          Course 403: Introduction to Discounted Cash Flow
Discounting and Discount Rates     In this course  1 Introduction 2 Estimating Future Cash Flow 3 Discounting and Discount Rates 4 Cost of Capital 5 Two Types of Capital, Two Costs 6 The Perpetuity Value 7 The Bottom Line              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.

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:

Present Value of Cash Flow in Year N =
CF at Year N / (1 + R)^N

CF = Cash Flow
R = Required Return (Discount Rate)
N = Number of Years in the Future

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:

\$1,000 / (1 + .07)^3 = \$816.30

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

\$1,000 / (1 + .07)^5 = \$712.99

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

\$1,000 / (1 + .10)^5 = \$620.92

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.

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