Let's start with first principles:
Receiving money today is worth more than receiving the same amount of money in the future. A dollar today is worth more than a dollar received a month, a year, five years or ten years from now. The reason is very simple. If you receive the money today you can put it in the bank and receive interest on it. For example, if you were to receive $100 today you could put it in the bank. If interest rates were 5%, in a year it would be worth $105. Therefore, receiving $100 today is the economic equivalent of receiving $105 a year from now. Another way of saying the same thing, which is the way banking and finance folks talk, is that $105 received a year from now is the equivalent of receiving $100 today. In corporate finance speak "The $105 has a present value of 100."
This is really nothing more than the concept of interest in reverse and the calculations reflect this fact. If I want to determine the value of $100 a year from now at 5% interest I do the following calculation:
r is the interest rate expressed as a decimal or 0.05. The calculation becomes 100 x 1.05=$105.
I can calculate the value at any point in the future just by adding an exponential notation to the (1+r). Accordingly, if I want the value after 2 years the formula is 100 x (1+r)^2. If after 3 years 100 x(1+r)^3. That is all there is to it.
Now if I want to do the calculation in reverse it is very simple. What is the value today of $105 received in 1 year if interest rates are 5%.
I get 105/1.05, which gives me $100. It is not any more difficult than that. Rather than refer to the 5% as the interest rate, people use the term discount rate to indicate that you are doing a present value calculation. I use the same exponential notation if I want to calculate the present value of cash flows 2 years, 10 years or 50 years in the future.
In the illustration above we assumed (even if we didn't state it explicitly) that the receipt of the money was absolutely certain. In the real world this is rarely the case. In finance the assumption is made that dollar payments to be received from the US Federal Government are certain (this is perhaps becoming somewhat less certain) but that other cash flows contain an element of uncertainty depending upon the nature of the cash flow. Interest to be received from a large and creditworthy corporation is obviously more certain than the cash flow expected to be received from a startup business. It is a fundamental tenet of corporate finance that when deciding the present value of an expected (you can substitute the word anticipated or hoped for) cash flow you use a discount rate (remember this is nothing more than the interest rate applied in reverse) that reflects the riskiness of receiving the cash flow. So, for example, the discount rate applied to expected payments from the large and creditworthy corporation would be a lot lower than the discount rate applied to the expected (hoped for) cash flows from a new startup company that faces financial, operational and competitive risks.
While this second principle may seem logical and indeed obvious, you might be surprised by how often people, including finance professionals, get themselves into trouble by failing to keep this very simple rule in mind. We will look at this more in detail when we explore project financing and the cost of capital. But for the moment, remember that there are no exceptions to this rule! You discount future cash flows based upon the riskiness inherent in those cash flows—not based upon your financial strength, your cost of capital, someone else's ability to access capital or the weather.