SBIR Monte Carlo Analysis


SBIR grants are a key source of early stage financing for many small companies – awards are frequent, transparent, 100% funded (allowing significant non-dilutive growth), and may result in product revenue as the agencies act as informed customers. Here is a useful link explaining SBIRs and a report by David Connell, which argues that the UK should urgently introduce the US SBIR scheme that has successfully converted billions of dollars of taxpayer-funded research into highly valuable products and helped build hundreds of successful companies.

Start-ups trying to embed SBIR into planning can use Monte Carlo methods to analyse

  1. Total SBIR contract revenue over a time period and likelihood
  2. Cash flow over time and the associated variances
  3. The effect of increasing the number of applications on total and revenue and cash profile
  4. Increasing future resources required to execute and support grants – Including increasing headcount and capital expenditures

Formulating a static income model – Download the excel model here

We begin with a functionally valid model of cash flow generation from SBIRs over time. The following is a static, logical model of cash flow generation through SBIR awards. An SBIR grant is typically divided into Phase 1 and Phase 2 (there is possibility for follow-on funding, however the intricacies will not be covered here), worth $100k and $750k respectively. Historical data is in the public domain enables us to estimate the likelihood of attaining a Phase 1 and subsequent Phase 2. The likelihood of a successful Phase 1 award is approximately 25% and Phase 2 is 50%.

Monte Carlo income model

Whilst traditional static NPV analyses take projections of the uncertainty drivers as input and produce a numerical estimate of the value of the project, a Monte Carlo simulation takes distributions of the uncertainty drivers as inputs and produces a distribution of the value. For example instead of assuming a fixed number of successful Phase 1’s per year we can create a distribution to reflect the fact that in one year we may get none while in another we may get 4.

The underlying technology for Monte Carlo simulation is that of random number generation. The total SBIR contract revenue spreadsheet can be “randomised” by replacing the number in each uncertain cell by a random number generator which samples a number from an appropriate distribution. Each time we press the re-calculate button, the computer fills all uncertain cells simultaneously with sampled values. In other words, the computer creates a scenario from appropriate distributions and calculates the corresponding SBIR contract revenue. We can ask the computer to do this many, say 5,000 times and to gather the corresponding revenues. The risk profile of the project is now obtained by setting up a value-at-risk chart from this list of revenues. This shape reflects the spread of revenue obtained from 5,000 simulated outcomes.

Modelling the number of successful SBIR awards

The starting point of the Monte Carlo simulation is finding a way to capture the uncertainty in how many grants we are likely to be awarded, for example, if we apply for 4 SBIR’s in one financial quarter what is the likelihood of getting one award? Two awards? No awards? The problem is identical to coin tossing. If there is a 50% chance of getting heads what is the chance of getting 3 heads if I flip the coin 4 times? This is described mathematically using a binomial distribution.

Where P(n) is the probability of exactly n successful SBIR awards

N is the number of SBIR applications

p is the probability of a successful application for one SBIR application.

The following is the probability density function for the binomial distribution of grant applications. If we make 4 applications and there is a 25% chance that a single application is successful then we see that there is a 31.6% chance that we will not receive any awards and 0.4% chance that we would receive all 4.

A similar model applies for Phase 2 awards, except they are also dependent on the number of successful Phase 1 applications.

Incorporating an uncertain number of successful SBIR awards into cash flow

Estimates of the number of awards have now been replaced with a binomial distribution to capture the uncertainty. Every time the computer recalculates it creates a scenario from the appropriate distributions and calculates the corresponding SBIR contract revenue. The yellow cells contain a binomial distribution. Here are two simulated outcomes

The two example scenarios are just two possible instances of what might actually happen and it is very clear that there can be a significant difference in the amount of contract revenue obtained. In the latter scenario there have been far fewer successful Phase 1 and 2 applications and a difference in over $4million in received contract revenues.

We can use the spreadsheet to re-sample from the distributions by pressing the re-calculate button. Each time we do this, we obtain new realizations of the uncertain quantities and a corresponding new contract revenue sample. Using the spreadsheet add-in software @Risk from Palisade tools we can automatically do this many times and collect these revenue’s in a list, and obtain a good idea of the distribution of the possible outcomes. The possible revenue outcomes can be graphically represented either as a histogram or as a value-at-risk chart.

Monte Carlo Income Statement results (4 applications per quarter)

Value at Risk – Total SBIR contract revenues (4 application per quarter). The curve on the value at risk chart gives the likelihood that the contract revenue lies below or above the target values given on the horizontal axis. Risk profiles are ideally suited to convey the variance associated with the contract revenue. For example, on the chart below, the likelihood of total SBIR revenues less than $6M is approximately 30% and the likelihood of more than $6M is approximately 70%.

