By most measures, Eli Lilly (NYSE:LLY) stock looks cheap. It trades at a P/E ratio of 7.7. It yields 5.6%, more than three times the yield on the S&P 500. But like other pharmaceutical companies, it faces a patent cliff, in this case beginning this year. Its bestselling drug, Zyprexa, loses U.S. patent protection in October. At $5.0 billion in sales, Lilly will be hard pressed to replace this 22% of revenue. And unlike some other companies, it does not appear to be able to immediately replace those revenues and earnings. Is Eli Lilly a value trap, sucking in investors with promises of a low P/E and high yield, only to eat their money alive?

The answer to that depends on determining an accurate valuation. So how do you value Eli Lilly, a company whose earnings are falling? Clearly a P/E isn’t sufficient, or all stocks would trade at the same P/E and company growth rates wouldn’t matter. A PEG ratio (given by the P/E ration divided by the earnings growth) fails spectacularly when earnings are constant or decreasing. Other metrics such as book value or dividend yield fail to take a company’s growth (or lack thereof) into account. A discounted cash flow valuation model, however, can easily incorporate falling earnings, and an analysis using this method shows that Lilly is slightly undervalued.

The discounted cash flow model simply says that a company is worth the total of all future cash flows. These cash flows must be discounted because dollars received from an investment today are worth more than dollars received from an investment in the future. The amount of this discount should be what investors could receive from an alternative investment. When comparing the relative value of stocks, the alternate investment is the market as a whole, so we want to use the market’s long-term return as a discount rate. Since it’s impossible to know the future return, history is a suitable guide. Let’s use an historical value of 11%.

To start our evaluation of Eli Lilly, let’s take a pessimistic case. Analysts already expect that 2011 earnings will be a decline from 2010, and predict a wide range of possibilities for 2012. So we’ll use the bottom analyst numbers for Lilly for 2011 and 2012, $4.15 and $3.15 respectively. More than three-fourths of Lilly’s revenues come from a mere 8 drugs, so Lilly is particularly sensitive to the impact of one and is more dependent on finding a replacement billion-dollar drug. However, none of these lose patent protection in 2012.

To continue our Debbie Downer projection, let’s assume earnings keep falling, at a rate of 15 cents a share per year for the next 4 years. After that, they remain constant. This projection has earnings per share decline by 9.3% annually for the next 6 years, even though Eli Lilly has over the last 10 years grown earnings per share at an annual rate of 6%. In this unprecedented scenario for Eli Lilly, the discounted cash flow model gives a fair value of $26.73.

In a medium case, let’s use a medium projection for 2011 of $4.30 in earnings per share, and a fall of 15 cents a share each year for the next 4 years. Earnings then stay constant at $3.70 a share from 2015 into perpetuity. Productwise, this would mean that Eli Lilly is able to introduce products to maintain current profits, but is unable to ever grow them. In this scenario a discounted cash flow model values Eli Lilly at $34.86 per share.

This is almost exactly the current share price of Eli Lilly, and so this (or a model similar to this) is effectively what the market thinks is either the most likely or a weighted average of all scenarios. Incidentally, another scenario that would give the same fair value is 2011 earnings of $4.25, decreasing by 50 cents each year to $2.25 in 2015, and then has earnings grow 5% annually in perpetuity.

Even an optimistic scenario for Eli Lilly involves decreasing earnings for the next two years. If Lilly’s earnings come in at the top of analysts expectations for 2011 and 2012 at $4.42 and $4.30 respectively, it is likely that earnings will continue to fall until new products are released to replace those sales. With 8 molecules in Phase 3 clinical testing and 21 molecules in Phase 2, it seems likely that revenue will eventually come back to current levels.

A modest projection for earnings is a fall to $4 a share for 2013, 2014, and 2015, and then growth at the average health care industry rate of 4%. This gives a fair value over $49 per share. A slightly more aggressive projection that involves 4% annual growth beginning two years earlier in 2014 gives a fair value of $54 per share.

How do we know which scenario is the most likely? The best answer is to pick the course of action you think is most likely, and act on that scenario. Alternatively, we could acknowledge the fact that we don’t know how Eli Lilly’s pipeline of drugs will contribute to earnings 5 years out and greater, and simply take a weighted average (also called scenario analysis). If we assign a 20% probability to the pessimistic case, 50% to the medium case, and 30% to the first optimistic case, we come up with an overall weighted fair value of about $37.50. This is about 7% more than the current share price of Eli Lilly, suggesting that it is nearly fairly valued.

With a nice fat dividend of 5.6% (which remains well-covered under all scenarios discussed above), Eli Lilly is an attractive stock perhaps more appropriate for those looking for dividend income than just capital appreciation. And if you believe that Eli Lilly will restock its pipeline and introduce new products to restart growth within the next 5 years, the stock looks quite attractive.

**Disclosure: **I am long LLY.