Recently, I explained how to forecast potential drug sales in Don't Be a Biotech Gambler and Unraveling Biotech Potential. The drug BAY 43-9006 from Onyx Pharmaceuticals (NASDAQ:ONXX) and Bayer (NYSE:BAY) provided a good example, which would fit most situations, but it had some shortcomings nonetheless. The biggest drawback is in using exact estimates for variables such as market share when it's not possible to pin down a specific figure.

Using my earlier method, I came up with an annual revenue estimate of $100 million for BAY 43-9006 in the treatment of renal cell carcinoma. While this yielded a convenient result, it is just one possible outcome and does not reflect all of the likely sales levels that a drug could reach. Any drug can attain a broad spectrum of potential sales if we take into account the variability of such estimates as market share and drug pricing.

A random solution
There is an alternate method to forecast drug sales: the Monte Carlo simulation. As you probably guessed, the method's name is from Monte Carlo, Monaco, because of the dice games at the casinos. Monte Carlo simulation is simply a way to model sales given the uncertainties involved in trying to predict the future. I highly recommend the in-depth tutorial in the link above.

To refresh your memory, the formula for drug sales is:

sales = number of patients X market share X monthly drug price X months of treatment

All four variables that go into the sales formula require quite a bit of guesswork and one's best assumptions. For example, I picked a market share of 25% for BAY 43-9006 if it was approved, even though I'm not prescient and have no way of knowing if actual market share will turn out to be 10% or 30%.

When using Monte Carlo simulations, we don't have to make these types of guesses. Sticking with market share, instead of using only 25% as the estimate, a broad range of 5% to 40% can be selected, and then the computer program that runs the simulation will select a random number within that range. (Some numbers are more likely to occur than others depending on the probability distribution.)

Once the likely range of values and the probability distributions for each variable have been chosen, it is time to sit back and let the computer do its thing. To run a sales estimate for BAY 43-9006 in renal cell carcinoma using a Monte Carlo simulation, I set up the following parameters:

Variable Low High Most Likely Distribution Type
Number of patients 10,600 21,400 16,100 Triangle
Market share 5% 40% - Uniform
Drug AWP $1,900 $2,700 - Uniform
Number of months of treatment 1 12 8 Triangle

Following the formula
Once the model is built and the parameters are in place, the program will go down the list and pick a random number within the range for each variable. For example, it could pick 15,000 patients, 10% market share, $2,000 drug cost, and seven months of treatment. Multiply all those together, and the sales estimate would be $21 million.

The power of the Monte Carlo simulation is that you don't just do that one time, but multiple times. After repeating this process thousands of times, you get quite a lot of information. Instead of just a single sales estimate like I demonstrated in the last article, Monte Carlo produces a range of sales and the probability that different sales levels will occur. Running 10,000 trials using the parameters above yielded the following results:

Average sales: $66.7 million
Standard deviation: $40.3 million

5%: $15.5 million
95%: $143.8 million

The probabilities of different sales levels are below:

$0-$24 million: 13%
$24-$48 million: 26%
$48-$72 million: 21%
$72-$96 million: 16%
$96-$120 million: 11%
$120-$144 million: 7%
$144-$168 million: 3%
$168-$192 million: 1%
$192-$216 million: 0.3%

The results using the Monte Carlo simulation provide quite a bit more information than the method I used previously. It is also interesting that the average sales estimate of $66.7 million from the simulation is considerably less than the $100 million in sales I originally worked out. Still, it is in the same ballpark, which is a good thing. The probabilities generated from the simulation give my original $100 million estimate about an 11% chance of occurring. According to this model, a sales range of $24 million to $72 million is most likely, as 47% of the trials gave an estimate in that range.

With the results of the simulation, I think we have a better feel for how a drug like BAY 43-9006 could perform than we did previously off of the original estimate.

Final thoughts
I'm a math geek, so I like to play around with drug-revenue-simulation models like Monte Carlo. I think the process has some strengths over trying to pin down a specific sales estimate. The big advantage is that using such a model changes the question from "What is the sales estimate?" to "What is the range of possible sales?" and "What is the probability that different levels of sales will occur?" In other words, the model lets you be "roughly right" instead of precisely wrong.

As with all models, there are some drawbacks. Even with a technique such as Monte Carlo that is designed to handle uncertainty, the results are still only as good as the assumptions used. A lot of careful thought needs to go into making the assumptions so that the results are meaningful. Using random assumptions that are not grounded in fact will create a garbage-in/garbage-out outcome.

Despite the caveats, if we are going to invest in drug companies, we need to have some idea of how well their drugs may sell. Otherwise we are flying blind. My preference is to use a bottom-up method like Monte Carlo, but others may want to use a top-down approach, such as attaining a percentage of the overall market size.

In a practical sense, the best investments are where the value is so clear and so obvious that number crunching on a spreadsheet is unnecessary. Despite their usefulness, revenue models are simply a tool and are not a replacement for common sense and rational thought.

For readers interested in following my biotech series, in coming articles, I'll get into valuing biotech companies using these sales forecasts as a starting point. We'll use more subjective math as we work from sales to derive the net present value of drug programs. That's where it starts to get into the meat of biotech company valuation.

For more on the biotech industry, check out Charly Travers' recent coverage:

Do the details of the Monte Carlo simulation mystify you? Post your questions to learn more about this useful modeling tool on the Biotech discussion board.

Fool contributor Charly Travers. Charly does not own shares in any of the companies mentioned in this article. The Fool is investors writing for investors.