Value at Risk – Yearly contract revenues (4 application per quarter)

Summary Income Chart – Quarterly contract revenues (4 application per quarter)

Monte Carlo Income Statement results (6 applications per quarter)

Phase 1 distribution function

It is clear an increased number of applications per quarter will result in higher total SBIR contract revenue

Value at Risk – Total SBIR contract revenues (6 applications per quarter)

SBIR Income Summary Table

The following table summarises the key information on the timing, likelihood and amount of contract revenues

3 Responses to SBIR Monte Carlo Analysis

  1. Shamus says:

    Nice discussion – the one thing it doesn’t take into account is the “shotgun” mentality that crops up when people start to rely on government grants – let’s apply for everything. At some stage it becomes clear that, in theory, applying for everything must have a positive outcome, if every one (or even all on average) has a positive cost:benefit – this doesn’t take into account that you are much more likely to win only a subset of them, rather than using the global/historical proportion of wins. So you have to also work out the varying probability of success in applying for less and less directly relevant ones.

  2. acasoanalytics says:

    In general I think reliance on ‘some types’ of public funding is actually bad and can stunt the growth of a company. The main issue is that it is more akin to consultancy; you find a government fund to pony up some money, do the work and bill it with a small margin (I use ‘you’ in the sense of a generic tech start-up). The limitation is that this doesn’t scale, you’ll always be bandwidth limited on people doing the work. At the end you may have a demonstrator that you then try and shop around a few customers, but crucially with the type of funding you get in the UK it is unlikely to be productised and ready for general sale.

    With the SBIR the difference is that the tender comes from a customer with a specific problem that needs to be solved – it is about procurement not just funding R&D. They will fund the development (100% funding through multiple phases so the agency controls its own risk exposure) and at the end of it they want to buy the resulting product because it has fixed their problem. Assuming you have more than one customer! you can start to build a scalable product business around this output. For example, monitoring air quality in the cockpit of a jet fighter maps across to generalised air quality monitoring where we leverage the investment already made in consumer applications.

    I agree with that a pure shotgun approach is a recipe for disaster. You should only bid if a proposal takes you in the right direction of a scalable product or if it helps to defray costs for elements on your technology roadmap that you would have paid for anyway from company money. Again there is a qualitative difference between the SBIR and funding models in the UK; for the latter you would be hard pressed to even find all the open proposals and they would all have different rules for applying. In the early stages of growing a company you are trying to keep your head above water and wading in the quagmire of government funding options is usually not the best use of your time.

    With the SBIR there are huge number of proposals and a lot of available capital (~$4billion every year). If your technology has broad application it becomes feasible to apply for a large number. Our gas detection technology has applicability across military, security, medical and environment applications so we can target proposals across a range of government agencies. We can start to look at global probability of success in this context, but even in reduced subsets you often have sufficient ‘directed’ requirements that you apply for quite a lot. This may not be the case where there is a well defined and narrow application, but you may be able to find ways to package elements from other parts of your roadmap and get that funded.
    Another key difference is the barrier for applications and complexity is reduced; the process is centralised, you can easily see what proposals are open across all the agencies, so you eliminate the problem of search. New ones are added on a regular basis (they’ll even send you direct email alerts). The IP rules etc are same across the board as is the actual submission process so there is no learning curve when applying across agencies. You can apply multiple times, reuse the main body of content and tailor it for specific requirements.

    There are examples of companies in the US that have applied for and a very significant number of awards. From David Connells report there is, Foster-Miller, a Boston-based engineering and technology development firm founded by three MIT graduates to solve difficult technical problems for clients. By 1997 Foster-Miller had won 573 SBIR and STTR awards, including 147 Phase II awards. In total these were worth $108m in revenue to the company and in 1998 they represented 20% of its annual sales. This is not appropriate for all companies but does provide an indication of how significant funding can be leveraged through SBIR. The success of the individual companies that benefit from SBIR is parlayed up to a national level through a higher degree of entrepreneurship and dynamism.

  3. David Blair says:

    The challenge for all early stage technology companies is that they need cash to get going. The trouble is that the technology might be fantastic but it is often less clear how you might make money out of it- and the days of investors taking a punt on something interesting without a clear route to market are gone.

    The SBIR programme is a classic win-win. The government gets a good value solution to an existing problem and the company focuses on a commercial opportunity with a ready made market at the end. It would be great to see a value added comparison between products already acquired through the SBIR route against more “traditional” procurement methods.

    And talking of analysis- lets make more use of Monte Carlo modelling in our business planning. In finance cash is fact, the rest is opinion. Lets get some sort of confidence interval into our thinking of how much funding is needed. Not only is it more intellectually stimulating it is actually meaninful in management terms!

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