On Thursday, February 27th, Arena Pharmaceuticals (NASDAQ:ARNA) reported disappointing sales of their new diet drug BELVIQ. BELVIQ sales came in at the low end of a wide range of estimates. Arena's worldwide sales partner Eisai and Arena enthusiasts predicted much higher BELVIQ sales by now, over six months after product launch. Friday, Arena stock is dropping in response to those disappointing earnings.

In its quarterly report and conference call, Arena noted a number of factors that could boost sales in the near future. Eisai doubled its sales force. TV ads will begin in April. Insurance company coverage is expanded now to cover most Americans with health insurance. The companies are seeking approval for BELVIQ in Switzerland, Mexico, Canada, Brazil, South Korea and elsewhere in the future.

Investors want an estimate of future BELVIQ sales to decide if Arena Pharmaceuticals is a worthy or risky investment. How fast may sales of BELVIQ rise to justify a higher stock price? What's the highest realistic rate of prescriptions BELVIQ may reach in the future? It may take a few years for M.D.s to feel comfortable prescribing a new drug and for insurance coverage to become nearly universal. It will take years for BELVIQ to be approved for use in additional countries. In order to invest early while Arena's stock price is relatively low, there needs to be some fact-based confidence in future sales. Or conversely, investing in Arena Pharmaceuticals might be judged too risky given the low sales of BELVIQ predicted for the next few years. Let's look at comparable products to estimate the sales of BELVIQ in future years.

There are some historical precedents to consider. These comparisons can be used as a basis to estimate future sales of BELVIQ. You may use these facts to make your own estimates. You may wish to research additional comparisons to add to the confidence of your projected BELVIQ sales estimates.

- Spencer Osborne tracks BELVIQ sales and publishes results regularly here at Seeking Alpha. He notes about 164,000 obesity prescriptions per month reported by Symphony alone. BELVIQ is up to about 7,000 (4% of obesity prescriptions) so far. Cheap, well-established generic Phentermine gets about 81% of those prescriptions. We might estimate that BELVIQ ends up with ten times their present number or 70,000 prescriptions per month in about two years. The total number of diet prescriptions may rise significantly. Total diet drug sales are not a fixed size pie to be divided. With only 2% of Americans using weight loss drugs, increasing attention to the dangers of obesity, and new drugs to treat obesity, those total sales should be expected to rise. Spencer Osborne typically adjusts Symphony numbers by 1.2, since Symphony doesn't cover all sales channels of BELVIQ. Multiplying by 1.2 would translate to 85,000 BELVIQ prescriptions per month. That's over a million BELVIQ prescriptions per year.
- Fen-phen was a popular but ill-fated diet drug available from the 1990s until it was pulled from the market in 1997. Some believe that the reluctance of M.D.s to prescribe BELVIQ involves potential fears that BELVIQ may cause similar heart valve damage. About 5 million people took Fen-phen. Thus far, about 100,000 have taken BELVIQ (about 2% of Fen-phen total). Assuming BELVIQ is proven over years of use to be a safe and effective treatment for obesity, one might estimate five million people to use BELVIQ. Since the number of obese Americans doubled since 1990, you may wish to double that estimate to ten million potential BELVIQ prescriptions over time. That may translate into one million prescriptions per year in about three years' time, and perhaps two million prescriptions in BELVIQ's peak sales year.
- Statin drugs to control cholesterol have been quite popular and lucrative for drug companies. In 2006, there were 13 million statin prescriptions per month. Lipitor sales alone reached $11 billion in sales in 2009 and 2010. Over 15 years, Lipitor had over $125 billion in sales! BELVIQ so far is less than 1% of that number of prescriptions. BELVIQ gross sales were reported as a comparatively paltry $7.3 million last quarter. We may not wish to believe that BELVIQ could reach those mighty sales numbers, but consider them the maximum possible. Besides, sales partner Eisai would get the majority of the proceeds according to their agreement with Arena. We might estimate BELVIQ and obesity drug combinations including BELVIQ to reach a quarter of statin, or 3 million prescriptions per month at its peak in five years' time. That's over 35 million BELVIQ prescriptions in its peak year.
- There were about 340,000 gastric bypass surgeries to treat obesity in 2011. Given the possible complications involving these surgeries, that appears to be a surprisingly high number willing to undergo surgery. There does not appear to be many reasons that people would not try BELVIQ before considering surgical procedures. Therefore, we might estimate at least 350,000 BELVIQ prescriptions yearly within 2 or 3 years.

So far, these estimates range from one-third to one million prescriptions per year by about 2016. Sales may peak at 35 million BELVIQ prescriptions in about five years.

