investigation of optimal valuation methods in the...

Master thesis in Finance and International Business

Investigation of optimal valuation

methods in the pharmaceutical

industry

Authors: Morten Vester & Andreas Holmgaard Petersen

Characters: 185.598

Supervisor: Özlem Dursun-de Neef

Aarhus University School of Business and Social Sciences

Department of Economics and Business

September 1st 2015

Abstract

This thesis has the purpose of determining the optimal valuation method for pharmaceutical

drug development projects. A literature review of valuation methods used by practitioners’

shows that more simple models, such as DCF valuation, are used, regardless of the industry

context. The motivation in this thesis is therefore to investigate the potential of using more

advanced models in the valuation of drug development projects. More specifically, one of the

objectives is to investigate the potential of using Real Option theory.

In order to fulfil the purpose of the thesis, it consists of both a theoretical- and practical

research approach. The theoretical part is an analysis and discussion of four valuation models;

Discounted Cash Flow, Decision Tree Analysis, Binomial-, and Quadranomial Real Option

approach. In order to investigate theoretical differences in each of the valuation models, four

evaluation criteria are constructed; Concept, Uncertainty, Strategy Flexibility, and Usability.

Each of the valuation models is then evaluated upon these criteria. The practical research

approach is a case study on a phase I pharmaceutical diabetes development project.

The thesis finds that the pharmaceutical industry is characterised by sequential dependent

clinical phases, which are uncertain in time-length, success, and cost. An optimal valuation

method must thus be able to comprehend and incorporate the uncertainty of each clinical

phase. We find that an optimal valuation model must be able to separate market and

technological uncertainty to provide strategic flexibility. From the evaluation of each criteria

and the practical implementation of the case study, the thesis finds that both the DTA and the

Quadranomial Real Options model have high potential. Both models can explicitly incorporate

future events i.e. the clinical phase success rates. The thesis further finds that the Real

Option approach in general has a good potential in the pharmaceutical industry, but is

challenged by the more complex practical implementation.

The thesis reaches the conclusion that Decision Tree Analysis is the best tool, when valuating

pharmaceutical drug development projects, from an external point of view. Since the findings

of this thesis are based on partly a practical research approach, it is likely that we influence

the result because of our pre-determined expectations.

Table of Contents

1 Introduction --------------------------------------------------------------------------------------------------------------------- 1

1.1 Methods of science ------------------------------------------------------------------------------------------------------- 3

1.2 Delimitations -------------------------------------------------------------------------------------------------------------- 5

2 Introduction to the pharmaceutical industry ------------------------------------------------------------------------- 7

2.1 Definition ------------------------------------------------------------------------------------------------------------------- 7

2.2 Size and sales ------------------------------------------------------------------------------------------------------------- 8

2.3 Research & development ----------------------------------------------------------------------------------------------- 8

2.4 Patents ---------------------------------------------------------------------------------------------------------------------- 9

2.5 Drug development ----------------------------------------------------------------------------------------------------- 10

2.6 Success rates, cost, and time ---------------------------------------------------------------------------------------- 12

2.7 Sum-up -------------------------------------------------------------------------------------------------------------------- 18

3 Valuation methods in the pharmaceutical industry -------------------------------------------------------------- 19

3.1 The Criteria -------------------------------------------------------------------------------------------------------------- 20

3.1.1 Concept -------------------------------------------------------------------------------------------------------------- 21

3.1.2 Uncertainty -------------------------------------------------------------------------------------------------------- 21

3.1.3 Strategic flexibility ---------------------------------------------------------------------------------------------- 21

3.1.4 Usability ------------------------------------------------------------------------------------------------------------ 22

3.2 Standard DCF model -------------------------------------------------------------------------------------------------- 23

3.3 Decision Tree Analysis ----------------------------------------------------------------------------------------------- 27

3.4 Real Options ------------------------------------------------------------------------------------------------------------- 31

4 Case study - practical implementation -------------------------------------------------------------------------------- 49

4.1 Practical implementation of standard DCF model ----------------------------------------------------------- 52

4.2 Practical implementation of Decision Tree Analysis -------------------------------------------------------- 63

4.3 Practical implementation of the Binomial Lattice approach ---------------------------------------------- 68

4.4 Practical implementation of the Quadranomial Lattice approach -------------------------------------- 73

5 Evaluation & recommendation ------------------------------------------------------------------------------------------ 76

5.1 Evaluation of the DCF model --------------------------------------------------------------------------------------- 76

5.2 Evaluation of Decision Tree Analysis ---------------------------------------------------------------------------- 78

5.3 Evaluation of the Binomial and Quadranomial approach ------------------------------------------------- 79

5.4 DTA vs. ROA ------------------------------------------------------------------------------------------------------------ 81

5.5 Future research --------------------------------------------------------------------------------------------------------- 84

6 Conclusion --------------------------------------------------------------------------------------------------------------------- 85

7 References --------------------------------------------------------------------------------------------------------------------- 88

List of figures

Figure 1.1 Chapter structure of thesis

Figure 2.1 The drug development process

Figure 3.1 Criteria for evaluation of valuation methods

Figure 3.2 Standard discounted cash flow model

Figure 3.3 Cost of equity

Figure 3.4 Summary of DCF

Figure 3.5 Example of a decision tree

Figure 3.6 Summary of DTA

Figure 3.7 The intrinsic value of options

Figure 3.8 Payoff positions

Figure 3.9 Recombining binomial tree

Figure 3.10 Binomial risk-neutral formula

Figure 3.11 Option value formula in a binomial tree

Figure 3.12 Option value tree for a two period call option

Figure 3.13 Brownian Motion

Figure 3.14 Possibilities in quadranomial tree

Figure 3.15 Quadranomial formula

Figure 3.16 Direct and indirect volatility estimation methods

Figure 3.17 Logarithmic present value approach

Figure 3.18 Market and technological uncertainty

Figure 3.19 Summary of Real Option

Figure 4.1 Illustration of the development – and commercialisation phase

Figure 4.2 Practical steps in DCF valuation

Figure 4.3 Cost of equity for case project

Figure 4.4 Sensitivity analysis of input in cost of equity

Figure 4.5 Sensitivity analysis of various input

Figure 4.6 Overview of steps in DTA

Figure 4.7 DTA calculations

Figure 4.8 Sensitivity analysis of the components in the discount rate

Figure 4.9 Sensitivity analysis of the technological success rates…

Figure 4.10 Sensitivity analysis of the research and development cost…

Figure 4.11 Practical implementation of the binomial lattice approach

Figure 4.12 Asset tree in the binomial model

Figure 4.13 Binomial option value tree

Figure 4.14 Sensitivity analysis of volatility and risk free rate

Figure 4.15 Steps in the quadranomial approach

Figure 4.16 Quadranomial option value

Figure 5.1 DTA versus ROA

List of tables

Table 2.1 Clinical success rates

Table 2.2 Cost of drug development

Table 2.3 Clinical time length

Table 3.1 Difference between financial and real options

Table 3.2 Overview of selected types of real options

Table 4.1 Development cost assumed for NN9927

Table 4.2 Cost assumptions in the commercialisation phase

Table 4.3 Free Cash Flow of project NN9927

Table 4.4 Overview of Beta estimation

Table 4.5 Calculation of DCF value

Table 4.6 Probabilities used for in each of the decision nodes

Table 5.1 Evaluation of the investigated models

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1 Introduction

Pharmaceutical drug development is a rather cumbersome and costly affair. Cost estimates on

the development of a new approved drug in the United States go as high as exceeding US$ 2

billion (DiMasi, Grabowski, & Hansen, 2014). This combined with the substantial time effort

required to develop a new successful drug and the relatively low probability of making a

successful blockbuster-drug are well describing characteristics of the highly uncertain

business environment pharmaceutical companies operate within. The drug development

process is composed of several stages, in which the drug company gathers evidence to satisfy

government regulations that it can consistently manufacture a safe and efficacious form of the

compound for the medical condition it is intended to treat. At the end of each development

stage, the company uses the technological and market information revealed up to that point to

decide whether to abandon or continue development of the compound (Kellogg & Charnes,

2000). This high uncertainty calls for considering financial decision tools that can expand the

notion of a static environment and enable the possibility of evaluating the decisions

management faces as time progresses. To address these concerns, real option valuation models

have been suggested as a suitable way to include uncertainty in investment decisions (Myers,

1984), and this is where this thesis has its starting point.

Both recent research and previous studies have shown that certain valuation methods are

more commonly used by practitioners than others. Particularly Discounted Cash Flow

methods and Relative Valuation are widely and intensively used by practitioners in valuation,

while Real Option valuation is hardly ever used (Bancel & Mittoo, 2014; Block, 2007;

Hartmann & Hassan, 2006; C. V. Petersen & Plenborg, 2012). In their articles (Bancel &

Mittoo, 2014; Demirakos, Strong, & Walker, 2004) more investigate what kind of theoretical

financial models financial analysts use in terms of valuation in different industries. Their

findings show that the only industry, in which a Real Option valuation approach is applied, is

the pharmaceutical industry. About 10 per cent of the participating analysts answered that

they use or have used a Real Option valuation approach to pharmaceutical project valuation.

The study showed that often not a single method is used but several methods are combined to

reach conclusions and recommendations on valuation.

Given the characteristics of the pharmaceutical business environment and the fact that

practitioners have preference towards simpler and more static valuation methods, the

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objective of this thesis is to investigate the differences between fundamental cash flow

valuation- and Real Options Valuation (ROV) models both in theory and in practical use.

Another objective with this thesis is to evaluate the potential of using real option theory in

valuation of pharmaceutical development projects, when having an external point of view. The

focus of the thesis is to evaluate the relative differences between the valuation models, and not

to analyse any mispricing. The focus is on the theory behind the different valuation models

which assumption they are based on, and how they can be implemented in practice, when

having the characteristics of the pharmaceutical industry in mind.

Based on the above and the authors’ curiosity the following research questions are examined.

What are the main theoretical differences between fundamental valuation models and real

option valuation and their underlying assumptions with focus on the pharmaceutical industry?

How do the different models differ in regards to practical implementation, considering their

ease of use and strategic opportunities?

What is the potential, with the case study and theoretical framework in mind, of using the Real

Option valuation in the pharmaceutical industry?

In order to answer the problem statement we have structured the thesis as seen in figure 1.1

below. The thesis will include both a theoretical and a practical research approach. The

theoretical approach will consist of a review and evaluation of different valuation methods,

having the pharmaceutical industry in mind. The theoretical evaluation will be based upon

four defined criteria, which are used to analyse the theoretical differences and help structure a

more in depth theoretical comparison of each valuation model. Each criterion is further used

to assure that the underlying assumptions of each valuation model are discussed in relation to

our research questions. In order to exemplify the discussed theory and differences in approach,

the thesis includes a case study of a Novo Nordisk pipeline project. The case study is a

practical approach, which will enable and ease the discussion of the different valuation

approaches. Before a more in depth evaluation of each valuation approach, it is important to

understand both the theoretical and practical differences between each valuation model.

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Figure 1.1: Chapter structure of thesis

Source: Own creation

As seen in figure 1.1, this chapter is followed by an introduction to the pharmaceutical

industry before the focus is on the evaluation of different valuation methods. In order to

investigate the implementation of the valuation methods, a case study is conducted next,

ultimately making it possible to answer the research questions proposed and making a

conclusion. A more detailed explanation of, how the chapters are structured, will appear in the

beginning of each chapter.

1.1 Methods of science

To improve the arguments and choices made throughout this thesis, the following section is an

explanation of our research approach and method of science. The purpose of this section is to

improve the general understanding of our assumptions and clarify the limitations of our

general research approach.

Economic science is in general build on the basic of the positivistic paradigm1, and financial

theory is grown upon the concepts of this philosophical position. The positivistic paradigm is

based on empiricism, the idea that observations and measurements are the essence of

scientific endeavour, and that research produces facts that correspond to an independent

reality (Eriksson & Kovalainen, 2011). The positivistic paradigm is based on strong

1 Positivism is a term coined by Auguste Comte (1898-1857), refers to an assumption that only legitimate knowledge can be found

from experience (Eriksson & Kovalainen, 2011).

Introduction Introduction to industry

Criteria anddifferent valuation methods

Case study of pharmaceutical project NN9927

Evaluation oftheory and

practical implementation

Conclusion

•Introduction

•Research questions

•Structure of thesis

•Methods of science

•Delimitation

•Industry definition

•Size, R&D, patens

•Development phases

•Succes, costs and time data

•Project NN9927

•Development

•Commercialisation

•DCF

•DTA

•Binomial

•Quadranomial

•Conclusion

•Future research

•Concept

•Uncertainty

•Strategic flexibility

•Usability

•DCF

•DTA

•Binomial

•Quadranomial

•Evaluation of

•DCF, DTA, ROA

•Quadranomial vs.DTA

•Tradable vs. risk

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assumptions about empirical requirements and theoretical independence2, which are often

subject for criticism (Holm, 2011). These assumptions are difficult to satisfy in reality, and the

assumptions may be violated to some extent. Based on our theoretical framework, chosen

paradigm, and assumptions, it is likely that we influence our empirical data to verify our pre-

expectations. Our following results may therefore be biased by our own influence and should

be interpreted in the context of the stated limitations and data input.

The research approach, used in this thesis, is based on both the inductive and deductive

research approach. Deduction is a form of reasoning, in which particular conclusions are

formulated from general premises, and the inductive research logic concludes from the

particular (Eriksson & Kovalainen, 2011). Both research logics are used in different parts of

the thesis, and must be considered as combined through the research process. A research

study based on both the inductive and deductive method is defined as the abduction logic

method3. The abduction research logic is used, when the research process consists of various

forms of reasoning and logic exploratory (Eriksson & Kovalainen, 2011). Our research

approach is using the deductive logic method in the answer of the first problem questions

regarding the theoretical differences between the valuation methods. We use general financial

theory to evaluate the specifics of the pharmaceutical industry and the stated criteria. The

inductive method is primarily used in the case study of development project NN9927, in which

we seek to evaluate upon the theory and the theoretical use of each valuation model.

The financial framework used in the thesis is based on important assumptions about market

efficiency and human rational behaviour. In the context of the positivistic approach, our study

should be based on valuation models that aim to reach the assumptions of the positivistic

requirements regarding valid empirical data and mathematical arguments.

Our case study is based on the development of a single pharmaceutical product. The case

study is built of both project specific knowledge and a large amount of industry data in order

to answer our research question in the best way possible. In relation to our research questions,

we focus on the theoretical differences and potential of each valuation method. The case study

2 Theoretical independence requires that observations must be unbiased (Holm, 2011). 3 The abduction research logic mentioned by Charles Sanders Peirce can be considered as the logic of exploratory data analysis

(Eriksson & Kovalainen, 2011).

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design is thereby inspired by the extensive case study approach4. This design emphasise the

theoretical differences between the different valuations models, rather than analysing the

specific case project. As mentioned, it is likely that we influence our findings, which also

influence the question if the case study can be generalized to similar studies. Based on our

input data, we believe our findings can be generalised and used for other pharmaceutical

project, since our data consists of mostly generalisable industry data.

1.2 Delimitations

Before proceeding, we find it important to state the delimitations in the thesis. A clear

explanation of these will help narrow the otherwise large field of study and give the reader a

more precise indication of, where the focus of the thesis is.

Of the many traditional valuation models used in corporate finance, we have chosen to focus

on a few specific models. We have chosen to focus on the standard Discounted Cash Flow

model (DCF), Decision Tree Analysis (DTA), and lastly Real Option Theory. The focus of the

Real Option theory is predominantly on the binomial- and quadranomial lattice models rather

than formula based methods, since these are the most used methods in the practical literature

(Bogdan & Villiger, 2010; Mun, 2002).

The thesis focuses on the American Food and Drug Administration (FDA) regulation of the

pharmaceutical industry. The reason for this choice is mainly because of the importance and

size of the U.S. drug-market. It is the largest market for most pharmaceutical drugs. In the

European Union, the European Medicines Agency (EMA) conducts regulation and approval of

new drugs. In the broad perspective the requirements and regulation are similar to FDA

regulation, hence it would not make any noticeable difference to conclusions of the thesis if the

focus was any different.

In the case study there will only be a limited focus on the strategic analysis in regards to the

DCF valuation of the project. We are aware that a thorough and detailed strategic analysis is

necessary in a useful valuation, but due to the fact that the DCF is limited to a single project

and not a main part of the problem statement, the strategic analysis is reduced to a minimum.

4 Extensive design aims at elaboration, testing or generation of generalizable theoretical constructions by replicating or comparing

cases (Eriksson & Kovalainen, 2011).

