in terms so that it can earn more interest. If the money is taken now, one can earn much more out of it. One can earn more interest over time. The value of $10,000 if received now, exceeds its future value by gaining interest over a period of time. If received now, in three years the value increases to $10,000 plus the interest gained in three years. The same amount of money if received three years later, the value would remain the same as $10,000. Thus, time increases the value of money.
The time value of money can be calculated in varied ways both in terms of future and present. Let’s begin with the future value basics:
Future value of money = P * (1 + i) n
Where P = original amount of money (principal amount), n = number of periods, and i = interest rate per period of time
Present value of money = FV * (1 + i) -n
Where FV = future value of money
All of these are inter-related concepts and derive from the concept of the time value of money. These answer the question, “What is the time value of money?”
Suppose you have $100. Woo hoo! Time to go buy a copy of Poor Charlie’s Almanack with enough left over for some coffee to sip while reading it. But, if you don’t want to buy anything right now, you can invest that money and have even more next year.
So, you decide to invest that $100 in a 1-year CD that pays 8% (hey, this is my fantasy, I’ll set the rules). When that CD matures, you’ll have $108. $100 * 1.08 = $108 Enough to buy two more cups of coffee at Starbucks than you could before. Not bad. But say you let that CD roll over and pull the money out two years from now. How much would you have then? Easy. $116.64. $100 * 1.08 * 1.08 = $116.64.
Three years from now, $125.97. Four years from now, $136.05, and so on.
To calculate this, you could do $100 * 1.08 * 1.08 * 1.08 * … and go as many times as you have years. But to save your poor fingers (not to mention the calculator’s computing power — you do know that a calculator only has a certain number of calculations it can perform correctly over its lifetime, right?), you can use a collapsed version. $100 * 1.08^n, where ” ^ ” means “raised to the power of” and “n” = the number of years. In more general terms, this can be expressed:
FV = PV * (1 + G)^n
where FV = future value, PV = present value, G = growth rate (interest rate), n = number of years
This is one view of the CAGR (Compound Annual Growth Rate) formula.
But suppose you wanted to have $100 two years from now. How much would you have to invest at 8% per year in order to have that? Well, I can tell you that the answer is not $100. At 8% per year, we’ve already seen that you’d get $116.64, not the $100 we want to have. What’s the least amount of money you could invest today to get $100 two years from now?
Well, let’s rearrange Eqn 1 above and solve for PV:
PV = \frac{FV}{(1 + G)^n}
Now plug in $100 for FV, 0.08 for G, and 2 for n. You should get $85.73. You can do this as follows, using the scientific calculator on your computer (open the calculator and look for all the extra buttons — if you don’t see them, change the “View”):
1.08
x^2
1/x
*
100
=
Or, you could do it as 100 / 1.08 / 1.08 =
So, you need to invest $85.73 at 8% per year to end up with $100 two years from now.
Note that this also happens to show that $100 two years from now is worth less than $100 today (getting back to the time value of money).
In this case, that 8% is called the discount rate. You are discounting $100 by that amount over a two-year time span.
The discount rate is also the required rate of return. Let me show you.
If you have $100 today, and you want to have $200 four years from now, you need to earn how much interest per year? In other words, what is the return per year that will double your money in four years?
Once more, we go back to Eqn 1, but this time, we solve for G:
G = ( \frac{FV}{PV} ) ^{\frac{1}{n}} - 1
For this, you do need your scientific calculator. FV = 200, PV = 100, n = 4.
Here are the steps:
200
/
100
=
x^y
0.25 (this is 1/4)
=
– 1
=
You should end up with 0.189207…
Rounding this off and converting to per cent, and you must invest that $100 at 18.92% per year in order to double it in four years.
CAGR
Compounding
Discounting
Internal rate of return
Time value of money is a concept that states the earlier you receive money the more it is worth. Sometimes called “present discounted value”.
The time value of money is a concept most people inherently understand. It is similar to “a bird in the hand is worth two in the bush,” but our version reads “$1 today is worth more than $1 tomorrow.”
For example, if you ask someone would they rather receive their pay today or next month, assuming the amount would be the same in each case, they almost universally would say “today.” Why? First, if you control the money today, you can put it to work earning more money for you — earning interest, invested in stocks, real estate or other assets that can appreciate in value. Thus for the investor, time is money because it represents opportunity to earn more. Second, inflation, decreases the purchasing value of that money as time goes on. It takes more money in the future to buy the same amount of stuff as you can buy today (10-cent loaf of bread, anyone?).
Let’s say you have a choice of getting $1,000 today or $1,000 one year from today. Suppose you picked the first option and you bought a CD that offered 4% interest. The next year you would have $1,040.00 instead of the $1,000.00 you would have had if you had opted to wait a year. Clearly the first option is superior.
This is even more important when you consider inflation. Let’s take the first example again but this time factor in 2% inflation. The $1,040.00 you had from your CD would be worth about $1,020 in today’s dollars while if you had waited a year, the $1,000 you’d receive would only be worth $980.39 in today’s dollars ($1,000 divided 1.02 {for 2% inflation}) !!! Thus time really is money as the ageless cliche says.
Clearly investors need to understand that there is an opportunity cost and a devaluing cost due to inflation in waiting to act when making investing decisions. While one should never act in haste, an investor would be wise not to procrastinate after receiving pay or other income. This especially applies to IRA contributions. You should always make contributions as early as you are able for each calendar year.
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This glossary post was last updated: 28th November, 2021 | 0 Views.