Arena nets 32-40% of BELVIQ revenues in their sales agreement with Eisai, including various milestone payments. A reasonable stock price can be estimated by multiplying their net income times 20, a typical price earnings ratio for a growing company. You may wish to subtract R&D and other expenses from their net income before computing a stock price. You may wish to add the potential value of other products in Arena Pharmaceuticals' drug discovery pipeline. By my calculations, Arena's BELVIQ product line is worth $8/share for a third of a million scripts, $31/share for 1 million prescriptions and $1,000 maximum per share if BELVIQ reaches a market dominating 35 million prescriptions per year. That highest prescription rate would have almost 15% of obese people using BELVIQ worldwide, or less since BELVIQ is used for overweight individuals, improving blood glucose levels and smoking cessation.

**Expected Value**

In probability theory and decision-making, there is a concept called "Expected Value." The expected value is the sum of the possible values of an entity, multiplied by the probability of reaching each of those values. For example, in early 2012, Arena Pharmaceutical stock was under $2 per share. The FDA Advisory Committee had rejected Arena's diet drug application initially in 2010. Rejection sent the stock from almost $8 to under $1.25 in 2011. However, the FDA Advisory Committee listed a number of analyses that had to be completed to re-apply. Although Arena did complete all the analyses successfully, their stock continued to languish below $2. I used the "expected value" analysis to determine the stock was a very positive gamble by computing an expected value. Here's a simplified illustration:

- If the diet drug was rejected again, its value would be cut in half from $2 to $1. Assume the probability of rejection is 50%.
- If the diet drug is approved, and approved later by the FDA, its value would climb over $8 again, probably 50% higher to $12. Assume the probability of approval is only 50%.
- Multiply $1 by 50% rejection probability to get $0.50 of value.
- Multiply $12 by 50% approval probability to get $6 of value.
- Add the values together to obtain $6.50.
- So the stock trading around $2 has $6.50 expected value. Its expected value is 3.25 times the current price. This appears to be a very good gamble, although the final outcome was not known.

Lately, Arena's stock has been ranging around $6-$7 per share. A similar expected value analysis could be done with the estimates for future sales.

- If it is discovered that BELVIQ has hidden disastrous consequences on health, assume Arena's value falls to $0. Assume this probability is 10%.
- If BELVIQ sales continue to languish not much higher than current levels, the stock may trade for $1 per share. Assume the probability is 25%.
- BELVIQ sales may rise modestly with more insurance coverage, a larger sales force and TV ads, and greater MD confidence as BELVIQ works successfully in treating obesity and other indications. If it reaches a third of a million prescriptions annually, assume the stock is priced fairly at $8 per share. Assume this probability is 30%.
- Assuming BELVIQ, future drug combinations, and additional medical uses for smoking cessation and diabetes prove lucrative; prescriptions could reach several million per year. Assume the stock price reaches $30 and this probability is 30%.
- Finally, BELVIQ could reach its maximum potential, with 35 million prescriptions in a year, and the stock price hits $1,000 per share. Assume the probability is 5%.
- Multiplying each of the possible stock price estimates by their respective probabilities yields an expected value of $61.65. The computation is:

**Expected value = $0 X .10 + $1 X .25 + $8 X .30 + $30 X .30 + $1,000 X .05 = $61.65**

This expected value is almost ten times the current Arena Pharmaceuticals' stock price. Eliminating the very high maximum potential scenario brings the expected value closer to $12, still about double the current stock price.

- Create your own scenarios, compute a reasonable value for the stock based on 20 times sales revenue estimates, and guess a reasonable probability for each of your scenarios. Make certain that the probabilities add up to 100%. Multiply each stock price by its probability, and add results to compute an expected value based on your assumptions.

**Concluding Comments**

BELVIQ has had a disappointing, slow rollout for investors in Arena Pharmaceuticals. M.D.s and large pharmaceutical companies do not want to risk involvement in a repeat of the Fen-Phen disaster. They may wait a couple of years to see if there are undiscovered problems that arise with BELVIQ. Doctors may continue with better-known alternatives until more data is available on BELVIQ's successes and failures. Many of us expected much faster BELVIQ sales growth given the initial data on BELVIQ's effectiveness and minimal side effects, and apparently positive impacts on blood glucose levels and sleep. But sales may ramp up substantially. Patience and patients are required!

This article provides some methods to estimate future sales of BELVIQ or other products. I do not recommend anyone invest in Arena Pharmaceuticals or any other stock based on the data or the methods illustrated in this brief article.

Everyone needs to do their own due diligence before making any investment.

**References**

Linda A. Johnson, Associated Press. "Against odds, Lipitor became world's top seller." USA TODAY, 12/28/2011.

Osbourne, Spencer. Arena's Belviq Sales To Hit $150 Million In 2014? Seeking Alpha, Feb 28, 2014.

Wikipedia article on Fenfluramine/Phentermine

**Disclosure: **I am long ARNA. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.