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The case study takes start in one of Novo Nordisk’s pipeline products. The product is called

NN9926 and is an oral GLP-analogue focused on treating Type II diabetes. The product is

currently in Clinical Phase I. The sales forecast and cost data will be based on a literature

walkthrough of pharmaceutical industry sales and costs data.

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2 Introduction to the pharmaceutical industry

The following will introduce some very general characteristics of the pharmaceutical industry.

Further greater focus is pointed towards the drug development process, and the chapter will

serve as reference point throughout the thesis. The chapter will last discuss cost, success rates

and time in relation to the industry, which will be used in the practical implementation of

each valuation method.

2.1 Definition

First, a definition of the pharmaceutical industry will be necessary for the further analysis

and data collection. In order to understand and define, what the pharmaceutical industry is,

one must look at two closely related terms – the pharmaceutical industry and the biotech

industry. The two terms are not straightforward and are often used indiscriminately.

Therefore, it can also be fairly difficult and rather confusing to precisely classify these terms.

Some make a strict distinction, while others do not distinguish between the two terms5. In

order to understand the different terms, it is important first to look at how pharmaceutical-

and biotech firms develop their respective drugs. Biotech companies use biotechnology6 in the

drug development process, whereas conventional pharmaceutical companies predominantly

rely on chemical-based synthetic processes to develop new drugs (Ferrara, 2011). Secondly, the

size and scope of operations are often different. Pharmaceutical companies usually have the

resources and capabilities to produce new drugs at large scale and successfully market them

thereafter. This is often not the case for biotech companies, since they are generally smaller

and more specialized in the research and development process. After initial development of a

new drug they typically sell or license the rights to produce and sell that drug to a larger

pharmaceutical company (Ferrara, 2011). Another difference is related to the threat of generic

products7. Biotech firms generally face less generic competition due to the fact that it is

usually more difficult, time consuming, and costly to develop a new drug using biotechnology

than using a traditional drug development process (Ferrara, 2011).

Even though there are some clear differences between pharmaceutical and biotech firms, a

strict separation of them may not be as forthright as one should think. This is mainly because

5 For statistical purposes no separating of the terms are often used. 6 Biotechnology is the manipulation of microorganisms (such as bacteria) or biological substances (like enzymes) to perform a

specific process. 7 Generic competition: Competition from look-a-like drugs that roughly offer the same efficacy but at a much lower price.

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many larger firms, which generally are perceived as pharmaceutical firms, i.e. Pfizer, Novo

Nordisk, and Eli Lilly use biotechnology in the development of new products as well. In sense

having a biotech company “in-house”8. This fact makes a separation of the two types of firms

into two completely separate industries rather unnecessary, since the development of new

drugs face the same regulations and requirements, and most data available do not distinguish

between the two terms. A common and simple definition of the pharmaceutical industry is an

industry comprised of firms engaged in the discovery, manufacturing, and sales of drugs,

biologics, vaccines and medical devices (Ferrara, 2011). In the following sections, when the

industry is mentioned, it is based on the just stated definition of a pharmaceutical company.

2.2 Size and sales

In the United States and Europe the pharmaceutical industry plays a major role in the society

and economy. The pharmaceutical industry is the second largest US export sector and a major

employer, estimated to directly provide jobs to 655,000 people in the US. In total, directly and

indirectly, the sector supports over 3.1 million jobs nationwide in the US (Ding, Eliashberg, &

Stremersch, 2014). The concentration of global sales is another clear indication of the

importance for these regions. In 2008 the US accounted for 48 per cent of the total global

sales, while Europe accounted for 29 per cent, between them sharing roughly 80 per cent of

the total global sales of pharmaceuticals drugs (Boldrin & Levine, 2008). The US drug market

and the appertaining medical legislation of FDA thereby have a major influence on the global

pharmaceutical industry. Putting these percentages into perspective, the global sales potential

of the pharmaceutical market was in 2009 estimated to be US$ 837 billion and today

estimates go as high as US$ 1,1 trillion (Ding et al., 2014). The pharmaceutical market is

estimated to be worth close to US$ 1,6 trillion in 2020 (PWC, 2012)9. The rapidly growing and

aging world population is the main driver for the increased demand for pharmaceutical drugs.

2.3 Research & development

A unique characteristic of the pharmaceutical industry is the amount of resources allocated to

Research and Development hereafter (R&D). Some estimates indicate that pharmaceutical

firms are accountable for 19 per cent of all R&D spending worldwide and that US

pharmaceutical R&D spending alone make up 36 per cent of the total pharmaceutical R&D in

8 In-house meaning that a part of the company is doing research by using biotechnology and combining the two approaches. 9 See appendix 5 for industry forecast.

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the world (Ding et al., 2014). These figures give a clear picture of an industry that is heavily

engaged in R&D processes but also indications of an industry that is extremely reliable on the

R&D process. According to the PhRMA, the Pharmaceutical Research and Manufacturers of

America, members of the organisation currently have close to 3,000 drugs in different stages

of development in their pipelines. Of the 3,000 different drugs under development naturally

most of pipeline-drugs lay within the groups that have some of the largest sales in the US. The

top three categories are oncologics, respiratory agents, anti-diabetics and lipid regulators10

(Ding et al., 2014). Industry measures on cost, time, and success rates of drug development

will be presented later in this chapter.

2.4 Patents

Innovation and R&D is undoubtedly connected with patents and intellectual property rights.

The close connection between the two is fairly obvious, when looking at the resources

pharmaceutical companies allocate to drug development and the threat from generics.

Pharmaceutical companies are of course then dependent on the protection that patents offer.

This thesis will not go in to detail about different patent-systems and their mechanics, but

instead focus on some few specifics about the industry. Pharmaceutical companies are, as

other industries, protected by 20 years of patent protection but beyond that there are some

specific characteristics about the industry (Clift, 2008). Unlike other R&D-intensive

industries, pharmaceutical firms do not have the option first to disclose their findings at the

final stage of development, but have to reveal their discovery very early in the development.

This is mainly due to requirements from government agencies and the fact that much

development involves human trails, as will be elaborated later (Lehman, 2003). The lengthy

R&D time period, which is also presented in the following sections, also constitute a special

case for the pharmaceutical industry. The time between filing the patent and releasing the

product to the market reduces that exclusivity a patent otherwise provides. In 1984 the US

government introduced a special act called the Hatch-Waxman Act, which enabled the

extension of a pharmaceutical patent with up to five years (Clift, 2008). The median or mean

peak sales of pharmaceutical drugs are undoubtedly connected with their patent periods.

Research suggests that the average percentage decline in sales the first four years after patent

expiry is 31, 28, 20, and 20 per cent respectively (Grabowski, Vernon, & DiMasi, 2002).

10 Lipid regulators are regulators that affect the levels of lipid, such as cholesterol and fat, in the blood.

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2.5 Drug development

In order to understand how pharmaceutical companies develop new drugs and some of the

challenges they face, the next section will describe a typical development process of a new

drug. It is worth mentioning that the process described follows the regulation of the US Food

and Drug Administrations (FDA).

“Importantly, creating new drugs in the twenty-first century is no longer a series of accidental,

serendipitous breakthroughs. Instead, a long and systematic process requiring steadfast commitment,

diligence, and meticulous work has taken the place of the previous haphazard experimentation” (Ding et

al., 2014, page 26)

In order to get an overview of the development process figure 2.1 is used to describe the

process of development in different steps. It shows in crude terms the different drug

development stages – from discovery of lead compounds through clinical phases (CP) and final

approval of the drug.

Figure 2.1: The drug development process


Discovery: The first step in the development of a new pharmaceutical drug is the study of a

disease at a molecular and cellular level. The discovery process is a complex process and

requires both the involvement of chemists and biologists. This stage is highly time-consuming

and uncertain, which results in a large amount of abandoned entities (Kellogg & Charnes,

2000). More detailed, the stage involves the analysis of basic cellular processes at both a

healthy and pathologic state, and by comparing the two different states several disease-

responsible actors are identified as possible drug targets. Before any of the discovered

compounds can be tested in a human body, several tests in vitro and in vivo, test in tubes, and

in living cells must be conducted. Furthermore, researchers must find the most appropriate

and safe dose of drug for the further tests in animals (Ding et al., 2014). Several candidate

drugs that seemed successful are often abandoned due to problems of low efficiency, toxicity,

Discovery CP I CP II CP IIINDA -

ApprovalPost

Approval

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or poor absorption (Bogdan & Villiger, 2010). Upon completion of the drug discovery process

researchers must prepare for the more critical stages in the innovation process – drug

development through clinical trials on humans. Before the candidate drug can be tested on

humans, the researchers must hand in an Investigational New Drug application (IND) to the

national drug agency. The application must include all evidence of the previous steps and

must proof that the candidate drug fulfils all present requirements and standards.

Clinical phases: In clinical phase I (CP I) the candidate drug is tested in humans for the first

time, and the study is usually conducted on a group of volunteers of 20 to 100 healthy persons

(Bogdan & Villiger, 2010). The test is conducted to establish a more precise dosage and to

gather more documentation about the absorption, distribution, embolic, and excretion effect of

the human body. Short-term side-effects are studied and the desired effects of the drug are

compared to the established treatments to determine if the drug provides a better alternative

(DiMasi & Paquette, 2004; Ding et al., 2014). If this is fulfilled, then it will move on to clinical

phase II.

In phase II a larger group of 100-300 people having the target disease or condition are tested.

The purpose is to define the most appropriate dose and further to prove the effectiveness of

the drug. The drug must proof its effectiveness, since the tested group of people in phase I

were healthy people (Bogdan & Villiger, 2010). Researchers strive to understand if the drug

has good efficacy, and whether the drug has any short-term side effects. Further, the drug

must prove a clear benefit over existing treatments in terms of efficacy, safety, and delivery

(Bogdan & Villiger, 2010; DiMasi & Paquette, 2004).

If the clinical phase II of the drug is successful, it is taking forward to a large-scale test of 500-

20.000 patients having the target disease, the clinical phase III. A large and diversified group

of people, often from different nations, are included as a diversified test group is necessary for

the following studies (Bogdan & Villiger, 2010). The aim of the large-scale phase III is to

confirm and significantly prove the effectiveness of the treatment under different conditions.

For establishing a significant evidence of efficacy and safety, the drug must be comparatively

tested against different placebo options and other standard treatments. If the drug succeeds in

being safe and effective the pharmaceutical company can file a New Drug Application (NDA)

to the drug agency requesting approval (Ding et al., 2014).

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NDA: The NDA must include all data, documentation, and statistics of the testing and proof of

the safety and efficacy of the drug. The approval must also include proposals for specific

labelling and manufacturing. A NDA may consist of more than 100.00 pages of data and

evidence. According to Bogdan & Villiger (2010) it is very likely that the regulatory authority

asks for further clinical trials or even rejects the marketing approval.

Post approval: After the pharmaceutical drug has been approved by the drug agency and sold

to the market, the test and research process has to continue. Pharmaceutical companies must

continue to monitor and observe carefully for newly found adverse and long-term side-effects

(Bogdan & Villiger, 2010). The company completes periodic reports to the drug agency on

quarterly basis the first three years and annually afterwards (Ding et al., 2014).

To sum-up the process of developing a new pharmaceutical drug, it is a complicated time-

demanding process affected by high uncertainty in each development stage. The next section

will present a litterateur walkthrough of some of the latest research within this field.

2.6 Success rates, cost, and time

The two previous sections have introduced the pharmaceutical industry and explained the

clinical phases of pharmaceutical drug development. The following section will investigate and

discuss the available data of clinical success rates, R&D costs, and time effort in developing

new drugs. This section is essential for the thesis, since these findings will be the source of the

industry data used in the later case study. Each section will start with a list of relevant

authors and continue with an explanation of these and conclude with a table that summarises

the findings.

From our research, we find that only few studies have investigated costs and success rates of

the pharmaceutical industry and that they differ significantly. The literature is further

complicated by the reluctance of the industry to publish confidential industry data of drug

development. Most data in the literature is derived from the Tufts Centre for the Study of

Drug Development (CSDD), where data is provided by big unnamed pharmaceutical

companies (Bogdan & Villiger, 2010). According to Light & Warburton (2011), the CSDD has

received substantial industry funding for years and is a repository, where companies submit

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their closely guarded figures on R&D. As several of the following studies are based on data

from CSDD, the studies of cost estimates are critically examined.

2.6.1 Success rates

The definition of the success rate is the chance that a pipeline-drug entering a development

phase reaches the next phase (Bogdan & Villiger, 2010; Ding et al., 2014). In the following the

average cumulative success rate is defined as the success rate from “first in man” to

marketing of the drug (Kola & Landis, 2004). The publication by Ding et al. (2014) advocates

that success rates are complex to understand and interpret upon, as the success rates

associated with passing each stage are different among different drug candidates. Meaning,

that probabilities of success vary quite substantially within different pharmaceutical classes.

Some of the most cited authors in the literature and industry are the publications by DiMasi

& Grabowski (2007) and DiMasi, Feldman, & Wilson (2010), who both are associated with the

before mentioned CSDD. The publication from DiMasi & Grabowski (2007) finds the success

rates of each clinical phase to be the following; CP I 71 per cent, CP II 44,2 per cent and CP III

68,5 per cent. Based on these, the clinical cumulative success rates is 21,5 per cent that a new

drug would be able to reach the market.

The later publication by DiMasi et al. (2010) studied a larger sample of drugs. The sample

consisted of 1.738 different compounds, from the 50 largest pharmaceutical companies in the

US11. They find that approximately one in six or 17 per cent of all new drugs were approved in

the period of 1994-2009. Their results show that failures occurred earlier in the clinical

phases. The success rate in each clinical phase was; CP I 67 per cent, CP II 41 per cent, and

CP III 63 per cent, and 90 per cent for approval.

The most recent study on pharmaceutical drug development success rates is an article

published by DiMasi et al. (2014) on behalf of CSDD. The study present the following success

rates; CP I 59,52 per cent, CP II 35,52 per cent, CP III 61,95 per cent, and last the approval

phase 90,35 per cent. The cumulative success rate is 11,83 per cent, which is much lower,

compared to the previous studies. Compared to the two previously mentioned studies the

11 The size was measured in sales numbers

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success rate of clinical phase I and II is substantially lower. The above results are presented in

table 2.1.

Table 2.1: Clinical success rates

Discovery CP I CP II CP III NDA Total Authors / Succes per cent

DiMasi & Grabowski, 2007 71% 44,2% 68,5% - 21,5 %

DiMasi et al., 2010 67% 41% 63% 90% 15,58%

DiMasi et al., 2014 59,52% 35,52% 61,95% 90,35% 11,83%


As seen in table 2.1, the studies of success rates show some different results. The differences

in percentage are caused by the different measurements, pharmaceutical classes or other

statistical estimations used by the authors. Given that the approval phase is not a part of the

total success rate in DiMasi & Grabowski (2007) the estimations is higher compared to the two

other studies. If we adjust the estimate with the approval phase from DiMasi et al. (2010) and

DiMasi et al. (2014), which is around 90 per cent, we estimate a total success rate of 19,3 per

cent.

2.6.2 Costs

Several studies have analysed the development process of the pharmaceutical industry but

only few of them have studied the costs of the R&D process. A significant variation in the cost

estimations among the studies complicates the findings. Through the literature we find that

drug development costs range from US $75mio to $4billion dollars (PWC, 2012). Most studies

lean towards the higher end of the range, as seen in the table below. The significant cost

variation makes it necessary to examine the following literature critically, as mentioned in the

introduction.

The significant cost variation can often be explained by two components (Ding et al., 2014).

The first component is a question of the definition of R&D costs. As just explained in the

previous section on success rates, the pharmaceutical industry is influenced by low success

rates meaning that several drugs are abandoned before a successful drug is discovered and

developed. Some argue that the R&D cost should include cost of both the successful and the

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abandoned drugs, while others do not. The second component is the allocation of opportunity

cost due to the long time horizon of the development process. The average time of a drug

development is 12 years and the opportunity cost thus has a significant influence on the total

cost allocation (Ding et al., 2014). Both components will be explained more in the following

examples.

Similar to the literature on success rates the publication by DiMasi & Grabowski (2007) is one

of the most cited by the industry. The authors estimated in 2007 an average out-of-pocket cost

per new drug of US$672 million and after capitalising that at an opportunity cost of 11 per

cent the total pre-approval cost was estimated to $1318 million dollars.

