*Editor's note: This article has been updated and corrected to fix errors in the Gordon Growth model example. We apologize for the mistake. *

Last week, we glimpsed at how relative valuation techniques apply -- or rather, *don't * apply -- to **Texas Instruments**

**Dividend discount**Since Texas Instruments pays a dividend, we can estimate the future value of all dividend payments and then discount their value back to present-day dollars. In this way, we can arrive at a fair price for those expected cash returns.

Let's look at the venerable Gordon Growth model first. It's a simple version of the dividend discount model, meant to apply to mature companies at which the dividend can be expected to grow at a steady rate, from here to eternity. For this model, we need two inputs: expected rate of growth, and cost of equity -- i.e., a discount rate to apply to the value of future earnings.

I'm using a 15.2% beta-adjusted discount rate (to account for the historical volatility of the stock; my base discount for most stocks is a less aggressive 11%) and a stable 5% dividend growth rate. That gives me a fair value of $1.65 per share, or a $2.5 billion market cap. If I lower my discount rate to my usual 11%, the implied market cap goes up to $4.2 billion, or roughly 68% higher than with my first discount rate. Lowering the discount rate even further to 8% returns an implied market cap of $8.4 billion -- twice the value when the discount rate stood at 11%!

Like I said, the Gordon Growth model depends on some very simple math, and the equation can produce some funky results when the growth rate approaches or exceeds the discount rate. This limitation is dramatically compounded when using the model on a company that pays a relatively small dividend such as Texas Instruments. The technique works better when applied to more generous dividend payers.

**Multistage discounting**So put that calculator away, and let's move to another method. You'll use a spreadsheet for the more advanced version, if you value your sanity. I'm using one of NYU Professor Aswath Damodaran's excellent (and freely distributable) valuation spreadsheets here, namely the two-stage dividend discount model (link opens an Excel spreadsheet). You can also find some discussion of this model.

With the same inputs as before for the first five years, and a conservative 5% dividend growth rate after that, we get a $71.7 billion fair-value cap, or $45.98 per share. That's a 50% premium over today's stock price, and at the end of the five-year high-growth phase, you would get $0.34 per share in annual dividend. Sweet.

But again, there are some weaknesses. If you increase the current dividend by a single penny per quarter, you get an $85 billion company. Decrease it by a penny, and Texas Instruments is just about fairly valued today. Because these guys don't pay a very large dividend, these models are susceptible to huge value swings on very small input changes. Therefore, it's tough to depend on this technique to value a growing boy like 56-year-old Texas Instruments, and again, it's better applied to dividend-happy companies such as large banks, old-line manufacturing companies, and so forth.

**So, what next?**That's two rounds of inappropriate valuation techniques. But I think we've seen some progress here, and you may have some other companies in mind for which discounted dividends make more sense.

Sometimes, it's the journey and not the destination that counts. Next time, your angelic patience will be rewarded as we'll finally meet the perfect match for tough valuation targets such as Texas Instruments in the discounted-cash-flow model.

Further Foolishness:

- Finding True Value: Relative Valuation
- What Is Valuation?
- Fool's School: Stock Valuation
- Foolish Fundamentals: Valuation

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*Fool contributor Anders Bylund is a Bank of America shareholder but holds no other position in any of the companies discussed here. You can check out Anders' holdings if you like, and Foolish disclosure is worth its weight in recycled electrons.*