### Using discounted cash flow (DCF) to value a stock

Background

DCF is a valuation method used to value a project, company or asset. In general, DCF uses future cash flow estimates and discounts them back to present day (using a discount rate).

Once future cash flows are discounted back to present value, one can determine whether or not a given investment is a good idea. When valuing a stock using DCF, you can estimae all future earnings of a company, and then use the discount rate to find the present value. The present value of a company's projected earnings is then considered the ‘fair market value’ of the stock. (keeping in mind the list of caveats at bottom)

Applying DCF to value Apple

The above can be hard to visualize - so, I made a small example to help explain what we're doing here. Imagine we're trying to use DCF to value Apple, given the following information:

• Earnings per share (EPS): \$9.2
• Earnings will grow 17% for the next 10 years, before leveling off to 2% after.
• The S&P 500 (an appropriate benchmark), is returning 11% per year.

Using the above, here's how Apple's earnings would look for the first 10 years (where earnings are growing at 17%) as well as years 11-infinity (where earnings growth has flattened off to 2% per year):

Now that we have a forecast of Apple's future earnings from years 1-10 and 11-infinity, we just need to take the present value of those earnings. We can do this using our discount rate (I'm using the S&P 500 return of 11% here). The discount rate is the cost of capital, or, in other words, the return we could have gotten by choosing a different investment (e.g. investing in S&P 500 instead of AAPl).

Simple enough, right? The difficult part here is really nailing the inputs, e.g.:

• How much will Apple's earnings initially grow and for how long? (here we have 17% and 10 years)
• After initial growth, how much will Apple's earnings grow by into perpetuity? (here we have 2%)
• What is the appropriate discount rate? (here we have 11%)

Nobody really knows the answers to the above, which is why this valuation method (and any stock valuation method) is just a guess.

Formula for valuing stock using DCF

Putting this DCF calculation into a formula would look something like this:

$$\sum_{0}^N \frac{E(1+g_0)^N}{(1+r)^N}+\frac{[E(1+g_0)^{N}\frac{(1+g_1)}{(r-g_1)}]}{(1+r)^N}$$

$$E =$$ Earnings per share
$$g_0 =$$ Earnings growth rate attached to first N years
$$g_1 =$$ Terminal earnings growth rate from N+1 to $$\infty$$ years. Should be around inflation.
$$r =$$ Discount rate, desired rate of return. S&P 500 return is a good proxy.
$$N =$$ # of years earnings will initially growth at rate $$g_0 =$$ (before leveling off to rate $$g_1$$ into perpetuity) .

As shown in the above formula, we are determining the 'fair market value' of the company by discounting two components back to present value:

• Present value of the company's future earnings growth at rate $$g_0$$ for N years.
E.g. Apple grows earnings at 17% for the next 10 years in example above
• Present value of the company's terminal earnings growth at rate $$g_1$$ from year N+1 to infinity.
E.g. Apple grows earnings at smaller rate of 2% from year 11-infinity in example above

Caveats/words of caution

This formula is just a single tool, and should not be used to solely make an investment decision. You can do all sorts of crazy things with how you define earnings (e.g. GAAP vs. FCF), and there are multiple different stances on the best way to value the terminal earnings component (e.g. EBIDTA exit multiple, limit terminal value to a # of years, etc).

The formula is best used as a framework to highlight core assumptions and check sensitivity to them. That said, below are some explicit words of caution to keep in mind when using this formula:

• You can manipulate the inputs to show whatever valuation you want - The stock valuation is of course very sensitive to the expected earnings growth rate as well as the discount rate. The real trick to valuing a stock is not just in knowing the formula, but in having a good basis for the formula's inputs. When in doubt, be conservative.
• Assumes the market is rational - Even if you were able to perfectly guess the formula's inputs, you'd still have to hope that the stock market acted rationally for the company to realize the 'fair market value' you calculated.
• Only works for companies with predictable earnings growth - If a company's earnings growth is all over the place (e.g. -XX% one quarter and +YY% another), then it will likely be too volatile to actually value using this framework. In other words, this framework is best used for more mature companies with more predictable earnings (otherwise, your inputs will just be wild guesses).

Calculator

Here is the calculator I made using the above methodology.