The paper by Light & Warburton (2011) criticises these estimates and argues that since none

of the drugs were titled or specified in therapeutic classes, it is not possible to verify these

results. The authors further argue that the estimates do not include any R&D tax

adjustments, and that they should be based on median numbers rather than a mean, which

decrease the influence of extreme outliers. Most criticised is the allocation of 11 per cent

opportunity cost, which doubles the total cost estimations from $672 million to $1318 million

dollars. Even if one accept the use of opportunity costs, US government guidelines call for

using 3 per cent and not 11 per cent opportunity cost. As a part of their critic, they calculate

their own cost estimations based on the data of DiMasi & Grabowski (2007) and found a

median cost ranging from US$180-231 million dollars.

In 2012 Price Waterhouse Cooper estimated the development cost of an average

pharmaceutical company (PWC, 2012). They found a significant variation in costs depending

on therapeutic classes similar to other studies. Based on average costs and average attrition

rates in each phase of the R&D process, the cost of the R&D process was estimated to be

around US$701 million dollars per pharmaceutical product. More detailed numbers for each

R&D process were given as; preclinical and development $87 million, CP I for $130 million, CP

II for $190 million, CP III for $268 million, and lastly $26 million dollars in approval. The

publication did not include the preceding calculations for the estimations and therefore not

possible to discuss further.

The 2010 publication by Bogdan & Villiger (2010) estimated the cost of each clinical phase in a

small and medium sized pharmaceutical company. Compared to the other literature, the

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estimations by Bogdan & Villiger (2010) provide some of the lowest cost estimates. This is

mainly due to the fact that the estimations are made for smaller companies. More essential

questions of both opportunity cost and failure costs are not clarified, and the reader must

assume that both components have been left out. This could also explain the low cost

measures in each phase of development. The total average cost accounts for: research and

discovery US$ 4-6 million, CP I for $1-5 million, CP II for $3-11 million, CP III for $10-60

million, and last the approval phase for $2-4 million dollars. The maximum total cost denotes

to $86 million dollars, which is incredible low compared to the other findings.

The latest report by CSDD DiMasi et al. (2014) estimates the average capitalised cost to be

US$2.2558 million dollars, allocated as $1.098 million cost in pre-human and US$1.460

million dollars in clinical testing. The cost estimate is calculated using a 11,4 per cent

opportunity cost, which almost doubled the out-of-pocket costs from US$ 1.395 million to 2.558

million dollars. The above results are presented in table 2.2.

Table 2.2: Cost of drug development

Discovery CP I CP II CP III NDA Total Authors / Costs million dollars

DiMasi & Grabowski, 2007* 150 522 672

DiMasi & Grabowski, 2007 439 879 1318

Light & Warburton, 2011 180/231

PWC, 2012 87 130 190 268 26 701

Bogdan & Villiger, 2010 6 5 11 60 4 86

DiMasi et al., 2014 1098 1.460 2.558


*Out-of-pocket costs not capitalised (DiMasi & Grabowski, 2007)

As seen in table 2.2 the different cost estimates differ quite substantially. Cost figures range

from US$ 86-2.558 million. When taking the different methods of approach and component

assumptions in each of the studies into consideration, the variation may not be as surprising

as first noticed.

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2.6.3 Time

According to Ding et al. (2014) a successful pharmaceutical company must be able to balance

returns, uncertainty, and not least time. The majority of the income of a pharmaceutical firm

is generated from drugs with patent protection, which will fade out as soon the patent ends

(Ding et al., 2014). The time of research and development has a significant impact on earnings

in the pharmaceutical industry, since a long development process reduces time of patent

protection (as mentioned earlier on page 9).

In 2010 Bogdan & Villiger (2010) found that small and medium sized pharmaceutical

companies had an average development time of; discovery and research 30-42 month, CP I for

18-22 month, CP II for 24-28 month, CP III for 28-32 month, and approval for 16-20 month.

The maximum length of the R&D process is 12 years, which is similar to Ding et al. (2014) and

a minimum time of nine and a half year.

The latest publication by the CSDD DiMasi et al. (2014), which is based on ten unknown

pharmaceutical and 106 new drugs in the US, estimates the following time length of the total

development process; discovery 31,2 month, CP I 19,8 month, CP II 30,3 month, CP III 30,7,

and last approval 16 month. The total time length from discovery to approval was observed to

be 10,6 years (DiMasi et al., 2014).

In 2011 Kaitlin & DiMasi (2011) completed a study on the length of clinical phases and the

approval time on new drugs in the US. The data was gathered using the before mentioned

CSDD database from the period 1980 to 2009. They grouped the data in to brackets of five-

year periods to see the development in clinical phase- and approval time. The earlier results

from their study seem less relevant for this thesis, why only the newest results will be

presented here. They did not distinguish between CP I to III but grouped them in one

category, but they had separate data for the approval time. The total clinical phase time was

in the last period of data, 2005-2009, 76,8 month, while the approval time comprised to 14,4

months. The total time from first in man testing (clinical phase I) to approval was 91,2 months

(7,6 years).

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Table 2.3: Clinical time length

Discovery CP I CP II CP III NDA Total Authors / Time in months

Ding et al., 2014 12 yr.

Bogdan & Villiger, 2010 30-42 18-22 24-28 28-32 16-22 12 yr.

DiMasi et al., 2014 31,2 19,8 30,3 30,7 16 10,6 yr

Kaitlin & DiMasi, 2011 76,8 14,4 7,6y r.


As illustrated in table 2.3, the variation in time length is rather low. From the above, we find

the typical time length of a drug development to be 7,6 to 12 years. It is worth noticing that

the publication by Kaitlin & DiMasi (2011) finds a shorter period of drug development. This is

mainly because the discovery phase is not included in the development period. Furthermore,

the study does not divide the clinical phases in to separate phases, which makes it less usable

and expressive.

2.7 Sum-up

This chapter has presented some of the main characteristics of the pharmaceutical industry.

Characteristics that give an indication of an industry that generally face high uncertainty and

risk. From complex patent legislation to the very risky processes and clinical phases

pharmaceutical companies go through in the development new drugs. Combining this with the

just presented actual industry measures on R&D-cost, drug development success-rates, and

time needed to develop a new approved drug, it is clear that valuation of pipeline-projects

within this industry calls for much consideration and attention. Do the well-known

fundamental valuation methods suit the characteristics of the industry or are other valuation

methods more suitable when valuating projects within this industry? During the theoretical

discussion of different valuation methods, continuous references will be made to this chapter’s

description of the characteristics of the pharmaceutical industry.

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3 Valuation methods in the pharmaceutical industry

The previous sections have introduced the pharmaceutical industry and some few significant

characteristics of it. To answer the problem statement, this section will analyse and discuss

some of the theoretical differences between fundamental valuation models and the more

complex real options valuation methods and their underlying assumptions. Each valuation

method will be theoretically discussed and evaluated upon four defined criteria. The potential

of each valuation methods will be evaluated after the practical implementation.

The decisions of financial analysts in corporate finance, in a very simplistic way, can be

divided into two overall decisions. First one is the investment decision, which is choosing the

projects that have positive NPV. Second one is the finance decision, which is deciding on how

to finance the selected projects. All decisions have the overall goal of maximizing the market

value of a given portfolio of investments. These decisions are undoubtedly connected with the

strategy a company pursues. And in an increasingly uncertain global marketplace, strategy

and strategic flexibility are becoming more important for firms in order to capture the

advantage of future opportunities, and limit losses of any unfavourable developments (Smit &

Trigeorgis, 2004). Having the previous chapter in mind, it is clear that the pharmaceutical

industry to a high degree face such challenges. Therefore, the purpose of this chapter is to

present, analyse, and discuss possible project-valuation methods for the pharmaceutical

industry in order to continue with an evaluation of the practical implementation through a

case study and finally make some statements regarding the optimal method to use.

As mentioned in the introduction, the perspective of view is of financial analysts, meaning it is

an outside-in perspective. Also, as mentioned earlier several studies have previously found

that financial analysts favour the present value approach and that the real options approach

is hardly ever used (Block, 2007; C. V. Petersen & Plenborg, 2012). And, this is where the

thesis has its merits – an investigation of which valuation methods are most suitable in theory

and practice when valuing pharmaceutical drug development projects.

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3.1 The Criteria

To carry out the discussion of the different valuation methods, we have constructed four

criteria to evaluate them. Each criterion will be explained in depth in the following section.

The four criteria are chosen to deepen the overall evaluation and improve the understanding

and the analysis of the different assumptions, limitations, and uncertainty factors of the

valuation methods. The criteria, which are seen in figure 3.1, touch upon what previously has

been characterised as fundamental requirements and cosmetic requirements (Plenborg, 2000).

The first, fundamental requirement, relates to whether a valuation model gives an unbiased

and realistic result, while the cosmetic requirements relates to the intuitive and

understandable use of the methods. The fundamental requirements always dominate the

cosmetic requirements, as the opposite may lead to irrational investment behaviour, which of

course is not preferable under any circumstances (Plenborg, 2000). The importance of the

cosmetic requirements should not be underestimated though, as a precise and unbiased

valuation method could be abandoned because of its cosmetic complexity. A later publication

by C. V. Petersen & Plenborg (2012) describes somewhat similar requirements to valuation

models. The authors use terms like value attributes and user attributes corresponding to the

fundamental and cosmetic requirements.

Figure 3.1: Criteria for evaluation of valuation methods


Inspired by this, we have created the four criteria above. Concept and Uncertainty are

influenced by the fundamental requirement, while the two last criteria are inspired by the

Criteria to evaluate valuation methods upon

Fundamental

requirements

Cosmetic

requirements

Concept

Strategic flexibilityUncertainty

Usability

ValuationModel

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cosmetic requirement. In the following section, each criterion will be explained and applied to

each valuation method.

3.1.1 Concept

In order to facilitate a discussion and be able to identify differences in valuation methods we

construct the concept criterion. The concept criterion is used for assessing basic conceptual

differences in the valuation methods. This will provide the fundamental insight in the

different models and make it possible to comment on general differences. This description of

the concept criterion corresponds to the fundamental requirement.

3.1.2 Uncertainty

This criterion is used to evaluate the perception and measure of uncertainty in each valuation

method. The criterion furthermore investigates which kind of uncertainty parameters the

valuation models include, and how they are affected. Additionally some of the underlying

assumptions of the models will be touched upon and discussed. This criterion is assumed to be

one of the most essential, as it affects the practical implementation and not least the value

provided by the different models. Again this criterion relates to the previously explained

fundamental requirement.

3.1.3 Strategic flexibility

The strategic flexibility criterion examines whether the valuation methods are able to

incorporate events in the future. Events are defined as what happens when new information

becomes available. Strategic flexibility is defined as the strategic decision for managers to

either maximize or minimize the influence of future events.

The previous chapter has given the picture that the pharmaceutical drug development is a

process involved with great uncertainty and high cost. This fact makes it highly relevant to

evaluate the different valuations methods ability to incorporate strategic flexibility because

this flexibility would intuitively add a substantial value to a project. Strategic flexibility is

related to the cosmetic requirement, since it makes it possible for the user to understand and

perceive flexibility through the way, it is cosmetically modelled.

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3.1.4 Usability

The usability criterion helps to evaluate how theoretically usable and user friendly the

different valuation methods are. The criterion will touch upon several aspects. The

intuitiveness of the results and by that also complexity of the methods is considered. In the

walkthrough of the different valuation methods usability will only briefly be touched, as it is

only theoretical usability, which the criterion focus on.

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3.2 Standard DCF model

In the following, the standard discounted cash flow model (DCF) will be shortly discussed

based on the four mentioned criteria. Assumed that the DCF model is more or less well known

by the reader, it will only be shortly evaluated. The model is one of the most widely accepted

models (Bancel & Mittoo, 2014; Mun, 2002).

3.2.1 Concept

The DCF model is based on the income approach to valuation. The income approach looks at

the free-cash-flow potential of an asset and quantifies, forecast and discount these cash flows

to a present value (Mun, 2002). Other valuation models are based on these principles as well,

but the most common and widely accepted valuation model is the standard DCF model, which

is depicted in figure 3.2. In the following, the model will be referred to simply as the DCF

model. As expressed in the formula, the model calculates the net present value of an

investment based on its potential to generate future cash flows, and then adjusting for the

weighted average cost of capital of debt and equity (WACC).

Figure 3.2: Standard discounted cash flow model

Standard discounted cash flow model

Net Present Value = I0 + ∑FCFt

(1 + 𝑊𝐴𝐶𝐶)𝑡

∞

t=1

I0: Initial investment

FCF: Free cash flow

WACC: Weighted average cost of capital

t: Time

Source: Own creation and (Koller, Goedhart, & Wessels, 2010)

As shown in figure 3.2, the model consists of four inputs where the initial investment and time

are known, and the free cash flow and weighted average cost of capital are estimated inputs.

The free-cash-flow is estimated as earnings after tax, less capital expenditure, less net

working capital, plus depreciations (Koller et al., 2010). The discount rate is estimated as the

weighted average of cost of capital of both debt and equity.

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3.2.2 Uncertainty parameters

The DCF model relies on some strong assumptions and limitations. The DCF model perceives

uncertainty as risk implying that more uncertainty increases the amount of risk in a specific

project and decreases the net present value. In the DCF model, all risk is completely

accounted for in the discount factor, which makes it a central and critical parameter in the

DCF model (Mun, 2002). In the following, only the cost of equity will be discussed in relation

to uncertainty, since the later case study does not consider debt financing, which will be

explained later. There are several methods to estimate the cost of equity. The most common

model is the capital asset pricing model (CAPM). The fundamental assumption of CAPM is the

law of one price, which states that in a competitive market, investments with similar risk

should have the same expected return. Investors can thereby eliminate firm-specific risk by

diversifying their own portfolios and only hold systematic risk (Berk & DeMarzo, 2014).

CAPM relies on the assumption that all investors have perfect information and are able to

hold a well-diversified market portfolio. The CAPM equation expressed in figure 3.3 is a linear

relationship between the risk free rate, beta, and the market risk premium.

Figure 3.3: Cost of equity

Cost of equity

Equity cost of capital = 𝑟𝑓 + 𝛽(𝐸(𝑅𝑚) − 𝑟𝑓)

rf: Risk free rate

𝛽: Beta

E(Rm)-rf: Market risk premium

Source: Own creation and (Koller et al., 2010)

Out of the four input factors, only beta is individually defined for each specific investment.

The risk free rate and the market risk premium are not defined individually for each

investment but are depending on the industry or sector. This causes the beta to be the factor

exposed to most uncertainty and thereby more difficult to estimate. Beta is defined as a

sensitivity factor measuring the expected percentage change in the excess return of a security,

relative to the change in the excess return of the market (Berk & DeMarzo, 2014). In order to

be able to estimate a reliable measure of beta, it is for example necessary to use average or

median long-term equity prices to avoid short-term fluctuations. Further, for non-traded

physical assets like pharmaceutical products it is difficult to estimate beta. The argument of

using a company’s beta is not adequate, as project risk may differ from the company risk.

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3.2.3 Strategic Flexibility

The standard DCF model can only in a very limited way incorporate future events. Through

scenario- and sensitivity analysis one can for example analyse the effect of changes in the

input variables. These considerations typically involve a worst- and best-case scenario and/or

calculations on how different parameters affect the DCF valuation, such as the discount rate,

growth rate etc. Although the standard DCF model can incorporate these events through the

case-analysis just mentioned, it does not capture the actual value of having the opportunity to

react to these events. Scenario-analysis only takes into account one path of uncertainty,

whereas in for example Real Option Analysis all future paths are considered (Triantis, 2005).

It is not possible for the standard DCF model to incorporate this strategic flexibility value

because of the model’s passive management assumption (Mun, 2002: 59). Expressed in other

words, the standard DCF model makes decisions based on today’s expectation of future

information (Koller et al., 2010). However, in the development of pharmaceutical drugs, this is

not the case. Usually a project is actively managed through the projects life cycle, through

either increased commitment or a reduction of exposure, such as budget constraints. The

standard DCF model is therefore not recommended in situations, where active management is

highly necessary in order to maximize project value. Meaning, that using a deterministic

model as the DCF in a stochastic world, may underestimate the value of projects grossly (Mun,

2002: 58).

In the context of the pharmaceutical industry one could argue that it is an industry that does

have a high need for active management. A clear example of that are the mentioned phases in

drug development. The need for active management is somewhat obvious since the value of a

project is heavily reliant on specific project events.

