# 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, C_{i} 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.

## Margin Of Safety

Let's say that you want a 10% rate of return and I offer to sell you this growing annuity for $140,000. You've calculated that the present value of all future annuity payments is $142,857, which means that you can buy the annuity at a discount to this value. There is one thing that you haven't taken into account though - the risk that I take your money and skip town. In other words, there is a risk that the annuity payments won't happen. How do you account for this risk? You introduce a *margin of safety*. A margin of safety allows you to be wrong a percentage of the time and still achieve your required rate of return. Imagine that there are hundreds of different people selling these annuities and you want to buy 50 of them, each from a different person. You determine that for each annuity salesman there is a 10% chance that they will steal your money and skip town. Because of this you apply a 10% margin of safety, meaning that you reduce your maximum purchase price by 10%. You only buy the annuities if you can pay $128,571 for each one. If 10% of these pay you nothing and 90% pay you the annuity payments, then your total rate of return will be your required 10%. The margin of safety allows you to be wrong a fraction of the time and still achieve your required rate of return.

This framework can now be used to value a company, since a company is essentially just a stream of future cash flows. Go to Discounted Cash Flow - How To Value A Stock to find out how.

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