## The time value of money is another very important investing concept. The application of this idea is what determines your parents' monthly mortgage, car loan payment, or installment loan payments. It also has an effect on the price of stocks.

## Time value of money simply says that a dollar received today is worth more than a dollar received in one day, one month, or a year because the dollar received today can start earning interest immediately. It is such a simple idea that you probably already know it, but you just haven't thought about how it can affect your actions. Let's consider an example of how this idea can be applied.

## Suppose someone told you that you can have $100,000 today or you can have $105,000 a year from now (assuming you have no immediate need for the money). Which would you prefer?

## You cannot really answer this question until we supply you with one more piece of information: the return you can earn in one year by putting the $100,000 in an alternate investment. You can easily answer the question if you know that you can put the $100,000 you'd receive today, in a bank account paying 10% yearly compound interest.

## Think about the choices again: receive $100,000 today or receive $105,000 one year from now. For those of you who would rather have the $105,000 one year from now, you would have cheated yourself out of $5,000. If you collect $100,000 today, you can deposit it in the bank and earn 10% interest for the year, or $10,000, on that money. In one year, you would have a principal and interest total of $110,000. This is $5,000 more than you would get if you'd opted to receive $105,000 one year in the future.

## If we told you that you can have $100,000 today or $110,000 one year from now, both choices are equivalent because the extra $10,000 we would give you one year from now exactly equals the amount of money you can earn by investing $100,000 in the bank for one year.

## This time value of money idea means that if you have a choice of receiving money today or a year from now, the money you should expect a year from now should be higher than the money you are offered today.

## Turning the situation around a bit, suppose someone told you that you are eligible to receive $100,000 one year from now. At the same time, she asks you how much money you'd require today such that you'd give up the $100,000 money you can receive in a year? Once again, this will depend on how much you can earn by investing the money you would get today for one year. Let's go through the numbers.

## Assume again that the interest rate you can get by putting your money in a bank is 10% yearly compound rate. The question you have to ask yourself is this: how much will I have to put in a bank account which pays 10% yearly compound interest such that at the end of one year I'd have $100,000? Mathematically, the equation to solve is as follows:

## Future Value = (Present Value) + (Present Value) x (Rate On Investment)

## Where Future Value is the amount of money you would get in the future, which is $100,000 in our example.

## Where Present Value is the amount of money you would need today such that if you invested it in a bank today, you would end up with the Future Balance.

## Where Rate On Investment is the interest rate you would be paid for your investment, which is 10% in our example.

## What we are trying to figure out in the equation above is Present Value-how much you would need today such that if you invest it, you would end up with $100,000 in a year. We can easily solve the equation as follows:

## Future Value = (Present Value) + (Present Value) x (Rate On Investment)

## With a bit of manipulation, we get the following formula:

## Future Value = (Present Value) x (1 + Rate On Investment)

## With more manipulation, we get the following formula:

## Present Value = Future Value / (1 + Rate On Investment)

## Substituting the numbers in our example, we get the following equation:

## Present Value = $100,000 / (1 + 10%) = $100,000 / (1 + .1) = $100,000 / 1.1

## Present Value = $90,909.09

## Remember the original question: how much cash would you require today such that you would not have to be paid $100,000 one year from now? As you can see from the formula above, the answer is that you should require at least $90,909.09 today, and we can prove it. With $90,909.09 on hand today, you could put it in a bank account earning 10% per year. The total amount of money you would have in one year if you invest this money in the bank (Future Value) would be calculated as follows:

## Future Value = $90,909.09 + ($90,909.09) x (10%)

## Future Value = $90,909.09 + $9090.909 = $100,000

## If we changed the original question and asked how much cash you would require today such that you would not have to be paid $100,000 two years from now, the answer gets slightly more complicated but the basic principle is the same. You just need to know how much money you would need today such that if you earn 10% interest in the first year, and earn another 10% interest in the second year, you would end up with $100,000. Without going through the mathematics, the answer is $82,644.63. We can prove it as follows:

## Year #1 Future Value = $82,644.63 + ($82,644.63) x (10%) = $90,909.09

## The investment balance for the second year's investment is now $90,909.09 so at the end of the second year, you would end up with:

## Year #2 Future Value = $90,909.09 + ($90,909.09) x (10%) = $100,000

## So as you can see, you should require $82,644.63 today such that you would give up $100,000 two years from now. Notice that we have quietly used the compounding concept here because we assumed that in the second year, the new invested balance includes the interest earned in the first year.

## The terms present value and future value have very special meanings in the investment world. Present value refers to today's value of a sum of money to be received in the future. If someone asks you for the present value of $100,000, you would need two pieces of additional information from them: how far in the future the money will be received and the rate of investment [or discount rate (not to be confused with the Federal Reserve Bank's discount rate), as it is commonly known in finance lingo when calculating present value] that is to be applied. In our example, the present value of $100,000 to be received in two years, and to which a discount rate of 10% is applied was $82,644.63. Though we didn't show you the calculation for this, the present value of $100,000 to be received in fifty years and to which a 10% discount rate is to be applied is $852.86. That's correct-if someone gave you $852.86 today, you would get $100,000 back in 50 years if the interest rate or discount rate were assumed to be 10%.

## Future value is easier to understand because you are already used to calculating it whether you know it or not. Future value is how much you would earn by making an investment today and collecting your money in the future. Like present value, you will need to know the rate of investment and the amount of time in which you will receive the cash. When calculating future value, however, the rate of investment is known as the investment rate-the percentage return (analogous to the interest in our bank deposit example). So, the future value of $82,644.63 in two years assuming a 10% compound investment rate is $100,000 (as we calculated earlier). Though we didn't show you the calculation for this, the future value of $100,000 to be received in fifty years and to which a 10% compound investment rate is to be applied is $11,739,085.

**How The Time Value Of Money And Stock Prices Are Related (for the Advanced Teenvestor)**

## In another, we briefly mentioned how inflation affects the stock market, but we didn't really give you a full explanation. We can now give you the details here because we've covered the meaning of present value.

## In general, stock prices depend on how much investors expect companies to make in the future. You can think of the change in the price of a stock as the result of a vote by investors on whether they think the company will make more or less money in the future. If more investors think the company will do better in the future than those who think the company will do worse in the future, the price of a stock will go up because of the law of supply and demand as discussed earlier in the chapter. Likewise, if more investors think the company will do worse in the future than those who think the company will do better in the future, the price of a stock will go down.

## When you add the element of inflation, the movement in the price of stock gets more interesting. The higher the inflation rate, the smaller the present value of a company's future earnings because inflation increases the discount rate to be applied to future earnings of the company. If you recall our previous discussion, the present value of money to be received in the future is as follows:

## Present Value = Future Value / (1 + Rate On Investment)

## Where Rate On Investment is the discount rate

## As the denominator of the equation above increases (that is, as the discount rate increases), the present value of the company's future earnings gets smaller and smaller. What this means is that a company's future earnings is worth less and less as inflation creeps up because inflation is reflected in the discount rate--the higher the inflation, the higher the discount rate. This is the main reason why investors hate inflation.