3.2.4 Usability

The standard DCF model is generally perceived as rather user friendly and easy to apply in

relation to theoretical usability. It is one of the most widely used valuation method regardless

of what industry context you operate within (Bancel & Mittoo, 2014). In general, the

estimation of input is perceived as having high usability, but this may be because of the

experience of using the model, rather than actual ease in estimating the input. This will be

elaborated later, when performing the case study. The DCF model is not complicated to use,

and the time effort needed for the actual valuation calculations are not demanding. However,

in some cases estimation of input can be rather cumbersome and time demanding, often

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depending on the level of detail needed. The intuitive appeal is clear though and the outcome

of the model is easy communicated through an organisation. What is to be communicated is if

benefits outweigh cost and NPV is positive (Berk & DeMarzo, 2014).

The below figure 3.4 is a summary of the main findings in each of the four criteria of the DCF

model.

Figure 3.4: Summary of DCF


- Valuates the FCF potential of an asset - Perceives uncertainty as risk through beta

- Discounts FCF at WACC or cost of equity - Difficult estimation of beta and the CAPM assumptions

- More uncertainty decreases project value

- Based on today's expectations of the future - Uncomplicated to perform

- Low flexibility through sensitivity analyses of input and result - Well-known and simple to communicate

- Low flexibility due to passive management assumption

UncertaintyConcept

Strategic flexibility Usability

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3.3 Decision Tree Analysis

One alternative valuation method is the Decision Tree Analysis. In the following this method

will be analysed through the four criteria.

3.3.1 Concept

Decision Tree Analysis (DTA) is a relatively simple model that can be used to evaluate options

and is often mentioned to be able to include the value of managerial flexibility. DTA is based

on discounting contingent12 payoffs and investment with appropriate discount rates (Koller et

al., 2010). However, instead of simply discounting a single line of payoffs as in the DCF model,

the DTA model constructs a tree consisting of events and decisions as seen in figure 3.5. The

DTA approach is sometimes referred to as a contingent valuation approach (Koller et al.,

2010).

Figure 3.5: Example of a decision tree


As seen in figure 3.5, calculating the value in each decisions node from right to left until

reaching time zero, solves the decision tree as the one above. Based on the specific

probabilities of something occurring in each of the events, the end value of the decision tree

can be calculated as a weighted average of the different outcomes discounted with appropriate

discount rates for respectively cash flows and investments. The probability of something

occurring can in the context of the pharmaceutical industry be translated into technological

12 Contingent payoffs are payoffs that are uncertain and dependent on certain conditions (Koller, Goedhart, & Wessels, 2010).

Decision tree

: Technological risk event Invest: Decision event

Invest

Invest

Succes

DTA

Failure

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uncertainty, which again can be translated into the success rates in each of the clinical

phases. One of the difficulties in using DTA lay within finding the appropriate discount rate

and the specific probabilities for each of the decision nodes, which is elaborated below (Smit &

Trigeorgis, 2004).


The DTA model perceives uncertainty as both risk and opportunities. Risk as the occurrence of

something undesirable (success) and opportunities as something desirable (failure). This can

be seen as the up and down arrows in figure 3.5. This stands in contrast to the standard DCF

model explained above, which only perceived uncertainty as risk – something that decreases

the value of a project. Since it is now assumed that management can make decisions regarding

the project along the way, and make decisions that optimizes the value of the project, the DTA

value will provide a greater value than a standard DCF valuation of the same project.

The contingent cash flows and investment should, as mentioned before, not be discounted with

the same rate. Otherwise, the DTA is likely to overestimate the value of flexibility and

ultimately the value of a project (Koller et al., 2010). Investment outlays are certain (private

risk) and they should then be discounted at a risk-free rate (Koller et al., 2010), while the

payoffs (cash flows) should be discounted at a market-adjusted discount rate, such as WACC,

since market risk is compensated and not the private risk (Mun, 2002). It is often difficult to

find the appropriate discount rate for the tree as a whole, because the discount rate changes

through time as the risk in the project also changes (Lander & Pinches, 1998). Furthermore,

there is no direct way of determining the appropriate discount rate for the tree other than

deriving it from alternative real option methods (Koller et al., 2010).

Another parameter of uncertainty concerns estimating the probabilities used in each of the

events (the technological uncertainty). The probabilities in each of the events must be known

and are specific to each project and event. In many cases it can be somewhat difficult to

reliably and consistently estimate these probabilities, which complicates and make DTA. On

the other hand, in cases where it is reasonable easy to derive these probabilities and use them

confidently, DTA may be the better choice.

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3.3.3 Strategic flexibility

The DTA model, compared to the more static standard DCF model, incorporates future events

and strategic flexibility. Through the decision tree, the DTA model incorporates future events

and decisions, which are the main differences from the standard DCF model (Smit &

Trigeorgis, 2004), and also what drives the uncertainty. The incorporation of future events

implies that the model is not simply based on today’s future expectations, but makes it

possible for managers to make decisions based on new information as time progress. The

decision-based approach of the DTA model makes it possible for managers to maximise a

project’s value based on future events. Thus theoretically creating more strategic flexibility to

managers or in other terms it helps “bridging the gap between strategy and finance” (Skjødt,

2001). The model is therefore also theoretically more suitable in situations where active

management is highly necessary in order to maximise project value. In the context of the

pharmaceutical industry the DTA model has some interesting valuation aspects, as the model

incorporates future strategic flexibility, which is relevant in the context of the different

clinical phases.

3.3.4 Usability

The DTA model has a lower degree of theoretical usability compared to the standard DCF

model, as the uncertainty parameters are more complex to estimate. The usability of the DTA

depends on, whether the input parameters such as discount rates and event probabilities can

be estimated accurate in each event node. Subjective probabilities of technological uncertainty

and discount rates are required in each event note, which complicates the estimations and

may result in wrong outcomes (Mun, 2002). As mentioned above, finding the appropriate

discount rate along each branch at different times is not an easy task (Smit & Trigeorgis,

2004). The complexity of the input parameters is further depending on the number of events

in the model, as the risk of estimation errors increases when managers have various events to

analyse. The DTA is evaluated to have a medium complexity of use taking the difficult input

parameters into consideration. The outcome of the model is easy to communicate and more or

less intuitive for practitioners, who are already familiar to the DCF model. Using DTA in

project valuation is evaluated to require more time and more resources.

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The below figure 3.6 is a summary of the main findings in each of the four criteria.

Figure 3.6: Summary of DTA


- Decision tree consisting of future events and decisions - Perceives uncertainty as both risk and opportunities

- Discounts contingent cash flows with appropriate rates - Difficult to determine correct discount rates

- Probabilities as clinical success rates - Requires knowledge of probabilities of future events

- The model captures future events through a decision tree - Requires more theoretical knowledge than the DCF

- Incorporates flexibility in the ability to act upon future events - Medium theoretical complexity

- Flexibility through probabilities i.e. technological uncertainty - Depends on the number of future events modelled


Concept Uncertainty

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3.4 Real Options

The following section will provide an introduction to the Real Options approach and evaluate

both the binomial and the quadranomial lattice model upon each of the stated criteria. First of

all, a brief introduction to financial options is presented, followed by real option theory, since

the Real Option approach is based on the basic concept of financial options.

3.4.1 Concept

Before the evaluation of Real Options upon the concept criteria, the basic concepts of financial

options are introduced. Financial options are options on financial assets such as shares of

stock, bonds, or tradable commodities. The basic in a financial option is that the option holder

has the right but not the legal obligation to either sell (put) or buy (call) an underlying asset

(S) at a pre-specified strike -or exercise price (K). If the option holder has the opportunity to

exercise the option before the maturity date (t), the option is known as an American option.

Otherwise, if the option can only be exercised at maturity, it is then known as an European

option. In general, there are four possible positions to take: buyer of a call, the seller/writer of

a call, the buyer of a put, and the seller/writer of a put (Mun, 2002), and for every position one

can take, there is a counter position. Meaning, that for every option owner (long position),

there must be an option seller/writer (short position) as well.

The payoff of an option on a stock is determined by the price of the underlying stock when

exercised. For call options, if the stock price (S) is greater than the strike price (K) it will be

exercised with profit. Since, the option holder can buy the stock from the option writer at the

pre-determined strike price (K) and sell it in the market to the higher price. If the stock price

(S) is less than the strike price (K), the option will then not be exercised. The contrary is the

case for put options. If the stock price is below the strike price, the option will be exercised,

since the holder will receive the strike price, while the stock is only worth the lower stock price

(Berk & DeMarzo, 2014). This can be seen in the figure below. The values are known as the

formula value or intrinsic value of an option.

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Figure 3.7: The intrinsic value of options

The Intrinsic Value of Options

Call Value: Put Value:

C = max(S-K;0) P = max(K-S;0)

Source: Own creation based on (Berk & DeMarzo, 2014)

The payoff structure of the four just mentioned possible positions are shown in the below

figure. It shows the asymmetric payoff in the options. A long position in an option will capture

only the upside and never have a value below zero.

Figure 3.8: Payoff positions

Source: Own creation based on (Berk & DeMarzo, 2014).

The value of an option is in general driven by three major factors. The underlying stock price,

as mentioned above, is the first and most apparent. If the exercise price is kept constant, the

movement in the underlying asset drives a large part of the option value (intrinsic value).

The second is time to maturity. The longer time the option has left, the more time there is for

the option to get in the money. Hence, the longer time to maturity, the higher the option value

Long call and put option

Value Call option Value Put option

Share price Shareprice

Short call and put option

Value Short Call Value Short put

Share price Shareprice

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is (time value). The last factor is the volatility of the underlying. Higher volatility means

higher option value. Higher volatility implies that the options have a greater chance of getting

in the money before it expires (Brealey, Myers, & Allen, 2008).

There are a variety of different methodologies and approaches used to calculate the actual

value/price of a financial option. They range from closed-form equations such as the Black-

Scholes model, simulation models like Monte-Carlo Simulation, lattices (binomial and other

multinomial trees), or using finite differences such as partial-differentiated equations

(Bogdan & Villiger, 2010; Mun, 2002). Each method should in theory provide the same

numerical output, which makes the decision on which method to use more a question of

methodology and appropriateness of the problem at hand, than the result of the valuation.

When valuing financial options, there is often no need for explicit explanation of the valuation-

process, more on the actual result, why closed-form solutions are the most frequently used

(Brandão, Dyer, & Hahn, 2005; Hartmann & Hassan, 2006; Kellogg & Charnes, 2000)

Real options, as the name imply, use option theory to value physical or real assets, opposite to

financial assets (Mun, 2002). Real Options have several similarities to financial options,

because the holder of a Real Option also has the right, but not the obligation, to exercise the

option. Some of the key differences between the input to financial and real options are listed in

table 3.1

Table 3.1: Difference between financial and real options

Variables

Financial options Real Options

Value of underlying asset S Stock price - financial asset Present value of project

Time to maturity t Fixed in contract Variable

Exercise price K Fixed in contract Cost of realizing option

Volatility σ Volatility of the stock -increases Volatility of the project - increases

Option price Price fixed by financial markets Not fixed – often negotiable

Control of the option value No control Possibility to affect option-value

Liquidity of the option Tradable in financial markets Most often not tradable

Rationality in exercising Mostly rational Affected by circumstances

Source: Own creation inspired by (Kodukula, 2006)

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The main differences are described in table 3.1. Some of the most interesting differences are

the liquidity, control of option value, and value of the underlying asset. A key distinction

between these two option approaches is that real options and the underlying assets are rarely

traded in competitive markets (Berk & DeMarzo, 2014). Relating to the pharmaceutical

industry, the exercise price is assumed to be equivalent to the R&D cost, and it is apparent

that pharmaceutical drug development projects are not traded. With these differences in

mind, we continue our investigating of the Real Option theory.

As mentioned in the introduction chapter the focus in the thesis is on a few specific valuation

models. The latter focus is on the binomial lattice model and the extended quadranomial

lattice model. These will in the following be discussed in relation to the concept criteria.

3.4.1.1 The binomial lattice approach

The binomial lattice approach is often praised for its mathematic simplicity and ease of use.

As most of the real option models provide the same results at the limit13, the binomial lattice

approach is often recommended as the simplest model to evaluate and capture the value of

management decisions (Bogdan & Villiger, 2010; Mun, 2002).

As previously outlined, the pharmaceutical industry is characterised by multiple clinical

phases. Each development phase can be characterised as an option of different opportunities,

which often is recommend, to be valued using the binomial lattice approach. In essence, a

binomial lattice model is simply a discrete simulation process of the value of uncertainty

(Mun, 2002). Meaning that the binomial lattice model estimates the potential values of a risky

underlying asset in a binomial tree (Koller et al., 2010; Mun, 2002). The model assumes that

the underlying asset follows a binomial distribution in each time stage (t), as the value can

either increase (u) or decrease (d). A simple binomial tree of the up and down stages is

illustrated in figure 3.9.

13 If the time steps in the binomial model has around 10.000 steps, the binomial and Black-Scholes approach gives the same

numerical result (Mun, 2002).

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Figure 3.9: Recombining binomial tree


Figure 3.9 illustrates the simplicity of the binomial approach, based on the symmetric up and

down stages of a binomial tree. It is often assumed that the trees’ steps are recombining,

which basically means that the same value is reached no matter if the steps are up-down or

down-up. The binomial approach can be solved using two different methods, the market-

replicating portfolio and the risk-neutral probability approach. The results of the methods are

identical, but the underlying assumptions and usage are very different, why each method will

be discussed in the following section.

The replicating portfolio values the option using a constructed replicated portfolio. The

portfolio replicates the value of the option in any given state and must be rebalanced if there

are multiple periods. As the replicated portfolio and the option must have the same payoff

profile, it is possible to calculate the present value of the option using the replicating portfolio.

In a financial world the replicating assumption is easy to accept, as stocks are freely traded

and often highly liquid. In a real option world, where physical assets and firm-specific projects

are being valued, it is difficult to accept the assumption of a replicating portfolio (Mun, 2002).

The essence of the risk neutral probability approach is that instead of replicating a portfolio,

the model simply risk-adjust the probabilities of future cash flows occurring at specific time.

Using risk-adjusted probabilities at future cash flows allow decision makers to use the risk-

free discount rate in the estimation process. The results of both approaches are as mentioned

identical, why the model of choice should be the one that best satisfies the mentioned

assumptions. In the context of the pharmaceutical industry, we believe that the risk-neutral

approach is theoretically a better choice, since it is for example not possible to estimate a

replicating-portfolio. This is mainly because, as we have already established, pharmaceutical

drug development projects are not traded. The formula of the risk-neutral approach is showed

in figure 3.10.

Binomial tree

uV

dV

d^2V

udV

u^2V

Vo

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Figure 3.10: Binomial risk-neutral formula

Source: Own creation and (Mun 2012)

The inputs for estimating the risk-neutral approach are the volatility of the underlying asset,

time to expiration, and the risk-free rate. The up and down movements are equal to the

discrete simulation steps, and the risk-neutral probability is used for backward induction of

the binomial tree. As seen in figure 3.10, the value of the option is depending on nothing more

than the constant volatility (σ) and the variable time factor (t). Higher volatility increases the

range between the nodes, and a volatility of zero collapses the binomial tree into a straight

line (Mun, 2002). The reciprocal relationship between the up and down stages makes the tree

re-combining. When the risk-neutral approach and the up and down movements are

estimated, the value of the option can in the risk-neutral world be calculated using the

formula below in figure 3.11.

Figure 3.11: Option value formula in a binomial tree

Source: Own creation and (Mun, 2002)

Binimial risk-neutral formula

p/q = risk neutral proberbility

u: up movement

d: down movement

rf: risk-free rate

∆t: time step

σ: volatility

p

q 1 −

u 𝑡

d 𝑡 1

Option value in binomial tree

OV0: Present value of option

OVu/d: value of option in up and down movements

p: risk-neutral proberbility

rf: risk-free rate

∆t: time in years

0 + 1 − 𝑡

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The formula in figure 3.11 shows that the value of the option is equal to each expected up and

down stages discounted at the risk free rate. To estimate the value of a binomial lattice model,

it is first necessary to build the asset value tree of the up and down stages of the underlying

asset. Based on the asset value tree, the option formula is used to calculate the present value

by solving it recursively, using backward induction. Figure 3.12 illustrates how the exercise

price (EX) is subtracted in the final node.

Figure 3.12: Option value tree for a two period call option

Source: Own creation inspired by (Mun, 2002)

The following section will present and discuss the concept of the quadranomial lattice

approach. The underlying assumptions will be discussed more in depth in the section of

uncertainty parameters.

