Conclusion

model is not such a model as it performs a very static valuation and does not incorporate the effects of changing input variables in the future. As changing input variables occur widely during the time span of a drug development project, the DCF model is far from optimal for valuing the project. The structural resemblance of a drug development with options suggests that real option analysis would be ideal for valuing drug development projects because the characteristics of the biotech industry as referred to above are all essential value drivers in a real option valuation.

The real option framework should not only be considered a tool for the calculation of the value of a drug development project but also as a tool that aids the understanding of the different real options that appear during the span of the project. This is exactly what lattices do as they visibly model future scenarios. On the contrary partial differential equations, such as the Black-Scholes model, are more a closed-end solution and are also mathematically more complex than lattices.

As the focal point for practitioners is applicability, a simpler model is preferred. Statistically based models such as simulations also violate this point of preference.

A lattice model which easily expands the DCF valuation to include a partial real option framework is a simple event tree that incorporates the risk of failure in each phase. The real option framework can be fully included in a valuation by the use of binomial trees, which are relatively easily applicable for a person with a sound financial understanding, and the most widely used real option valuation method.

Fuzzy real options analysis

Fuzzy numbers can be applied to perform a real options valuation by using the fuzzy pay-off method. It uses a fuzzy number, most often in the form of a triangular fuzzy number, to represent the expected future distribution of the cash flows also known as the FNPV, which is the pay-off possibility distribution of the project. To obtain this the forecasted cash flows are rearranged to portray the extreme possible scenarios. The real option value can be calculated from the FNPV as the fuzzy mean value of the positive area of the fuzzy net present value multiplied with the ratio of the positive area to the total area of the fuzzy net present value. Only the positive

outcomes of the fuzzy net present value are included as the negative outcomes are valued at zero in the real option framework.

The fuzzy pay-off distribution from where the real option value is derived can be constructed directly from the cash flow scenario of a given project. So the fuzzy pay-off method is not dependent on a given process to model the future, which makes it applicable in most valuations of uncertain R&D projects.

The fuzzy approach can also be applied to binomial tree valuation where each single node is portrayed as a triangular fuzzy number by applying a fuzzy volatility. The jumping factors are being fuzzified by the fuzzy volatility hence creating two extreme binomial trees to depict the diverse development of the underlying asset. The value of option can then be calculated from the fuzzified risk-neutral possibilities.

Valuation settings

Valuing a drug development project requires an extensive amount of research on the different input variables. A lot of comprehensive studies have been conducted on phase lengths, success rates, costs and sales for the different therapeutic areas and they should be used as a guideline for estimating the cash flow forecast. Contextual analyses should be used to clarify whether the historical findings are valid as a proxy for the future values or if they should be adjusted. As the drug will not be marketed the first many years the contextual analyses also aid to understand the future market conditions. For the actual valuation it is important to discuss the cost of capital that is used to discount the cash flows as it has a significant impact on the final value as found in the sensitivity analyses in section 6.6. Also the uncertainty related to the project is important to discuss in order to ensure a reliable estimation of the volatility.

Fuzzy valuations

From our analysis in part 5 we found that a fuzzy approach to traditional valuation methods in general yields a more positive outcome than without the use of fuzzy numbers, as it puts more emphasis on the potential upside of an uncertain project than the potential downside. In section 6.3 our case study showed that the application of the fuzzy pay-off method to a DCF valuation yielded a higher real option value than the stand-alone DCF valuation did. Due to the

construction of the fuzzy number the possible upside of a project is enlarged and the possible negative outcomes are valued at zero. When adjusting the DCF valuation for the risk of failure by the use of an event tree, our risk-adjusted valuation in section 6.4 showed that the fuzzy

slightly positive number. Again this is due to the possible use of abandon options which can terminate projected loss-making projects. As a fuzzy valuation per definition cannot estimate projects to have a negative value as analyzed in part 4 it is necessary to settle on a minimum threshold value which the valuation should exceed in order to offset the unavoidable costs related to the termination of a project as discussed in section 6.7. In the clean real option valuation performed in section 6.5 the fuzzy approach again demonstrates its ability to value the value of managerial flexibility. The binomial tree setting shows how the diverse development of the potential sales can be better captured and valued with a fuzzy approach. The results obtained for all three valuation perspectives are considered to be robust as the sensitivity analysis in section 6.6 showed an unequivocal result when changing the key input variables.

To answer our primary research question our findings in part 5 confirm that the use of fuzzy numbers to perform a real option valuation of a biotech project is well applicable compared with the traditional valuation methods because it captures the real option thinking without the normal difficulties of implementing it for practitioners. It can be relatively easily applied to different levels of valuations and is therefore applicable for practitioners both in companies with advanced valuation approaches and companies with more simple valuation practices. For practitioners with a simple valuation approach the fuzzy event tree is recommended as it combines the inclusion of a risk perspective as well as the value of managerial flexibility with an uncomplicated

implementation. For more advanced practitioners the fuzzy binomial tree valuation could be interesting to apply as it stresses the managerial value stemming from the possible excessive development in the underlying asset.