Discounting and Discount Rates

Once we project the cash flows we expect a company to generate in the future, we have to discount those future cash flows back to the present to account for the time value of money. After all, a dollar today is worth more than a dollar 10 years from now, because the dollar today can be invested to earn a return over the next 10 years.

How to visualize it

Suppose it is possible to invest our money at a 5% annual rate of return. In that case, $1 today will become $1.05 one year from now. Two years from now, it will become $1.1025 ($1.05 x $1.05). Three years from now, it will become $1.053, or $1.1576, and so on.

To find the present value of $1 of future cash flow, divide that future cash flow by the appropriate multiplier from the above example. A cash flow of $1 one year in the future is worth $0.9524 ($1/$1.05) in the present. If we invest that $0.9524 at 5%, in one year we'll have exactly $1. A $1 cash flow two years in the future is worth $1/$1.1025, or $0.9070, in the present. The further into the future we go, the less a given cash flow is worth right now. Generalizing this concept, the following formula is quite important:

Let's go through a few more examples. Suppose we have a $1,000 cash flow three years in the future with a 7% rate of return. The present value of that cash flow is:

The same cash flow five years in the future would be worth:

And finally, a $1,000 cash flow five years from now, but this time with a 10% discount rate, would be worth:

As you can see from these examples, the further out a cash flow is, the less it is worth in today's dollars. Also, the higher the rate of return used to discount the future cash flow, the lower the present value.