3.4.1.2 Quadranomial lattice approach

This section will evaluate the quadranomial lattice approach upon the concept criteria. In

relation to the problem question concerning the potential of option valuation, the

quadranomial lattice approach is interesting to analyse, since the model investigates more

than one source of uncertainty and is less mentioned by practitioners and the general

literature (Rogers, Gupta, & Maranas, 2002). The potential of this model is therefore not as

well studied and why we find it interesting to investigate in relation to the pharmaceutical

industry. The quadranomial lattice approach is an extension of the binomial model, since the

model can theoretically incorporate two sources of uncertainty instead of one. The model is

able to include, what we term as both the market- and technological uncertainty associated

Option Value tree for an two period call option

0 + 1 − 𝑡

0 + 1 − 𝑡

0 + 1 − 𝑡

0 0 − 𝐸

0 0 − 𝐸

0 0 − 𝐸

Backward induction

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with a specific project (Copeland & Antikarov, 2001). Market and technological uncertainties

are very different in nature, but both are assumed to influence the development of a

pharmaceutical development project. This will be explained below. Using two sources of

uncertainty results in four outcomes in each time node, hence the name quadranomial, which

can be seen in figure 3.13

Figure 3.13: Possibilities in quadranomial tree

Source: Own creation and (Rogers et al., 2002)

Figure 3.13 illustrates the influence of both technological and market uncertainty.

Technological uncertainty can either influence a drug development project to either succeed or

fail a clinical phase, illustrated by the horizontal line. If the project fails because of

technological uncertainty, for example low efficacy or unwanted side effects, the value of the

project becomes zero illustrated by O3 and O4. This makes the market movements without

effect on the project value. If the project succeeds technological uncertainty, the project can

either increase or decrease by the effect of market movements. This is illustrated by O1 and O2.

The quadranomial model thus has four different outcomes, illustrated as O1 to O4, instead of

only two, as the binomial model. These outcomes are used in the calculation of the option

value.

Possibilities in quadranomial tree

O1: up

O2: down

Succes

Failure

O3: up

O4: down

V0

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Figure 3.14: Qudranomial formula

Source: Own creation inspired by (Koller et al., 2010; Mun, 2002)

Figure 3.14 shows the backward induction formula of the quadranomial lattice model. The

first equation shows the influence of technological uncertainty. This is expressed as the

probabilities of technological success (S) and technological failure (F). The second equation

shows that the probability of technological failure (F) can be separated from technological

success (S). In the third equation the probability of technological failure is left out of the

formula, as a failure of technological uncertainty causes the drug development project to have

a value of zero, as explained in the above section.


This section will discuss the underlying assumptions of the binomial and quadranomial lattice

approaches and further discuss the most uncertain parameters. As both models rely on the

same assumptions, the term real options approach will be used as reference for both models in

the following section.

3.4.2.1 Market Completeness and Market Asset Disclaimer

Since it is difficult or almost impossible to find a twin security of a real option, several authors

argue that it is sufficient to estimate the real options value as if the asset were traded, if a

reliable value of the underlying asset can be estimated (Smit & Trigeorgis, 2004). To do so,

most of the literature recommends using the present value of the underlying asset, without

flexibility as the twin security (Copeland & Antikarov, 2001; Smit & Trigeorgis, 2004). To

estimate the value of the underlying asset without flexibility, the previously explained DCF

Quadranomial formula

S: technological succes

F: technological failure

EX: excercise price

e-rf ∆t

discount of one period

OV: option Value

On: outcome in n

p/q: risk-neutral probability

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model is often used. The DCF model additionally relies on the assumption of market

completeness, which assumes that all assets can be traded in the market without any

transaction costs. By using the DCF value as the underlying asset, the real option valuation

can help determine the value of the option relative to the estimated underlying project (Smit

& Trigeorgis, 2004). This assumption is also known as the Marketed Asset Disclaimer (MAD),

which is accepted in the following case in the next chapter. By assuming the MAD assumption

and the DCF value of the underlying asset, it can be argued that the above assumptions of the

real option approach are not stronger than the DCF model.

The next couple of sections will discuss the uncertainty variables, when using real options

models. The choice of approach determines the sources and measurements of uncertainty.

First, we introduce the market uncertainty, which is the building block of the lattice

approaches.

3.4.2.2 Market uncertainty (σ) & volatility estimation

The real option approach perceives in general uncertainty as both risk and opportunities.

More specifically market uncertainty is perceived as the possibility of the underlying asset to

either decrease (d) or increase (u). In the binomial model market uncertainty includes both

diversifiable and non-diversifiable risk.

Both the binomial and the quadranomial approach estimate market uncertainty by a constant

volatility (σ), expressing the volatility of the underlying asset (Mun, 2002). Since volatility (σ)

is assumed to be constant, it is the increase in time (t), which increases the stochastic term

𝜎 𝑇 and thereby the total uncertainty. One important assumption for market uncertainty to

increase over time is that the above stochastic term follows a Brownian Motion. The Brownian

Motion is a widely accepted standard assumption necessary for pricing options and it is often

praised for its relative simplicity, since it does not allow the value to be zero (Mun, 2002).

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Figure 3.15: Brownian Motion

Source: Own creation and (Mun, 2002)

The deterministic part accounts for the growth rate of the Brownian Motion process. The

growth rate of the motion has in real option analysis already been intuitively accounted for.

Since the binomial lattice approach is a discrete simulation model, it is not necessary to re-

simulate in each time step, and the remaining stochastic term is simply 𝜎 𝛿𝑡(Mun, 2002).

Another important input is the volatility estimation. Volatility is the most significant value

driver in a real option valuation, and since there are several different ways to estimate

volatility in the literature, the following section will discuss and review the most common

methods. The different estimations methods are first divided into direct and indirect

approaches as showed in figure 3.16.

Figure 3.16: Direct and indirect volatility estimation methods

Source: Own creation and (Kodukula, 2006)

Brownian Motion

deterministic term

stochastic term

stochastic term in discrete simulation

Up movement

Down movement

𝛿𝑡 𝜎 𝛿𝑡

𝛿𝑡 𝜎 𝛿𝑡

𝛿𝑡

𝜎 𝛿𝑡

𝜎 𝛿𝑡

𝜎 𝛿𝑡

𝜎 𝛿𝑡

Volatility estimation methods

Mangement Assumptions

Direct

estimations

methods

Indirect

estimations

methods

Product ProxyLogarithmic present

value

Logarithmic cash flow Market Proxy

σ

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The direct approaches are based on the actual project, and the underlying asset. The indirect

approaches are based on market- and product proxies. Management assumption is a

combination of both the direct and indirect approach. This gives a good indication of two major

perspectives on volatility estimation. Based on the importance of the volatility parameter, we

explain each volatility estimation method more in depth.

Logarithmic Present Value Approach

The logarithmic present value approach is a direct approach. It collapses all future cash flow

estimates of the project at hand into two sets of present values, one for the first time period

and another for the present time (Mun, 2002). The values obtained from the sets of present

values are summed, and a logarithmic ratio is calculated.

Figure 3.17: Logarithmic present value approach

Source: (Mun, 2002)

Assigning distributions to specific variables of the underlying asset and by simulating these,

the standard deviation of the forecasted distribution is the volatility. One of the downsides of

using this method is that simulation is required, because it increases the complexity. Another

point of critique is that the distributions used in the simulation are subjective. Furthermore,

since capital budgeting is very impartial and subjective matter, the volatility could suffer from

very biased estimates.

Logarithmic Cash Flow Returns Approach

The logarithmic cash flow returns method provides a volatility estimate based on the

variability of the underlying asset cash flow (Kodukula, 2006; Mun, 2002), and is also one of

the direct estimations methods. The method calculates the volatility based on the relative

future cash flow estimates and their logarithmic returns. The standard deviation of these

logarithmic returns, are used as volatility (Mun, 2002). The model has some important

Logarithmic present value approach

( 𝐶

=1

𝐶 =0

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shortcomings, when cash flows are negative over certain periods, the relative return will be

negative and not possible to measure in a natural logarithm. The method is often praised for

its simplicity and ease of use, as it is mathematically simple to use compared to other methods

(Kodukula, 2006).

Project Proxy Approach

A project proxy approach is an indirect volatility estimation approach. This approach uses a

proxy for the volatility like historical data from another project that have the same

characteristics. Using historical data from a previous project is the same as using real world

market information, which at first gives this approach an appealing feature. An example could

be a pharmaceutical company that uses cash flow data from a previously developed drug that

have the same cash flow profile, and use this to estimate volatility for the new project

(Kodukula, 2006). Even though this approach has its advantages, it can be difficult to find

another project with identical cash flow structures. Furthermore, using comparable projects

will in many cases not provide a very realistic or precise estimate of the volatility of the new

project.

Market Proxy Approach

The market proxy approach uses publicly available market data to estimate volatility for a

specific product (Mun, 2002). Instead of using cash flow of similar historic projects as the

project proxy approach, the market approach uses stock prices of listed companies with cash

flow profiles similar to the cash flow of the project under consideration (Kodukula, 2006).

Using equity prices, as basis for project volatility, will in most cases not be representative for

the specific project, since these are often based on multiple projects/products, market

psychology, and other factors as well (Kodukula, 2006). Another pitfall is that firms are often

levered and many projects may not be. Meaning, that adjustments are necessary before equity

prices can be considered as a proxy for project volatility (Mun, 2002).

Management Assumption Approach

There is not one specific way to define the management assumption approach. It can be a

combination of the just mentioned approaches, but the important difference from the other

approaches lies within the notion that it is the management’s assumptions that drive the

estimation of the volatility. It could be that management assumes that a project will generate

a certain cash flows and then these are used for simulation (Mun, 2002). Additionally, there

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can be situations where specific project calculations are pointless, and where the experience

and knowledge of management will provide the best estimation of volatility (Copeland &

Antikarov, 2001).

The above has introduced several methods of calculating volatility. We will later, in our case

study, argue for the method that is most suitable for our case and industry.

3.4.2.3 Technological uncertainty

As explained before some valuation methods allow a project to be subject to more than one

source of uncertainty, the market uncertainty explained above and a technological

uncertainty. The following section will clarify, what is understood by technological

uncertainty.

Technological uncertainty is assumed to be independent of market conditions and of time

dependencies, and are assumed to be diffuse in the beginning of a projects timeline, but then

reduced through time (Copeland & Antikarov, 2001). Relating to the industry it means the

technological uncertainty is independent of market conditions. It only encompasses the

specific technological uncertainty of each clinical phase. A technological uncertainty could be

the uncertainty of toxic side effects or the uncertainty of non-consistent efficacy and safety of a

drug development. Technological uncertainty is opposite to market uncertainty decreasing

trough time, as the project are exposed to less technological uncertainty as more clinical

phases are approved. The approval of a clinical phase reduces the accumulated technological

uncertainty of the project. Later in the practical implementation and evaluation, technological

uncertainty is discussed more in depth.

Figure 3.18 below summarises the theoretical principles of market- and technological

uncertainty. The market uncertainty is expected to increase as time progress while,

technological uncertainty on the other hand is resolved over time. Furthermore, it is worth

noticing that because we assume technological uncertainty is linked with the clinical phases in

the drug development process, the uncertainty is resolved step-wise. The steps symbolise the

phase-approvals that occur over time. Once a phase is approved the cumulative technological

uncertainty decreases.

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Figure 3.18: Market and technological uncertainty


3.4.2.4 Time

Another parameter of uncertainty is time, or more precisely the time-steps. The time-steps

determine the granularity of the lattice models (Mun, 2002). Many time-steps will result in a

large “web” of possible outcomes and increases the scope of outcomes as well – increasing the

extreme values in the end nodes. Typically the time-steps are yearly or quarterly

corresponding to using 1 or 0,25 as time steps.

3.4.3 Strategic Flexibility

Real Option models can theoretically incorporate, quantify, and add the value of decisions

related to future events. Real Option valuation always provides a greater value than for

example a DCF valuation of the same project or asset, since it adds the value provided by

flexibility (Mun, 2002). This incorporation of flexibility is based on the fact that Real Option

valuation models do not assume passive management through a project’s lifetime, as the

standard DCF model does. This ability to incorporate strategic flexibility and quantify it is the

key essence in Real Option thinking.

Uncertainty is the main driver in the real options models, and strategic flexibility is thereby

depending on, how each model estimate and perceives uncertainty and future events. In the

binomial model, uncertainty and the up and down movements is incorporated in the volatility

estimate. The question is therefore whether the volatility estimate is able to incorporate all

future uncertainty of a pharmaceutical drug development project. Another important question

is related to the assumption that uncertainty is resolved continuously over time, and the

Market and technological uncertainty

Tu

Market uncertainty

Mu

Time

Technical uncertainty

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question to ask is thereby if this assumption corresponds to the changing uncertainties in each

of the development phases. To get the optimal execution of a real option, it is necessary to

build an event tree that reflects the actual resolution of uncertainty over the development

process. Separating major uncertainties and to model their different interactions, is the best

way to do this (Copeland & Antikarov, 2001). Opposite to the binomial model, the extended

quadranomial model separates market and technological uncertainties. The model is

theoretical able to incorporate the changing uncertainties in each clinical phase, and thereby

in theory separates the technological uncertainty and events from the general market

uncertainty. This separation should theoretically increase the strategic flexibility of the

quadranomial model compared to the binomial mode.

Besides the way of incorporating uncertainty, strategic flexibility depends further on if

management is rational, strategies are executable, the level of uncertainty that drives the

project value and the availability of options (Mun, 2002). This will be evaluated more in depth

in following chapters. Whether management have strategic flexibility depends on the

availability of options, and the following will present a variety of different types of options. It

is necessary to consider the different option types and their characteristics what kind of

flexibility they offer and how they fit with the industry under investigation. In table 3.2 below

a short list of different types of real options is listed.

Table 3.2: Overview of selected types of real options

Source: (Berk & DeMarzo, 2014; Brealey et al., 2008; Copeland & Antikarov, 2001; Mun, 2002)

Different options

Option to abandon An option to abandon a giving project for a salvage value or to avoid future cost.

Option to expand Option to expand current capacity in case of favourable development.

Option to contract An option to sell of capacity and shrink the scale of operations.

Option to delay Delay investment until market conditions has developed further.

Compound options

Simultaneous compound optionsOptions that is contingent on the value another option, and are alive at the same

time.

Sequential compound optionOptions that are contingent on the value of another option, and are staged and not

alive at the same time.

Sophisticated options

Rainbow options An option with more than one sources of uncertainty

Learning optionsAn option with two uncertainties where market uncertainty increases over time and

technological uncertainty decreases/resolves over time

Simple Options

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It is difficult to precisely point out one type of option that would fit best in the development of

pharmaceutical drugs. One could argue for almost all the listed simple options. For example

the option to abandon a pipeline drug if the human clinical trials turn unfavourable. Or, the

option to delay the decision on beginning new phase-trails or delaying an NDA to a drug

agency. When furthermore taking the development phases into consideration, compound

options seem to be a relatively obvious match. The decision or options regarding the latter

development phases are dependent on previous phases, which again match the characteristics

and definition of compound options – options that are contingent on the value of another

option. Furthermore, the drug development process can be seen as a sequence of phases that

occur in continuation of each other, indicating that a sequential compound option would be an

obvious choice, when having a Real Option approach to valuing pharmaceutical drug

development.

3.4.4 Usability

The real option approach is evaluated to be more theoretically complex, time demanding, and

more difficult to apply compared to the two previous valuation methods. The ability to

incorporate the value of flexibility is intuitively and relevant for this industry. But as written

before, it is not a very commonly used method of valuation. We believe that the limited use of

real options can be explained by inexperience in use and a theoretical complex first impression

than actual difficult calculations. Though the calculations may not be very demanding, the

estimation of the input parameters can be difficult to estimate. The Real Option approach can,

as just explained, incorporate one and two sources of uncertainty depending on the model of

choice. Two sources of uncertainty will complicate the process, and make it a more challenging

process. Additionally, the real option approach incorporates more input parameters than the

previously mentioned valuation methods, which increase the use of resources and knowledge

requirements in order to the valuation. The below figure 3.19 is a summary of the main

findings in each of the four criteria.

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Figure 3.19: Summary of Real Option


The first research question regarding the theoretical differences and the underlying

assumptions of the three different valuation approaches are answered through this chapter.

The findings based upon the defined criteria are summarised in each of the summary figures.

To see the main theoretical differences each summary figure should be compared.

- Value estimated based the movements of an underlying asset - Perceives market uncertainty through volatility (σ)

- Option value calculated through backward induction - Perceives technological uncertainty as clinical success rates

- Follows a Brownian Motion - Difficult to estimate uncertainty parameters

- Flexibility through a broad variety of options - Theoretical complex and difficult to estimate

- Models flexibility through an asset tree - Depends on the granularity of the model i.e. time steps

- More flexibility in separating market- and technological - Separating the uncertainties increases the complexity

uncertainty

Concept Uncertainty


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4 Case study - practical implementation

This chapter will seek out to answer the second research question stated in the introduction.

