The deterministic versus stochastic model in valuation is an issue worth considering when considering different approaches. In valuation, we refer to future events and forecasted quantities. Why do we generate forecasts and plans as if future events were certain to occur?
We operate as if we were heavily burdened by a deterministic view of reality. We assume we will enter the market in 2026, with revenues growing by 5% annually. Furthermore, the economic life of this innovative technology will be exactly nine years. Based on these point-based (certain) assumptions, we determine the present value of this technology. In practice, such assumptions will only prove true by chance, and this is precisely what our intuition suggests.
Key Valuation Concepts – Value and Risk
Definition of value
Value in the economic sense is the amount of money that must be paid today for future benefits. See other articles: : Value and price, Identification of the valuation object, and Formulation of valuation conclusions.
Definition of risk
“Risk” is a random event that may occur and, if it actually occurs, will have a significant negative impact on the achievement of the objectives of the activity.” The consequence of adopting such a definition [1] is the assumption that:
- There are realistic event scenarios.
- The likelihood of each scenario occurring can be estimated.
- The strength and direction of how events influence goal achievement can be estimated.
Risk measurement for the valuation process is particularly important in the case of:
- valuing technology rights at an early stage of commercialization,
- drafting licensing or franchise agreement provisions,
- designing brand development strategies,
- etc.
Alternative models of reality
Deterministic model
Historically, cause-and-effect analysis of phenomena led to the development of an extreme model (known as a “Laplace demon or machine”). It claimed that having complete information about specific entities would allow confident prediction of their future behavior. Therefore, planning effectiveness would be solely limited by the availability of information.
Information gaps, as business practice shows, are a vital part of the decision-making process. We now use this understanding to identify one of the main risk factors, called “uncertainty.” There are methods to reduce uncertainty by gathering more information. We can minimize risk by reducing uncertainty, for example, by conducting additional market research.
Supporters of the “Laplace machine” believed that reality could be modeled as “deterministic” or fatalistic.
The deterministic model failed to stand the test of time, and the conclusions drawn from the “Heisenberg uncertainty principle.”
Stochastic model
This principle demonstrates the random nature of phenomena and contributed to the development of a “nondeterministic model” of perceiving reality.
As a consequence, planning can be effective even in conditions of incomplete information and high variability of phenomena. This requires the use of stochastic planning models. As a result, stochastic analysis and practical applications of simulation analysis have developed. It has been accepted that variability, alongside uncertainty, is a significant source of risk.
Variability is a characteristic of a given system and cannot be reduced by acquiring additional information. Reducing variability for risk management purposes, e.g., a licensing contract, requires intervention in the system. This can be achieved by supplementing the contract with new clauses, including option clauses.
Risk measurement in valuation
Valuation practice has developed modern methods for identifying and measuring risk in both qualitative and quantitative terms. Risk measurement methods are used in practice when:
- The valuation process requires risk measurement.
- Reality is complex and multi-threaded, with systems characterized by high variability of phenomena and events.
- There is a need to make decisions under conditions of uncertainty.
- A more desirable “single-value point estimate” is a range of values with a specific probability density distribution.
Identifying risk-generating events and measuring their probability of occurrence will enable the use of stochastic models in valuation. A stochastic model enables correct risk implementation. The model is constructed by accounting for recognized stochastic processes and employing probabilistic methods.
Let’s start with a simple case of valuing an IP Portfolio (know-how + patents). An IP portfolio protects technology that has been in use for some time. This generates revenue and profits through product sales.
We will use two available valuation methods, based on data on concluded licensing agreements and M&A transactions of entities with comparable IP Portfolios:
- RFR method – Relief From Royalty,
- CTM method – Comparable Transaction Multiplies.
Let us compare two different approaches to IP portfolio valuation, focusing solely on how the financial models are built.
Deterministic Model
Assumptions:
Financial parameters
- The financial analysis was conducted using current prices. The valuation was presented in thousands of PLN. A standard income tax rate of T=19% was assumed.
- The 11.9% cost of equity was used to determine the discount rate, accounting for the IP Portfolio’s specific risk and forecast risk.
- The revenue forecast for products manufactured from the IP Portfolio was based on projected 2025 volume and an average CAGR of 5.5% for 2026-2029. After that, the CAGR declined linearly to a long-term growth/inflation rate of 2.5%.
