This is the first of a multi-part series exploring the time value of money. I will attempt to answer how much a dollar is worth today and tomorrow based on the opportunity cost available to you. This is called the Time Value of Money (TVM). The power behind the equations you’ll learn (if you haven’t already) is the basis for much of modern finance theory and the decisions based on that theory. Getting a firm grasp on this subject will allow you to make sound financial decisions, not just in the stock market, but in your daily life.
First, we’ll go over some basics. On April 16th, I posted the “5 forces of Finance.” These primary ideas are what form the background behind TVM and more specifically the Present Value (PV) of Money, especially point 2.
The Present Value of Money is actually fairly intuitive. If you have $100,000 today, how much is it worth? Obviously the answer is $100,000. But if you were to receive $100,000 a year from now, how much would it be worth? The answer to that is based on what you could do with the same money if you had it today. This “Discount Factor” is the same as the opportunity cost. If we had that $100,000 today, we could invest it at a certain rate. If I put it in the bank, and earned 3% annual interest, at the end of a year, I would have $103,000. This is actually called the Future Value (FV) of Money.
Because of the opportunity cost or the income I would lose, $100,000 a year from now is not worth $100,000 today. To figure out how much it would be worth, you use the Discount Factor or Discount Rate ( r ) in the following equation where r is the opportunity to make money on another investment and C1 is the expected cash flow in the first period:
PV = ( 1 / 1 + r ) x C1 or PV = C1 / 1 + r
If we solve the above problem with this equation, assuming that we could get 3% annually, it looks like this:
PV = ( 1 / 1 + .03 ) x $100,000 = $97,087.38
$100,000 a year from now is actually worth $97,087.38 today. Why is this valuable? Let’s apply it to a realistic problem. Let’s say you have a business project that you know will result in $60,000 income in 6 months. Right now, investors could get an annual return of 3.19% by buying a no-risk, 6-month treasury bill (we’ll talk about risk another time). If you wanted to sell that project today, how much would you ask for it or what is the fair value (a.k.a. PV)? Let’s plug it into the equation:
PV = $60,000 / 1 + [half the annual return is 0.01595] = $59,058.24
So there you have it. A fair price for the project would be $59,058.24.
Now you can tell how much something is worth today based on the opportunity cost of investing the money elsewhere. In the next part we’ll explore some more practical applications of PV and cover Net Present Value. If you have any questions, please post a comment and I'll try and answer it quickly. Keep checking back!
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