In order to answer the question the focus will be on, how the different valuation methods can

be implemented when valuating pharmaceutical drug development projects. This will be done

through a case study of a pipeline product from the Danish pharmaceutical company Novo

Nordisk. Using a case study to analyse the practical implementation will provide a more clear

view of the general potential, focusing on the challenges and advantages, and how the

methods are applied most effectively. Additionally, it will later make it possible to make some

concluding comments on which valuation method is the most suitable for the industry under

investigation.

As written previously the focus is not on a numerical valuation of the case project, or to test if

the value of Novo Nordisk is priced correctly in the market, but on the assumptions and

practical implementation of the methods we have chosen to investigate. Each of the valuation

method described earlier will be investigated separately through this chapter. The comparison

of them will first be touched upon in the next evaluation chapter. Therefore, this chapter

should only be seen as a step towards fulfilling the objective of this chapter and thesis.

Throughout this chapter references will be made to the industry. These references will make

basis for, mostly, the DTA and ROV of the pipeline product. It is primarily the data on the

length of R&D periods, cost of R&D, and the success rates involved in developing new drugs

that will be used. Using these general industry data to analyse a specific product may

intuitively lead to inaccurate valuations, but since the focus is an outside-in perspective, this

is accepted as being appropriate.

Appendix 6 serves as support to the calculations shown.

The case product – NN9927

The case product, NN9927, is a new long-acting oral GLP-1 analogue14 that is intended to act

as a once-daily tablet treatment for Type-2 diabetes (Novo Nordisk, 2014). The product is

14 Glucagon Like Peptide 1 (GLP-1) enhances the glucose-stimulated insulin secretion and inhibits the release of glucagon i.e. a

treatment for diabetes (Novo Nordisk, 2014).

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currently in development phase 1, which makes it ideal for the purpose of our study. We

believe it provides a realistic case for investigating different valuation methods. Moreover, the

new drug introduces a new treatment type, which makes it interesting to investigate and

analyse, how to estimate the most appropriate project value.

Assumptions for practical implementation

In the following valuation of the oral diabetes drug NN9927 some simplifying assumptions

will be made. Key elements in a valuation-purposed thesis will be ignored or only shortly

mentioned. This includes a complete strategic analysis of the project. Because of this, some

simplifying assumptions are made in order to conduct the valuation for the evaluation of

practical use.

In the valuation of the project under investigation several considerations on how to setup the

actual valuation are necessary in order to implement the methods in the most appropriate

way. A major issue to consider is the development phase; mainly its lengthy time period and

the fact that in this period only cash out-flows exits. The DCF method as explained in the

previous has no problem in comprehending this fact and can easily incorporate this, however,

for the other methods to be able use the DCF as underlying asset, a separation of the

development phase and the commercialisation phase will be beneficial. More specifically, the

separation is carried out in a way such as the free cash flow and present value of the

commercialisation phase can be used as the underlying assets in the real option approaches,

where development costs are first deducted, when the option/decision is exercised/taken. This

will be elaborated later.

Figure 4.1: Illustration of the development –and commercialisation phase


Development Commercialisation

11 years 14 years

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The value obtained from the commercialisation phase cannot itself be used for comparison or

as a decisions-making value. It is only the value of the commercialisation of the drug under

the assumption that the development process is successful and already completed.

Based on the industry findings in Chapter 2, the development-period is assumed to be eleven

years, while the commercialisation period is assumed to span fourteen years, totalling a time-

line of 25 years. The length of the commercialisation phase is based on the assumption that

after patent expiration (assumed a patent of 20 years), the drug will face rapid declining sales

and will eventually be phased out. This is primarily caused by intensified competition from

generic products. The development period is based on the previously found industry averages

(see page 17). Notice that the total timeline exceeds the patent period of about 20 years. This

is because we assume that some research is done before patenting and because of the

possibility of gaining patent extension as previously explained.

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4.1 Practical implementation of standard DCF model

The steps we have chosen to go through in the practical implementation of the DCF model is

shown in the below figure. The implementation of the DCF model is important especially in

relation to the previously explained and accepted MAD assumption i.e. the underlying asset.

This is the reason, why we go through the following steps in detail even though it is a well-

known model.

Figure 4.2: Practical steps in DCF valuation

Source: Own creation inspired by (Copeland & Antikarov, 2001)

Each step in the practical implementation of the DCF model is illustrated in figure 4.2. The

first step is to forecast future earnings of the development and commercialisation phase.

Calculating the free cash flow is the second step. The third step is an estimation of the

discount rate. The last step is a sensitivity analysis of the different variables in the model and

the outcome.

In the following each step will be elaborated. Again we refer to appendix 6 for a detailed view

of the succeeding calculations.

4.1.1 Step One: Forecast

4.1.1.1 Sales

One of the difficult steps in the implementation of the DCF model is the first step. The

practical forecasting of a pharmaceutical drug is a difficult and a complex process, since it

requires great knowledge of for example epidemiology and medical legislation. There are

Step 1

Forecast future earnings

Forecast of

future sales and

cost of the

development and commer-

cialisation phase

Step 2

Estimate of free cash flow

Step 3

Estimate discount rate

Step 4

Estimate DCF value

Step 5

Sensitivity analysis

Calculation of

FCF by

deducting NWC

from NOPLAT

Estimation of the

risk free rate and

cost of equity as

discount rate

Discounting the

FCF by the

discount rates to

present value

Analysing the

result and input

variables by 5 to

20 per cent changes

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several different forecasting methods suggested in the literature, and the following section will

shortly discuss two different forecasting methods and their practical difficulties. Lastly, a

forecast of NN9927 future sales will be estimated.

A publication by Cook (2006) discusses the main differences between the patient- and the

prescription-based algorithm, which are two common forecasting methods used in the

pharmaceutical industry. The patient-based algorithm is focused on estimating the theoretical

number of potential patients, who are receptive to a specific drug treatment. The number of

potential patients is compared to the number of people, who are already receiving similar drug

treatment, and the future growth potential can then be estimated. To calculate the number of

potential patients, the algorithm is based on several different criteria of epidemiologic,

symptomatic and diagnosing, which are applied as filters to a specific market population. The

prescriptive-based algorithm uses data of prescriptive patients, who are already receiving

similar drug treatment. The prescriptive algorithm estimates the minimum number of people,

who are already treated and thereby useful to forecast future sales.

The main difference between the two methods is the different focus on the theoretical

maximum number of patients and the minimum number of already patients in the market.

There are several arguments for using each one of the forecasting methods, and the author of

the publication does not argue that one model is superior, as both models rely more or less on

the same input. Both models are complex, unsure, and require great knowledge of disease

states, epidemiology, and treatments in order to forecast a precise number of patients.

Because of the high demand for technical- and epidemiology insight and since we do not have

the required expertise to make a useful forecast, the forecast of NN9927 will be based on data

from third parties. The approval of NN9927 has for example an unknown cannibalisation

effect on the current diabetes product of Novo Nordisk, as the product has a new GLP

analogue treatment effect. External parties have forecasted a sales potential of NN9927 to

peak around USD 6 billion (Frovst & Thomsen, 2015; F. M. Petersen & Hansen, 2015). The

peak sale is assumed to occur after approximately eight years. This is in accordance with a

previous study, which showed that peak sales often occur around 8-10 years after initial

product launch (Grabowski et al., 2002). Lastly, the forecasted sale is adjusted with the

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cumulative probability of development success15, since only the expected cash flows of the

commercialisation phase should be included (Koller et al., 2010).

4.1.1.2 Cost

The forecasted costs are divided into two categories. The cost associated with the R&D

activities and the cost linked to producing and selling the developed drug. The following will

describe the considerations necessary in order to reliably estimate these cost figures. Research

and development costs are assumed only to appear in the development period and the cost of

producing and selling the drug in the commercialisation period only.

Research & Development

The cost figures for the R&D phase are based on the industry. As shown previously (see page

14) there is not a common understanding and opinion on the cost of developing a new

pharmaceutical drug. The estimates vary substantially depending on source and author. This

therefore raises the question on what numbers to use when forecasting the development cost.

From an external point of view it is necessary to evaluate the industry figures provided by the

litterateur and experts. If the viewpoint is internal, one could look at other drugs with similar

characteristics, and use data from these projects. Since we take an external view, we base the

R&D cost on general industry data.

The development cost assumed for the case project is inspired by PWC (2012). After having

investigated the area, it is our opinion that these estimates will provide the best and most

unbiased foundation for forecasting the development cost for the case project. Furthermore,

this choice will be in accordance with the sceptical view of the estimations from CSDD (Light

& Warburton, 2011). The specific development cost assumed for this project is the figures

provided by the report from PCW adjusted slightly. In table 4.1 the development cost is

shown.

15 The cumulative success-rate is acquired from table 2.1. Since our litterateur review of the success rates provided different

estimates, we have chosen to use the middle ranged estimate.

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Table 4.1: Development cost assumed for NN9927

Source: Own creation inspired by (PWC, 2012)

Cost in commercialisation phase

The cost estimate assumptions are based on different sources; Novo Nordisk’s annual reports

from the three last years and a publication by Kellogg & Charnes (2000). The two sources

provide somewhat similar estimates and the cost assumptions used in this study are shown in

table 4.2 below. See appendix 1 for more specific information the data used.

Table 4.2: Cost assumptions in the commercialisation phase

Source: Own creation based on (Kellogg & Charnes, 2000; Novo Nordisk, 2012; Novo Nordisk, 2013; Novo Nordisk, 2014)

4.1.2 Step Two: Estimating the free cash flow

Since this is a project valuation some simplifying assumptions are made in relation to the

estimation of these free cash flows. The working capital is assumed to be relevant from the

period the new drug is introduced to the market, meaning the first period of the

commercialisation period. The reasoning behind this assumption is that it is first within this

period the elements, that constitutes the working capital, actually becomes, pertinent. Before

Development cost for NN9927

Discovery CP I CP II CP III NDA

Cost in USD millions 90 130 190 268 26

Development cost for NN9927

Item

COGS/Cost of revenue

Marketing expense

Year 1 after launch

Year 2

Year 3-4

Year 5-14

General and administration expense

Tax

20

5

25

Pct. of revenue

20

100

50

25

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the drug is produced, no inventory is build up nor any significant change in payables or

receivables. The working capital is calculated as percentage of sales a given year.

Table 4.3: Free Cash Flow of project of NN9927


Strict assumptions are made for both the depreciations and capital expenditures. We assume

that no further investment in production assets is required, why both capex and depreciation

are assumed to be zero.

4.1.3 Step Three: Estimation of discount rate

The previous two steps have forecasted and estimated the free cash flow, where this step will

now focus on the practical estimation of the discount rate and the underlying technicalities.

In the practical estimation of the discount rate, it is first central to focus on the previous

separation of the forecasted cash flow. The cash flow separation in the development and

commercial phase implies adjustments to the discount rates used in each phase. The cash

DCF of development and operational phase

Phase NDA

Year, US $ million dollars 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 … 25

Total sales - - - - - - - - - - - 43,9 100,3 151,5 250,2 38,4

Cost of gods sold - - - - - - - - - - - 11,2 25,6 38,6 63,8 9,8

Gross Profit - - - - - - - - - - - 32,7 74,7 112,8 186,4 28,6

General and admin cost - - - - - - - - - - - 2,2 5,0 7,6 12,5 1,9

Marketing cost - - - - - - - - - - - 43,9 50,2 37,9 62,6 7,7

Research and development cost 53,5 53,5 69,0 69,0 72,7 72,7 72,7 96,7 96,7 96,7 26,0

EBITDA -53,5 -53,5 -69,0 -69,0 -72,7 -72,7 -72,7 -96,7 -96,7 -96,7 -26,0 -13,4 19,6 67,4 111,4 19,0

Depreciation and amortisation

EBIT -53,5 -53,5 -69,0 -69,0 -72,7 -72,7 -72,7 -96,7 -96,7 -96,7 -26,0 -13,4 19,6 67,4 111,4 19,0

Carry forward previous period 0,0 -53,5 -107,0 -176,0 -245,0 -317,7 -390,3 -463,0 -559,7 -656,3 -753,0 -779,0 -792,4 -772,8 -705,4 0,0

Carry forward current period -53,5 -53,5 -69,0 -69,0 -72,7 -72,7 -72,7 -96,7 -96,7 -96,7 -26,0 -13,4 19,6 67,4 111,4 19,0

Remaining carry foward -53,5 -107,0 -176,0 -245,0 -317,7 -390,3 -463,0 -559,7 -656,3 -753,0 -779,0 -792,4 -772,8 -705,4 -594,1 -

Taxable income - - - - - - - - - - - - - - - 19,0

Tax - - - - - - - - - - - - - - - 4,7

Profit after tax -53,5 -53,5 -69,0 -69,0 -72,7 -72,7 -72,7 -96,7 -96,7 -96,7 -26,0 -13,4 19,6 67,4 111,4 14,2

FCF calculation

EBIT -53,5 -53,5 -69,0 -69,0 -72,7 -72,7 -72,7 -96,7 -96,7 -96,7 -26,0 -13,4 19,6 67,4 111,4 19,0

Tax - - - - - - - - - - - - - - - 4,7

NOPLAT -53,5 -53,5 -69,0 -69,0 -72,7 -72,7 -72,7 -96,7 -96,7 -96,7 -26,0 -13,4 19,6 67,4 111,4 14,2

Add depreciation - - - - - - - - - - - - - - - -

Less Capex - - - - - - - - - - - - - - - -

NWC - - - - - - - - - - - 7,5 17,1 25,7 42,5 6,5

Less ΔNWC - - - - - - - - - - - 7,5 9,6 8,7 16,8 -8,8

FCF -53,5 -53,5 -69,0 -69,0 -72,7 -72,7 -72,7 -96,7 -96,7 -96,7 -26,0 -20,8 10,0 58,7 94,6 23,0

Discovery CP I CP II CP III

Discovery and clinical trials Commercialisation phase

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flows of the development phase should be discounted at the risk free rate, since the project is

only affected by costs and private risk. Cash flows of the commercialisation phase should be

discounted by the market-adjusted discount rate, since it is affected by market risk in

earnings (Mun, 2002). The market-adjusted discount rate is in most cases WACC, but will in

this case be the cost of equity, since no debt financing is considered. The cost of equity is based

on three inputs; the risk free rate, the market premium, and beta. Beta is the only project

specific parameter and the most uncertain and difficult parameter to estimate. The practical

estimation of each parameter will be discussed in the following sections.

4.1.3.1 Market risk premium

The market risk premium is the difference between the risk free rate of return and the return

of holding the market portfolio, and defined as the additional return that investors expect to

earn to compensate for risk (Berk & DeMarzo, 2014). There are in general two different

methods to estimate the market risk premium; the historical based ex-post approach and the

forward-looking ex-ante approach. The ex-post approach is often based on larger number data,

and the ex-ante forward-looking risk premium is often based on expectations from

practitioners. The well-know Aswath Damadoran estimates an average risk premium from

1960 to 2015 of 4,07 per cent, and the average risk premium for year 2015 is estimated to 5,7

per cent (Damodaran, 2015). A publication by Fernandez, Linares, & Acín (2015) finds a

similar average risk premium of 5,5 per cent. We use a risk premium of 5 per cent based on

the above and our case.

4.1.3.2 Beta value (β)

Beta is assessed to be the most uncertain parameter of the DCF model in the previous

discussion of uncertainty, and the practical estimation of this is thus important for the

valuation. For the valuation of project NN9927 beta should theoretically reflect the specific

risk of the project and not the company risk, which complicates the estimation. In practice the

literature in general suggest that a common method for estimating a project’s beta is to

identify comparable firms in the same line of business, and compare these to the beta of the

firm undertaking the project. Based on the comparable firms it is possible to estimate a proxy

for the project (Berk & DeMarzo, 2014; Brealey et al., 2008). The assumption makes the

practical estimation easier, but the literature has no answer to the number of peer companies,

which makes the estimation fully dependent on practitioners’ own considerations. In our case

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comparable peer companies and the industry will be used in the practical estimation of beta. A

typical method to estimate beta is to calculate the return of a company stock and regress these

on a large market portfolio index (Berk & DeMarzo, 2014). Which time frame and market

portfolio that should be used are depending on the specific project, as the literature has no

straightforward answer. In this specific case a time frame of six years and both monthly and

weekly returns are used (Damodaran, 2015). The chosen market portfolio index is the MSCI

World Index, which is a free float-adjusted market capitalisation weighted index of 23

developed countries. This index is chosen to avoid the influence of a local market index, which

may be weighted towards some few industries. To choose a local market index is a common

estimation error in the literature, as a small local market index may be weighted towards one

or few industries and thereby not representative for a weighted market portfolio.

