Complex structures and financial instruments 

We were commissioned to value a complex structured convertible bond, the interest rate of which was partly dependent on the company’s performance and the exercise of which was mandatory in the case of certain exit events and optional in the case of others. The aim was to develop a valuation model in accordance with IFRS 9 that would be used for accounting purposes and could also be used as a basis for regular revaluations. In addition, the notes to the financial statements were to be prepared. 

The valuation of such hybrid financial instruments with equity and debt characteristics places high demands on the modelling of future cash flows and valuation parameters. In this specific case, particular attention was paid to the systematic modelling of the various exit events, their probabilities of occurrence and their correlation with the underlying enterprise value. In particular, it had to be worked out that certain exits – such as an IPO – appear increasingly likely as the company valuation increases, while others, such as a financing round, appear more plausible in lower valuation ranges. 

A critical success factor in the modelling was therefore initially the probabilistic recording of the exit events, including the timing-related dimension, which we mapped using stochastic processes. Building on this, the relationship between the specific exit scenario and the company value when the event occurs was formalised. In order to capture this consistently, we anchored the valuation in a risk-neutral valuation framework. The necessary calibration of key parameters – in particular volatilities, exit probabilities and adjusted risk-neutral growth rates – was carried out using capital market benchmarks and plausibility checks based on the share price data of comparable companies and market volatility data. 

Another key modelling aspect was the mapping of the cash flows, which are influenced by both the development of the company’s value and the exit constellation. This was of importance in particular in the case of performance-related interest payments, the amount of which was linked to certain profit development of the company. In order to map these dynamics appropriately, a simulation-based method was developed that maps both the stochastic paths of the company value and the resulting cash flows for all scenarios. 

The result was a modular valuation model that transparently illustrates the valuation logic and is equipped with a sensitivity calculation that clearly shows the effects of key parameter changes. In addition, a structured description of the notes was designed, which documents the accounting approach, the methods used and key assumptions in a way that is appropriate for the target audience. The model is also suitable for future continuous measurement as part of periodic financial statements. 

Overall, the model was able to fulfil both the regulatory requirements of IFRS 9 and create a reliable measurement basis for internal decision-making processes – with a particular focus on the traceability of a complex hybrid instrument in a stochastically uncertain environment. 

We were commissioned to value different classes of shares in a now established company (former start-up). The shares to be valued had been created as part of several financing rounds and differed considerably in terms of their securitised rights – particularly with regard to liquidation preferences in the event of a potential exit.  

The core challenge in this valuation assignment lay in the complex legal structure of the share classes. Depending on the amount of the exit proceeds, different payout mechanisms were provided for – from preferential repayment to participatory participation in exit proceeds. An equal distribution of the exit values across all share classes only occurred within certain value ranges. The valuation therefore had to be able to accurately reflect these non-linear distribution patterns in economic terms. To solve this challenge, we based the valuation on the Option Pricing Method (OPM). This involved modelling the different value zones – within which different classes had the same entitlements – as staggered call options. The underlying methodology is based on the fact that the economic value of each share class is derived from the difference between several successive options. This concept allows a differentiated quantification of the value distribution along the entire company value spectrum. 

The parameterisation of the model was based on empirical benchmarks and our own data measurements – particularly with regard to volatility and expected exit timings. Due to the high complexity of the legal structures and additional differences – for example in relation to tag-along and drag-along rights, veto options or information claims – it was not possible to use closed analytical models (such as Black-Scholes-Merton). Instead, simulation-based methods were used, which enabled a realistic depiction of the value trends and probability distributions. 

A key focus was on the transparency of the results, as the underlying methodology is sophisticated in terms of financial mathematics but must be communicated in an understandable way – especially to stakeholders without in-depth quantitative background knowledge. For this reason, particular emphasis was placed on a figures-and-graphs supported presentation of the results, which made both the economic logic of the financial options and the value distribution for the respective share classes comprehensible. The result was a robust and understandable valuation model that not only depicted the structural characteristics of the share classes, but also served as a basis for discussions with investors and for reporting. 

We were commissioned to develop a conceptual valuation and risk model for Power Purchase Agreements (PPAs) – i.e. long-term electricity supply contracts typically concluded between energy suppliers or project companies and commercial customers.  

The aim of the project was to develop a model that, on the one hand, appropriately depicts the economic value of a PPA and, on the other hand, visualises the differentiated risk contributions of the various cash flow components.  

Our methodological approach was based on carrying out the valuation along the two central cash flow components: 

• Merchant Leg: The market price-dependent payment flows whose risk is largely characterised by the volatility of the electricity price. 

•  Fixed Leg: The fixed, contractually guaranteed cash flows, which are significantly more stable but still dependent on product-specific factors such as production volatility or counterparty risks. 

For modelling purposes, each leg was initially discounted separately using a risk-adjusted discount rate based on CAPM logic. To make this possible, the underlying “project beta” was derived and adjusted using the underlying cash flow characteristics. The aggregation of both legs then provided the fair contract value of the PPA from the perspective of a rational investor. In an alternative valuation approach, we directly modelled the net cash flows (merchant minus fixed) and determined the discount-consistent capitalisation rate in order to arrive at an equivalent result.  

The model developed enables scenario and sensitivity analyses to be carried out, for example in the event of changing electricity price expectations or regulatory framework conditions. It is suitable for project developers and operators who want to evaluate and structure their PPA offers, as well as for investors who want to integrate PPAs as a contractual component in company valuations – without access to complete business plans. The result is a practical, investor-compatible valuation model that meets the increasing demands for transparency and risk differentiation in the electricity market. It thus forms a sound basis for the economic assessment of PPAs – both in the context of project financing and for transactions and strategic portfolio valuations