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# Discounted cash flow

Discounted cash flow (DCF) is a valuation methodology used to estimate a security's intrinsic value.

## Expanded Definition

As has been stated elsewhere, the value of a business is how much cash it can return to its owners over its lifetime. You would be small-f foolish to invest in a company that doesn't give you anything back for your investment. The question, though, is how to avoid that? How do you find businesses that will give you a great return?

One way to start is to estimate a value based on estimates of the cash flows the business produces or may produce.

"Estimate" is the mot juste, not "calculate," because the results from calculations like these are just that -- estimates. They are based on several assumptions, any one of which can be wrong and throw off the whole thing without you realizing it. So, if you ever hear or read someone saying that "Microsoft is worth $39.57 per share," run away. The best that could probably be said is that it might be worth anywhere from$30 to $50 per share. Intrinsic value is a fuzzy target, at best. ### The basics Back to estimating the value. In a DCF model, one is estimating the cash that the business generates and which could be paid to the owners, the shareholders. If that cash flow is a dividend, then the model is called a dividend discount model. However, what if the company doesn't pay a dividend? Other cash flows must be used. A popular substitute is free cash flow (FCF), which may be simply defined as cash flow from operations (CFO) minus capex. Both cash flow from operations and capex are found on the statement of cash flows. Note that in calculating FCF, capex is already a negative number, so don't subtract the negative (which means adding). CFO - capex and just go with it. Since FCF can be somewhat lumpy, it might be a good idea to use an average from two to five years. #### Growth rate Now you need a growth rate. How fast will the company grow free cash flow? That's the question, now, isn't it? And it is right here that the biggest errors creep in. People tend to overestimate how fast a company can grow. One idea is to look at the past several years, take an average, and then reduce that in stages. A three-stage model might take the last 3-years' growth rate, apply it to the next five years, chop it in half for the next five years, and then reduce it to 3% (the long term rate of inflation, e.g. no "real" growth) from then on. Maybe you should use several different sets, such as an "aggressive," a "moderate," and a "conservative" scenario. #### Discount rate Once you've got the growth rate, you need a discount rate. This could be the firm's weighted average cost of capital (WACC). It could be Buffett's 10-year treasury yield plus 5%. It could be your expected rate of return. It could be 12%, which is slightly better than the long-term return of the S&P 500. It could be weighted higher for "riskier" companies and lower for "safer" companies. See the problem? The calculated intrinsic value varies greatly with the discount rate used and will be lower the higher the discount rate is. You want one that is reasonable. Maybe you should choose several to see what the calculation kicks out under different scenarios. ### The calculation $V_0 = \frac{CF_0*(1 + g)}{1 + r} + \frac{CF_1*(1+g)}{(1 + r)^2} + \frac{CF_2*(1 + g)}{(1 + r)^3} + ... + \frac{\frac{CF_n*(1 + g)}{r - g}}{(1 + r)^n} = \frac{CF_1}{r - g}$ Looks pretty hairy, huh? Well, actually, all that is each year's estimated cash flow (CF) -- grown from the previous year by the estimated growth rate, "g" -- discounted back to present-day dollars by the discount rate, "r." Note that it starts off with next year's estimated cash flow because this is an estimate of future cash flows. So, if you had a 2-stage model of 3 years growth at 10% and 3% thereafter, with a 12% discount rate, and$1,000 in starting FCF, it would look like:

$V_0 = \frac{1,000*(1.10)}{1.12} + \frac{1,100*(1.10)}{(1.12)^2} + \frac{1,210*(1.10)}{(1.12)^3} + \frac{\frac{1,331*(1.03)}{0.12 - 0.03}}{(1.12)^3}$
$V_0 = 982.14 + 964.60 + 947.38 + 10,842.23 = 13,736.36$

### Use a spreadsheet

Using Excel, the above is done as follows:

 A B C D E 1 Rate Year CF DCF 2 g1 10% 0 \$1,000.00 3 g2 3% 1 =D2*(1+B2) =D3 / ((1+B4)^C3) 4 r 12% 2 =D3*(1+B2) =D4 / ((1+B4)^C4) 5 3 =D4*(1+B2) =D5 / ((1+B4)^C5) 6 Terminal =(D5*(1+B3)) / (B4-B3) =D6 / ((1+B4)^C5) 7 8 Total =sum(E3.E6)