The estimated betas will be based on closing adjusted prices to avoid the influence of

dividends, and will furthermore be unlevered and adjusted for debt, because the development

of NN9927 is considered to have no debt financing. An average of a three-year debt/equity

ratio of each company will be used to estimate the unlevered betas. The calculations are

clarified in appendix 2. The estimated betas of Novo Nordisk, peer group, and the industry is

shown in table 4.4.

Table 4.4: Overview of Beta estimation

Source: Own creation from DataStream, Damodaran (2015)

Weekly Monthly Weekly Monthly

Beta 0,74 0,85 Beta 0,94 1,03

R-squared 0,27 0,30 R-squared 0,45 0,49

Standard Error 0,07 0,15 Standard Error 0,06 0,12

BetaUnlevered-avg 0,73 0,84 BetaUnlevered-avg 0,86 0,94

Observations 313 72 Observations 313 72

Avg D/E 0,017 0,017 Avg D/E 0,12 0,12

Weekly Monthly

Beta 0,56 0,36 Beta 1,03

R-squared 0,26 0,08 R-squared -

Standard Error 0,05 0,13 Standard Error -

BetaUnlevered-avg 0,43 0,28 BetaUnlevered-avg 0,91

Observations 312 72 Observations 151

Avg D/E 0,40 0,397 Avg D/E 0,13

Novo Nordisk Sanofi

Eli Lilly Industry

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Table 4.4 shows the levered and unlevered beta estimations and the statistical output. The

output is carefully interpreted. The beta estimations differ between the weekly and monthly

data, and it is seen that the standard error is larger in the monthly data. Sanofi is estimated

to have a higher beta value and Eli Lilly a lower beta value than the unlevered monthly beta

of Novo Nordisk. The industry consists of data from 151 companies, which have a higher beta

value but the statistical output is unknown for this. Based on the above estimations a beta

value of 0,9 is chosen for this project. The value is primarily based on the beta value of Novo

Nordisk and the industry of 151 different companies. We assume project NN9927 have

similarities to the general industry and thereby outweighs the influence of the competitors’

beta estimates.

4.1.3.3 Risk-free rate of return

The risk free rate of return is theoretically the return of an investment with no risk or loss,

and the minimum return any investor would expect. Practically government bonds with no

default-risk are used to represent the risk-free rate (Berk & DeMarzo, 2014). The literature

has no mutual answer on which government bond to use. Some practitioners argue that the

maturity of the government bond should match the time period of the cash flow of the project,

while others argue that a government bond of 10 year should be used (Koller et al., 2010). We

use an American treasury bill with a 10 year maturity, which corresponds to an effective

interest rate of 2,38 per cent.

After having estimated the market risk premium, beta, and last the risk free rate of return,

the cost of equity can now be estimated in the following section.

4.1.3.4 The cost of equity

The unlevered cost of equity can now be calculated based on the above. The calculation is

shown below in figure 4.3. We estimate a cost equity of 6,88 per cent. This is the rate used to

discount the commercialisation phase.

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Figure 4.3: Cost of equity for case project


4.1.4 Step Four: Estimate of DCF value

After having estimated the cost of equity in the previous step, the free cash flow of each year

can now be discounted. Both the free cash flow calculation and the discount factor are

presented in table 4.5 below. The discount factor is calculated as the reciprocal value to show

the influence in each year.

Table 4.5: Calculation of DCF value


The discounted cash flow value of project NN9927 is equal to US $2,71 million dollars. It is

important to mention, that the discounted cash flow includes both the development and

commercialisation phase, and that the R&D period is discounted at the risk free rate and

commercialisation period with the cost of equity. The DCF value used for the real option

approach, the underlying asset, is only the discounted cash flow value of the

Cost of equity

rf: risk free rate

6,88% = 2,38% + 0,9 x 5% β: Beta

E(Rm)-rf: Market risk premium

+ ( − )

Calculation of DCF value

Phase NDA

Year, US $ million dollars 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 … 25

EBIT -53,5 -53,5 -69,0 -69,0 -72,7 -72,7 -72,7 -96,7 -96,7 -96,7 -26,0 -13,4 19,6 67,4 111,4 19,0

Tax - - - - - - - - - - - - - - - 4,7

NOPLAT -53,5 -53,5 -69,0 -69,0 -72,7 -72,7 -72,7 -96,7 -96,7 -96,7 -26,0 -13,4 19,6 67,4 111,4 14,2

Add depreciation - - - - - - - - - - - - - - - -

Less Capex - - - - - - - - - - - - - - - -

NWC - - - - - - - - - - - 7,5 17,1 25,7 42,5 6,5

Less ΔNWC - - - - - - - - - - - 7,5 9,6 8,7 16,8 -8,8

FCF -53,5 -53,5 -69,0 -69,0 -72,7 -72,7 -72,7 -96,7 -96,7 -96,7 -26,0 -20,8 10,0 58,7 94,6 23,0

Discount factor 0,98 0,95 0,93 0,91 0,89 0,87 0,85 0,83 0,81 0,79 0,77 0,45 0,42 0,39 0,37 0,19

Discounted FCF -52,3 -51,0 -64,3 -62,8 -64,6 -63,1 -61,6 -80,1 -78,2 -76,4 -20,1 -9,4 4,2 23,1 34,9 4,4

DCF value 2,71

Commercialisation phase


Discovery and clinical trials

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Input Variables, pct change -25% -20% -15% -10% -5% 0% 5% 10% 15% 20% 25%

Success rate -151,9 -121,0 -90,1 -59,1 -28,2 2,7 33,6 64,3 95,1 125,8 156,5

COGS 88,4 71,3 54,2 37,1 19,9 2,7 -14,5 -31,7 -49,0 -66,2 -83,4

Tax 38,7 31,5 24,3 17,1 9,9 2,7 -4,5 -11,7 -18,9 -26,1 -33,3

GA cost 19,6 16,2 12,8 9,5 6,1 2,7 -0,7 -4,0 -7,4 -10,8 -14,2

Working capital 7,9 6,8 5,8 4,8 3,7 2,7 1,7 0,7 -0,4 -1,4 -2,4

Input Variables, pct change -25% -20% -15% -10% -5% 0% 5% 10% 15% 20% 25%

Beta 152,3 119,8 88,6 58,8 30,1 2,7 -23,6 -48,8 -73,0 -96,1 -118,3

Market risk premium 152,3 119,8 88,6 58,8 30,1 2,7 -23,6 -48,8 -73,0 -96,1 -118,3

Risk free rate 53,7 42,9 32,4 22,2 12,3 2,7 -6,6 -15,7 -24,5 -33,1 -41,4

commercialisation phase, without development cost. The DCF value will be discussed more in

depth in the evaluation section.

4.1.5 Step Five: Sensitivity Analysis of input variables

In order to test what we have previously determined as being the most theoretical uncertain

parameters, we conduct a sensitivity analysis in the following. The sensitivity analysis is

evaluated to be the only way to incorporate strategic flexibility in the DCF model, which will

be tested now and commented on in the later evaluation chapter. The analysis provides an in

depth understanding of each input and how the DCF result is influenced by changes in

different input variables. The analysis is performed on the cost of equity and the free cash

flow. The analysis is presented in the following figures and shows the DCF value, when one

input variable is affected by a percentage change, ceteris paribus.

Figure 4.4: Sensitivity analysis of input in cost of equity

Source: Own creation through crystal ball

The first figure 4.4 shows the sensitivity analysis of the input variables to the cost of equity.

As seen, the practical estimation of both beta and the market risk premium is important, since

a relative percentage change in beta and the market risk premium have a great impact. This

is in accordance with our previously findings. In relation to our previous assumptions, the cost

of equity is only influencing the commercialisation phase and the risk free rate the

development phase. The development phase is thereby affected with less uncertainty.

Figure 4.5: Sensitivity analysis of input of various inputs

Source: Own creation through crystal ball

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The cumulative technological success rate has the greatest impact on the project’s DCF value.

An increase of the cumulative success rate has a positive influence on the project value, which

is opposite for the remaining input variables. COGS is the only input variable, which also has

a significant effect.

From the above sensitivity analyses, the input in the cost of equity and the cumulative success

rates are found to have the greatest impact on the DCF value. It is thereby confirmed that the

practical estimation of these input variables should be carried out with great caution and

precision.

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4.2 Practical implementation of Decision Tree Analysis

This section will go through the practical implementation of the DTA and demonstrate, how

the discussed theory can be practically applied to the project valuation of project NN9927.

Step 1 and Step 3 will be shortly considered, since they are somewhat similar to what

previously has been discussed in the implementation of the DCF model.

Figure 4.6: Overview of steps in DTA


Firstly, a forecast of the sales and free cash flow is estimated in step 1, and next the

probabilities used in each of the decisions nodes are estimated. Step 3 is the estimation of an

appropriate discount rate for the model. Finally, the two last steps are the actual estimation of

the DTA value and a sensitivity analysis.

4.2.1 Step One: Forecast

The first step of the DTA model is the practical forecast of future earnings and the free cash

flow. As mentioned above, this step is similar to the first steps of the previous DCF model, and

both models are based on the same forecasting methods. In spite of this, there are some few,

but rather important differences between the forecast of the DTA and DCF model. The free

cash flow of the DTA model is not adjusted by the cumulative success rate, since each step of

the backward induction is adjusted by the success rate of each clinical phase. The forecast step

is similar to the previous DCF model, but the estimations are used differently in the further

valuation.

Step 1

Forecast future

earnings

Forecast of future sales and cost of

the development

and commer-cialisation phase

Step 2

Estimate probabilities of

each phase

Step 3

Estimate discount rate

Step 4

Estimate DTA value

Step 5


Investigation of clinical success

rates from

previous drug developments

Estimation of cost of capital used for

FCF and

development phase

Using backward induction and

clinical success

rates

Analysing the result and input

variables by 5 to

20 percent changes

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4.2.2 Step Two: Probability

The second step of the practical implementation is the estimation of the probabilities, which

we determine as the probabilities of either success or failure in the development phases.

Determining the probabilities of success and failure are rather difficult, as the probability

must be estimated based on either previous results or rough estimates. The probabilities are

highly project-specific, and it is difficult to compare different pharmaceutical development

projects. Since the model is set up to consider the probability of success or failure, the

discussed technological success rates are used as proxies for these estimations. The probability

of success in each of the phases must be considered, as these constitutes each of the decision

nodes. The probabilities chosen for the case product are shown in table 4.6 below and are

based on historical estimates (DiMasi & Grabowski, 2007; DiMasi et al., 2010; DiMasi et al.,

2014).

Table 4.6: Probabilities used for in each of the decision nodes


4.2.3 Step Three: Discount rate

The third step of the practical implementation of the DTA is the estimate of discount rate. The

practical estimation is similar to the DCF model, and according to the arguments earlier, the

development and the commercialisation phase should be discounted by different discount rates

(Mun, 2002). The development phase should be discounted by the risk free rate, since the

clinical phases are uncorrelated to market uncertainty and are subject to private risk. The

commercialisation phase should be discounted by the cost of equity, as these cash flows are

subject to market risk. As no debt financing is considered in the development of project

NN9927, the cost of equity is used as the market discount rate. The risk free rate has been

estimated to 2,38 per cent and the cost of equity was estimated to 6,88 per cent previously in

the last section.

Probability and technological uncertainty

Phase CP I CP II CP III NDA Cumulative

Probability 68% 42% 66% 90% 17%

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The practical estimation of the discount rate, particularly the cost of equity, is subject to great

uncertainty, since the input parameters are estimated based on strong assumptions, and the

results of the practical estimations should be evaluated in the context of the sensitivity

analysis.

4.2.4 Step Four: Estimate DTA value

Now we calculate the DTA value in the fourth step. The calculations are illustrated in figure

4.7. Based on the value of the commercialisation phase, the technological success rates, and

the costs of research and development in each clinical phase the DTA value is calculated.

Figure 4.7: DTA calculations


From figure 4.7 it is seen, that the value of the commercialisation phase (without adjusting

with the cumulative success rate) is equal to USD 3666,7 million dollars, discounted by the

cost of equity. The cost of R&D of each clinical phase is discounted by the risk free rate, and

the costs are assumed to occur at the end of each clinical phase. The technological success

rate, the chance entering the next phase, is showed for each of the five phases and the

cumulative rate is equal to 17 per cent, as in the our DCF case. Using the explained backward

induction method, the discounted cash flow value of the commercialisation phase is multiplied

by each of the technological success rates, and the corresponding research and development

costs are deducted. The DTA is equal to US$ 182,4 million dollars, when the different

probabilities of future events are taking into consideration. Compared to the previous DCF

model, the DTA generates a much higher value.

Decision Tree Analysis of development and commercialisation

Phase

Year

Technological success rate

Research & Development

PV of R&D

DTA

DTA Value 182,4

218/(1+ 2,38%)^5 MAX(3667,7*90% - 20;0)

Commercialisation phase

NDA

3280,8

11

90%

26

20

Development phasse

107

107

182,4

3

138

128,6

289,4

Discovery CP I CP II

42%68%

1

614,7

194

218

5 8

66%

290

1925,1

240

CP III

3667,7

11 - 24

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Input variables, pct change -25% -20% -15% -10% -5% 0% 5% 10% 15% 20% 25%

Beta 321 291 262 234 208 182 158 135 112 91 70

Market risk premium 321 291 262 234 208 182 158 135 112 91 70

Risk free rate 243 230 218 206 194 182 171 160 150 139 129


CP I success rate 78 99 120 141 162 182 203 224 245 266 287

CP II success rate 45 72 100 127 155 182 210 237 265 292 320

CP III success rate 28 59 90 121 151 182 213 244 275 306 337

NDA success rate 27 58 89 120 151 182 214 245 276 307 338

4.2.5 Step Five: Sensitivity

In the last step of the DTA model, the result is analysed through a sensitivity analysis. Since

the DTA model incorporates more uncertainty and more variables, the sensitivity analysis

shows that the DTA value is influenced differently. Given the uncertainty in the cost and

success rate estimates found in the introduction chapter, we find it important to conduct a

sensitivity analysis on these parameters. The analysed variables are the input of the discount

rate, the technological success rate, and the research and development cost of each clinical

phase. The results of the sensitivity analyses are showed in the below tables.

Figure 4.8. Sensitivity analysis of the components in the discount rate


The discount rate has a lower influence on the DTA value, which is an important difference

from the DCF model, and therefor focus should be on the below findings.

Figure 4.9: Sensitivity analysis of the technological success rates of each clinical phase


The sensitivity table of the technological success rates shows that the NDA, CP III, and CP II

have the largest influence on the DTA value. This supports the importance of being able to

practical estimate a reliable technological success rate of each clinical phase. The technological

success rates are influenced by high uncertainty and have the largest influence on the

estimated DTA value.

Figure 4.10: Sensitivity analysis of the research and development cost of each clinical phase



R&D Discovery 209 204 198 193 188 182 177 172 166 161 156

R&D CP I 215 208 202 195 189 182 176 170 163 157 150

R&D CP II 215 209 202 196 189 182 176 169 163 156 149

R&D CP III 200 196 193 189 186 182 179 176 172 169 165

R&D NDA 183 183 183 183 183 182 182 182 182 182 181

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Figure 4.10 shows that the research and development costs of each clinical phase have the

lowest influence on the estimated DTA value. The table shows a clear relationship of an

increase in development costs implies a decrease in the DTA value. The costs of each phase

depend on the technological success rate, and even if the costs are affected by a large

percentage change, the DTA value is rather stable in comparison to the other input variables.

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4.3 Practical implementation of the Binomial Lattice approach

This section will examine the practical implementation of the Binomial Lattice approach in

relation to our case project. The below figure illustrates the five practical steps that will be

implemented in the following.

Figure 4.11: Practical implementation of the binomial lattice approach

Source: Own creation inspired by (Copeland & Antikarov, 2001)

The first step is to estimate the underlying asset of the commercialisation phase, and further

identify and estimate the volatility of the underlying asset in step two. The third step is the

creation of the asset tree, which the backward induction is conducted upon in the fourth step.

Lastly, a sensitivity analysis is analysing the different input variables and the result.

4.3.1 Step One: Estimate underlying asset

The first step in the practical implementation of the model is to determine and estimate the

underlying asset. In our case the underlying asset is equal to the discounted cash flow value of

the commercialisation phase in accordance with the MAD assumption. The underlying sales

and earnings forecasts of the commercialisation phase are similar to the two previous

valuation methods. For the binomial model the future sales are assumed to peak around US

$6 billion dollars, discounted at a cost of equity of 6,88 per cent.