- The cash flow capitalization period was assumed to last until the patent expires and the innovation covered by the know-how is exhausted, which is expected to occur by 2034. The royalty rate based on sales revenue was assumed to be 5.5%, based on comparable licenses or transactions.
Market parameters
- The “Tech/rev” and “Tech/EV” market multiples for the CTM method were estimated from an analysis of market multiples in the M&A transaction portfolio. The revenue for the CTM method was projected using the 2025 forecast.
- The invested capital value for the CTM method was estimated using an EV/REV ratio derived from an analysis of the M&A transaction portfolio, at 3.42.
The market value of the IP Portfolio ranges from PLN 1,865.6 thousand to PLN 1,940.5 thousand. It is based on the results of the two methods applied.
Stochastic Model
Assumptions:
Financial parameters
- The 11.9% cost of equity was used to determine the discount rate, accounting for the IP Portfolio’s specific risk. To evaluate how the discount rate affects valuation, this parameter was modeled as a random variable with a “Uniform” distribution, perturbed by ±3 % of its initial value (all values within the range are equally likely).
- The revenue forecast for products produced using the IP portfolio was developed assuming a CAGR of 4.5% to 6.3% for 2026-2029, based on various market analyst forecasts. In later periods, this rate was decreased linearly to align with the long-term inflation rate, estimated to range from 2.5% to 3.0%. These figures were incorporated into the financial model as a random variable with a “Uniform” distribution. The cash flow capitalization period was assumed to extend until the patent expires, including the year 2034.
Market parameters
- The royalty rate relative to sales revenue was assumed to range from 5.32% to 7.10%. In the financial model, the royalty percentage was treated as a random variable with a right-skewed “Beta4” distribution, meaning values closer to the lower end of the range are more likely.
- The “Tech/rev” and “Tech/EV” market multiples for the CTM method were derived from analyses of market multiples within the ranges 0.07-0.16 and 0.36-0.42, respectively, based on M&A transaction portfolios. In the financial model, these indicators were treated as random variables following a right-skewed “Beta4” distribution. Revenue estimates for the CTM method were based on the 2025 forecast.
- The value of invested capital for the CTM method was estimated using an EV/REV ratio derived from an analysis of the M&A transaction portfolio, which ranged from 2.23 to 5.62. This ratio was incorporated into the financial model as a random variable with a symmetric “Beta4” distribution.
The calculation results are shown in the tables:
The valuation results are shown in charts and tables:\
As shown in the graph, the RFR method produces a more even distribution of results than the CTM method. The distribution of the CTM method “‘s results is more clustered.
This provides some insight into the financial model’s parameter uncertainty.
Therefore, we present two valuation results:
- The result of the RFR method ranges from PLN 2,052.60 thousand to PLN 2,248.92 thousand. Median of the distribution equals PLN 2,146.94 thousand.
- The result of the CTM method ranges from PLN 2,048.64 thousand to PLN 2,278.81 thousand. Median of the distribution equals PLN 2,184.72 thousand.
The single range of IP Portfolio value can be objectively approached by a weighted average. We used variability indices from individual methods to create a weighted variable that is inversely proportional to these indices. This approach is demonstrated in the chart and table.
The Tornado Chart also improves our understanding of how the variability of individual random variables affects the total variability of the valuation outcome, thereby illustrating the uncertainty involved in estimating specific parameters of financial models.
Conclusions:
- The example shown was processed using Vose Software’s Model Risk software (https://www.vosesoftware.com/Risk-In-Excel/). I have been using it in my consulting practice for many years, and almost since the first versions of this software.
- I showed how to apply a stochastic model in valuation with a simple example. In real-world situations, more complex scenarios arise where stochastic modeling provides much greater benefits.
- The valuation accounts for contracts that contain multiple real option clauses.
- An event has been identified that, if it occurs, will significantly affect the valuation subject’s earning capacity. Some parameters of the financial model are correlated.
- The large number of parameters in a financial model makes it very difficult to include them in a sensitivity analysis. This is because of the ceteris paribus principle.
- Choosing random variable distributions (“long tails”) allows capturing “unknown uncertainty” when a cautious approach is especially needed.
- Analyzing thousands of scenarios quickly helps identify the most likely extreme outcomes.
- After updating the forecasted contracts, such as reducing or reallocating risk, we immediately see the valuation of that action.
[1] (Definition of risk according to David Vose, “Risk analysis – a quantitative guide”, Wiley&Sons, 2008).
