Introduction
SBIR grants are a key source of early stage financing for many small companies – awards are frequent, transparent, 100% funded (allowing significant nondilutive 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 taxpayerfunded research into highly valuable products and helped build hundreds of successful companies.
Startups trying to embed SBIR into planning can use Monte Carlo methods to analyse

Total SBIR contract revenue over a time period and likelihood

Cash flow over time and the associated variances

The effect of increasing the number of applications on total and revenue and cash profile

Increasing future resources required to execute and support grants – Including increasing headcount and capital expenditures
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 followon 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 recalculate 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 valueatrisk 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 resample from the distributions by pressing the recalculate button. Each time we do this, we obtain new realizations of the uncertain quantities and a corresponding new contract revenue sample. Using the spreadsheet addin 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 valueatrisk 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