It is known that intangible assets are long-lived and used in the production of goods and services, however they lack physical properties. In most of the cases, intangible assets represent legal rights or competitive advantages developed by a firm. For valuation purposes, intangible assets must be readily identifiable and separable from other assets in the firm. Intellectual property (IP) is a subset of intangible assets; the ability to determine the market value of IP is a prerequisite for optimal patent strategies and for value-based IP management.

In the last decade, we have monitored increased patent litigation activity in the pharmaceutical and biotechnology sector, due to the scientific complexity and interconnections of the new biomedical discoveries but also due to the current regulatory environment. Although the examination process in the US Patent and Trademark Office (USPTO) takes 2-3 years in average, a patent examiner spends on average 2 days per application. Furthermore, the current system rewards examiners only when they approve a patent but not for rejecting applications, resulting in 80-85% of the US patent applications to be approved.

Nowadays, there are multiple risks for pharmaceutical and biotechnology industries related patents. Pharma and biotech R&D follow a pre-defined process towards drug development and there is a specific statistical probability calculating the success for each phase. These probabilities differ between different diseases and the nature of the therapeutic (cell-based, chemical, nucleic acid inhibitor). In addition, during the last decade the pharma industry has seen unprecedented levels of patent expiration, having more than 25 blockbuster drugs losing patent protection. This outlook poses a severe threat to big pharma, because these products were the driving force of growth and profitability. Furthermore, although the patent litigation rates are 1-1.5% for all the industries, the litigation rates for biotech and pharma patents is 5-6%. Most frequently, the patents involved in litigation are those which are valuable enough to justify litigation costs and risks. According to recent studies, patent suits filed in 2015 will generate more than 4 billion dollars in legal fees. The main objective of capital budgeting is the efficient allocation of resources under uncertainty and all the types of risks that we have described, should be part of this analysis.

Litigation represents an investment with an uncertain outcome, thus we propose to examine the option value of litigation and its impact on capital budgeting decisions. For example, a researcher in a US biomedical institute owns a patent related to a new chemical compound having anti-cancer {properties, expiring at time T. The commercialization of the drug is related with some expected revenue, which fluctuates randomly and this randomness is captured by identifying the revenue rate as a stochastic process.

The dynamics of the net cash flow Πt under the martingale measure P* are described by:

d Πt = α* Πt dt + σ Πt d Wt    (1)

or in integral notation:

Πt = Π0 + * Πs ds +  Πs dWs  (2)

Where α* is the risk-adjusted drift, σ is the corresponding volatility, that is the standard deviation of returns and W = {Wt}t ≥ 0 is the one-dimensional Brownian motion.

Both (1) and (2) describe the profit rate process in an equivalent risk-neutral scenario, thus allowing us to discount cash flows at the risk-free rate.

Due to the limited life of patents, cash flows will not continue indefinitely and the profit rate will drop substantially after the expiration of the patent, having a terminal value of M Πt, where M is a multiple.

Let EP denote the expectation operator under the risk-neutral measure. In the absence of additional costs, the value of the project to the researcher at time t is:

V1 (Πt, t) = EP*

[ t e-r(s-t) ds + M Πt e-r(T-t)I Ft ]         where F signifies the option

The commercialization value must satisfy the PDE, thus the solution to this problem can be derived as:

V1 (Πt, t) = (1 – e-δ(T-t)  Πt,/δ + e-δ(T-t) M Πt

V1 (Πt, t) represents the valuated of the drug project under perfect patent protection, neglecting the effect of competitive action and the absence of flexibility of the researcher since he/she has committed to commercialization. According to real options, the patent risk could be regarded as an optionality. As the option value is heavily influenced by volatility, the drug project turns out to be sensitive to changes in this important parameter as well.

Thus, based on an alleged infringement of a related patent, a big pharma challenger may decide to litigate at any time τ Є [0,T] and if successful, it will receive a fraction of ζ Є [0,1] of the value of past cash flows, compounded to time τ. If the big pharma does not depend on the researcher to market the product θ becomes a unity.

Although it would be interesting to examine the case in which the big pharma challenger is active in the market and together with the researcher forms a duopoly, the big pharma is assumed to be idle at time t = 0. Such a variation in the model could lower the big pharma’s expected gain over the status quo and diminish the incentive to litigate.

Let’s hypothesize that the litigation costs of the researcher and the big pharma challenger are L1 and L2 and also let p denote the probability of successful litigation.

The expected payoff from litigation would be: EP* [V2 (Πt, t) – L2 Ι Ft]

The expected payoff is maximized by choosing an optimal litigation time. At time t = 0, the option to litigate is: F2 = EP* [e-rt* (V2 (Πt*, t*) – L2) +]

The value of the drug project to the researcher, including this patent risk would be:

Expected PV= EP* [(1 – e-δT) ω/δ + MΠT e-δT] – F2 (ω, 0) – EP* [1{t≤T}e-rτ (L1 + L2)]

This is the expected present value of cash flows from commercialization minus the litigation option value and the PV of additional litigation costs.