# Discounted Cash Flow - The Basics

Discounted cash flow analysis is the most fundamental method of stock valuation. The basic premise is that a company is worth the sum of all future cash flows which the company generates discounted back to today at an appropriate discount rate. The equation that captures this is

where V is the value which we're calculating, Ci is the cash flow in year i, and r is the discount rate. Before we attempt to apply this equation to a company, let's look at a simple example to explain how discounted cash flows work.

## Value Of Cash Flows

Imagine that I offer you a deal. I agree to pay you \$10,000 dollars a year every year for the rest of time. In return, you pay me a one time payment today. This is essentially an annuity which continues into perpetuity. How much is this annuity worth? The answer is that there is no answer. In other words, it depends. It depends on what rate of return you personally require on any investment which you make. Let's say that you only make investments when you can get at least a 10% annual rate of return. The most that you would be willing to pay for this annuity is \$100,000, since \$10,000/\$100,000 is 10%. If someone else wants a 15% return, for them the annuity is worth \$66,667. This rate of return is your discount rate, the rate at which all future cash flows, or annuity payments, are discounted by. Below is a table of the most someone would be willing to pay for this perpetual annuity for various discount rates.

Discount Rate Value of Annuity
3% \$333,333
4% \$250,000
5% \$200,000
6% \$166,667
7% \$142,857
8% \$125,000
9% \$111,111
10% \$100,000
12% \$83,333
15% \$66,667
20% \$50,000

The takeaway is that the value of a stream of future cash flows depends on your required rate of return. And your required rate of return is up to you. You'll see people using formulas to calculate discount rates - these people are missing the point. There is no "correct" discount rate. If you want a 10% rate of return and someone tells you that they've calculated that the discount rate for an investment that you're looking at should be 7.5%, ignore them. If you can't get your 10% return, don't invest. It's as simple as that.

## Growing Cash Flows

Now imagine that I sweeten this deal. Instead of a \$10,000 annuity payment every year I increase the payment by 3% each year after the first year. The calculation is now slightly more complicated - we need to use the discounted cash flow equation from above. The equation for the value of the annuity now looks like this:

For a discount rate of 10% this new growing annuity is worth \$142,857. For a discount rate of 15% the growing annuity is worth \$83,333.