4.3.2 Step Two: Identify and estimate volatility

Second step is estimating the volatility, which is used to create the asset tree in step three. As

previously mentioned, the volatility estimate is the most significant value driver in Real

Step 1

Determine and estimate

underlying asset

Estimate DCF value as the

underlying asset

of the ROA

Step 2

Identify and estimate

volatility

Step 3

Create and estimate asset

tree

Step 4

Conduct binomial Real Option

analysis

Step 5


Estimate the volatility by

Monte Carlo

Simulation

Estimate asset tree by the up

and down stages

of the distribution

Using backward induction

adjusted by the

up and down probabilities

Analysing the result and input

variables by 5 to

20 per cent changes

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Option valuation, why it also is essential to do thorough reflections on this parameter before

continuing. Referring back to uncertainty parameters of Real Options there are different

methods of calculating the volatility. There is no simple and easy choice and it is largely a

matter of preference. The market proxy approach can in our case relatively quickly be

rejected. It would be nearly impossible to find a stock that will match the risk profile of the

project. If any, it should be the volatility of Novo Nordisks share price. Finding a portfolio with

a similar risk profile can be extended to the other proxy approach as well, the product proxy

approach. The development of pharmaceutical drugs are such a specialised and unique chain

of events that finding a similar product that can be used as proxy would be difficult. Unless it

is possible to find an identical project with similar risk and use that as proxy, using a product

proxy would not provide a very precise estimate of the volatility of project NN9927. The

specific project under investigation introduces a brand new oral type of diabetes treatment,

which makes our project even more matchless and makes the indirect methods irrelevant.

This leaves the two direct approaches described earlier. As explained, the two methods are

somewhat similar, why the choice between them is a question of preference. We have chosen

to focus on the logarithmic present value approach, since we find it more appropriate to use

simulation in the volatility estimate. Our specific setup, calculations, and estimation of the

volatility can be found in the in appendix 6 and a deeper elaboration of the chosen assumption

can be found in appendix 3. The input assumptions for the volatility estimation are the

variables with the highest influence on the underlying asset. These were found in the tornado

diagram showed in appendix 4. The six most influential variables were chosen. In this

appendix it can be seen that these six variables are; Cost of goods sold, Marketing expense

year 5-14, Cumulative success rate, Beta, Market risk premium, and the Risk free rate. Using

15.000 simulations the volatility was estimated to 19 per cent. See appendix 3 for further

details.

4.3.3 Step Three: Create asset tree

The underlying asset value of the binomial tree is implemented in the following. Figure 4.12

shows the practical calculations of the underlying asset tree. The first value shown in time

zero is the present value of the commercialisation phase of US$ 677,2 million (adjusted with

the cumulative success rate). The asset tree is subsequently calculated by letting the

underlying asset value follow the up and down movements in each of the 11 years.

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Figure 4.12: Asset tree in the binomial model


Moving from left to right the asset tree is expanding as more nodes are occurring in time. In

last node, NDA, it can be seen that the underlying asset theoretically can result in two

extreme values. The maximum value is obtained if the underlying asset is only affected by up-

movements, while the lowest value is the opposite.

4.3.4 Step Four: Conduct Real Option analysis

In step four the option value tree is constructed seen in figure 4.13 below. The option tree is

based on a European compound option and the option to abandon the development of project

NN9927. The option tree is practically solved from right to left by using backward induction,

starting with the last end-node of the asset value tree. In each node, the option value is

weighted by the risk-neutral probabilities of p and q and further adjusted by the risk free rate

and an annual time factor. The risk neutral approach is used in this case rather than the

replicating portfolio, since it has not been found reliable to practical estimate a replicating

portfolio, which has a similar payoff structure.

In each end-node of the clinical phases, year 2,7,10, and 11 the exercise price EX, which is the

research and development costs, is subtracted from the option value. The option to abandon

will only be exercised, if the value is less than zero, otherwise the option will not be exercised

and the development project of NN9927 will be continued.

Asset tree

Phase NDA

Year, US $ million 0 1 2 3 4 5 6 7 8 9 10 11

677,2 819,0 990,3 1.197,5 1.448,1 1.751,2 2.117,6 2.560,7 3.096,5 3.744,4 4.528,0 5.475,4

560,1 677,2 819,0 990,3 1.197,5 1.448,1 1.751,2 2.117,6 2.560,7 3.096,5 3.744,4

463,1 560,1 677,2 819,0 990,3 1.197,5 1.448,1 1.751,2 2.117,6 2.560,7

383,0 463,1 560,1 677,2 819,0 990,3 1.197,5 1.448,1 1.751,2

316,7 383,0 463,1 560,1 677,2 819,0 990,3 1.197,5

6,772 * 1,2092 = 819,0 261,9 316,7 383,0 463,1 560,1 677,2 819,0

V0 216,6 261,9 316,7 383,0 463,1 560,1

6,772 * 0,8270 = 560,1 179,1 216,6 261,9 316,7 383,0

148,1 179,1 216,6 261,9

122,5 148,1 179,1

101,3 122,5

83,8



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Figure 4.13: Binomial option value tree


The value of development project NN9927 and the real option are equal to US$ 132,878

million. By deducting the previously calculated DCF value, the real option value is calculated

equal to US $130,2 million dollars, which is the value reflecting the option. A discussion of the

different findings of each valuation method is carried out in the later evaluation section.

4.3.5 Step Five: Sensitivity Analysis.

The last step in the practical implementation of the binomial model is a sensitivity analyses,

analysing. Each input variable is analysed by holding all others constant, which is showed in

figure 4.14 below.

Figure 4.14: Sensitivity analysis of volatility and risk free rate


From figure 4.14 it is seen, that an increase in the risk free rate has a large negative influence

on the value. The influence of the risk free rate is greater than the volatility variable, which

on the other hand has a positive influence on the option value. The volatility variable is used

Binomial Option Value

Phase NDA

Year, US $ million 0 1 2 3 4 5 6 7 8 9 10 11

132,9 226,4 375,1 675,8 913,8 1.335,6 1.692,1 2.124,9 2.848,7 3.490,7 4.268,1 5.455,4

39,9 79,3 299,8 456,0 782,0 1.022,6 1.315,4 1.869,8 2.306,9 2.836,6 3.724,4

- 74,8 148,5 403,4 564,8 761,8 1.200,4 1.497,4 1.857,7 2.540,6

- - 156,3 251,7 383,2 742,5 943,8 1.188,3 1.731,1

- 31,5 62,6 124,3 429,5 565,2 730,5 1.177,5

- - - 215,4 306,3 417,4 798,9

- - 78,6 129,3 203,3 540,0

- 14,4 28,6 56,9 362,9

- - - 241,8

- - 159,0

- 102,4

63,7

Excercie Price EX 107,0 128,6 193,8 240,3 20,1

Total value 132,9

Option Value 130,2

MAX(0,52*2.848,7+0,48*1.869,8)*EXP(-2,38%*1)-193,8;0)

MAX(5.475,4 - 20,1;0)

(0,52*913,8 + 0,48*456,0)* EXP(-2,38%*1)




Volatility 112,5 116,3 120,4 124,5 128,6 132,9 137,2 141,5 145,8 150,2 154,6

Risk free rate 163,3 157,0 150,8 144,7 138,8 132,9 127,1 121,4 115,9 110,4 105,0

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in the estimation of the underlying asset tree, and the risk free rate is used in the adjustments

for the risk neutral probabilities, which explain the different influence on the result. This is in

accordance with previous findings.

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4.4 Practical implementation of the Quadranomial Lattice approach

The following will show the implementation of the quadranomial option approach. It also

consists of five steps.

Figure 4.15: Steps in the quadranomial approach


4.4.1 Step One, Two, and Three

The quadranomial approach is simply an adjustment to the binomial approach. The concept of

adding another source of uncertainty is complicating the practical implementation slightly.

Now the model contains both market uncertainty (the volatility) and technological uncertainty

(the clinical phase success rates). The overall approach is the same as the above steps and is

only marginally adjusted compared to binomial approach.

The principle of estimation of the underlying asset is the same. But since we now have to

construct a model that explicitly takes into account the technological success, the underlying

asset must be different from the binomial approach, which implicitly had taken the

cumulative success rates into account. The underlying asset used for conducting the

quadranomial option analysis is therefore the un-adjusted present value of the

commercialisation phase used in the DTA-analysis. It does not include any modifications for

technological uncertainty, which is necessary because otherwise the success rates would be

accounted for twice. The volatility estimate is the same as before, and the principle in creating

the asset tree is the same as before as well, and to avoid redundancy these steps are not

explained separately here.

Step 1

Determine and estimate

underlying asset

Estimate DCF value as the

underlying asset

of the ROA

Step 2

Identify and

estimate

volatility

Step 3

Create and

estimate asset

tree

Step 4

Conduct

quadranomial

Real Option

analysis

Step 5

Sensitivity

analysis

Estimate the volatility by

Monte Carlo

Simulation

Estimate asset tree by the up

and down stages

based on the distribution

Using back-wardinduction

adjusted by the

up and down probabilities and

technological

uncertainty

Analysing theresult and input

variables by 5 to

20 per cent changes

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4.4.2 Step Four: Conduct quadranomial analysis

In step four, the quadranomial option tree is estimated based on the underlying asset tree,

which is showed in figure 4.16. The quadranomial option approach is constructed as a

European compound option, holding the option to abandon the development project NN9927

after each clinical phase, depending on the outcome. The practical estimation of the

quadranomial option tree is almost similar to the binomial model, and is solved from right to

left starting with the last node of the underlying asset tree. By using backward induction,

each node is weighted by the risk neutral probabilities of p and q and is further adjusted at

the risk free rate and a time factor. The option to abandon in each clinical phase is exercised if

the value is less than or equal to zero, otherwise the development project is continued.

The quadranomial option approach is in simple terms adjusting the option value by the

technological uncertainty of each clinical phase, which is resolved in year 4,7,10, and 11. By

doing so we take each of these technological uncertainties into consideration and explicitly use

them for calculating the option value.

Figure 4.16: Quadranomial option value


The value of development project NN9927 is equal to US$ 355,5 million. This value reflects

both the project value and the value of the quadranomial option. As we use the un-adjusted

DTA value of the commercialisation phase as underlying asset, we subtract the previously

found DTA value to obtain the quadranomial option value of US$ 173,1 million.

Quadranomial Option Value

Phase NDA

Year, US $ million 0 1 2 3 4 5 6 7 8 9 10 11

356 479,3 630,1 923,4 1.149,3 2.224,9 2.716,6 3.311,7 9.798,8 11.879,2 14.395,7 26.669,5

241,4 342,5 575,5 728,7 1.476,9 1.812,1 2.218,0 6.649,7 8.071,2 9.790,9 18.232,6

145,8 337,7 441,1 965,4 1.193,5 1.470,0 4.496,2 5.467,0 6.641,8 12.462,8

175,0 244,4 615,6 770,5 958,5 3.023,4 3.686,1 4.488,2 8.517,1

109,9 376,4 481,3 608,7 2.016,3 2.468,3 3.015,5 5.818,8

212,8 283,4 369,5 1.327,6 1.635,4 2.008,4 3.973,6

148,2 205,9 856,6 1.065,8 1.319,6 2.711,7

94,0 534,5 676,3 848,6 1.848,7

314,2 410,0 526,5 1.258,5

227,8 306,3 855,0

155,6 579,0

390,2

107,0 128,6 193,8 240,3 20,1

68% 42% 66% 90%

Total value 355,5

Option value 173,1

MAX(29.652,9-20,1;0) * 90%

(0,52*1.149,3 + 0,48*728,7)*EXP(-2,38%*1)

MAX(0,52*9.798,8 + 0,48*6.649,7)*EXP(-2,38%*1) -193,8;0)* 42%



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4.4.3 Step Five: Sensitivity Analysis

The last step, the sensitivity analysis of the input variables of the quadranomial option

approach differs from the previous. The sensitivity analysis showed that in order to change

the option value the input volatility variable requires more than a 25 per cent change. This is

why, we exclude the sensitivity figure.

4.4.4 Sum-up

To answer the second research question regarding the difference in practical implementation,

ease of use and strategic opportunities, we have made the practical implementation of each

step figure, implemented our different assumptions in relation to the industry, and estimated

a project value. These findings will be further evaluated in the next chapter.

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5 Evaluation & recommendation

This chapter has the purpose of answering our last research question; what is the potential of

using real option valuation with the pharmaceutical industry in mind.

Firstly, in order to evaluate the potential of one method we find it necessary to consider other

possible methods as well. Therefore in the following, the different methods will be discussed in

relation to each other and how they differ, both in a structural context and in their final

results. This will help show the possible reasons, why practitioners favour certain methods of

valuation than others. The evaluation will take into consideration the fact that the

development of new drugs is costly, time lengthy, attached with great uncertainty, and

generally a complicated business, which is kept in mind in the following evaluation.

As we already have determined that real options analysis will always provide a greater

valuation value than a standard present value valuation16, the objective of this chapter is

consequently not to emphasise this statement, but to take the discussion and evaluation

further. The objective is to investigate, which of the different valuation methods that matches

the industry in the best way – which one of the methods provide the optimal value based on

the theory and the practical implementation. Furthermore, we look in to the depth of the

usability, suitability, and potential of the models.

Finally, it is worth mentioning that we are aware that especially the evaluation of practical

implementation will be severely biased by the way, we have formed the implementation, and

the assumptions we have made. We will try to see beyond that and stay as objective as

possible in the evaluation.

5.1 Evaluation of the DCF model

The DCF model estimates the discounted free cash flow of the development and the

commercialization phase equal to US$ 2,71 million. The DCF model valuates product NN9927

to the lowest present value compared to the other valuation models, which was expected

taking the discussed theory in mind. The relative low DCF value reflects the critical limitation

16 A real option analysis will always provide a greater value than a traditional DCF valuation. The only case where they would

provide the same value is when the volatility estimate is zero. The asset tree collapses in to a straight line i.e. becoming a

standard DCF (Mun, 2002). It will never provide a lower value.

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of the DCF model, and reflects the difficulties for decision makers to decide whether to invest

in an uncertain development process and project.

The practical estimation of the DCF model has previously been evaluated as less complicated

to implement compared to the other valuation models, which we agree after our

implementation. The main critic of the model is based on the general characteristics of the

input variables rather than the practical calculations in the valuation process. The discount

rates used; the risk free rate for the development phase and cost of equity for the

commercialisation phase, are both static input variables and are not affected by the

uncertainty in the clinical phases, which we find to be important in order to reach an optimal

value. Compared to the other valuation models, the DCF model only perceives uncertainty

through the estimation of beta in the cost of equity and does not integrate any specific

technological uncertainty of any kind. Further, the estimated beta has a critical influence on

the valuation, since it affects a US$ 50 million dollar change by a 10 per cent change in the

beta value. The ability to estimate a correct and reliable beta estimate is thereby highly

important in our valuation of product NN9927. Another critical aspect of the DCF model is the

adjustment of the free cash flow of the commercialisation phase, which is adjusted by the

cumulative success.

Compared to the other valuations methods, the main critic of the DCF model is the lack of

strategic flexibility and the lack of explicitly perceiving the technological uncertainty in each

of the development phases. As we showed in the practical implementation, the only way to

consider events in the future is through sensitivity analysis. We find that the sensitivity is not

an adequate tool for analysing the uncertainty that lies within the development process.

Furthermore, the result from the sensitivity analysis is found from hypothetical changes in

specific values, which makes the tool less useful for unbiased evaluation of unknown future

events.

The uncertain phases of a pharmaceutical development project require a flexible valuation

model, which challenges the simplicity of the DCF model. Compared to DTA, Binomial, and

Quadranomial valuation model, we believe that the DCF model has a low potential for

valuating NN9927, or any pharmaceutical projects in general. Moreover, we find that the DCF

should only be used as an underlying asset, since it offers a simple valuation value without

any flexibility. The potential of the DCF model to valuate NN9927 is overall evaluated as low.

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5.2 Evaluation of Decision Tree Analysis

Applying the theory on DTA to our case project produce a value of US$ 182 million, which is

higher than the DCF value. The estimated DTA value is furthermore higher than the value

found through the binomial option method and lower than the extended quadranomial

method. We believe that the higher DTA value reflects an improved ability to valuate some

strategic flexibility and to recognise the technological uncertainty in each of the clinical

phases in development process.

Taking a deeper look at the practical implementation reveals some interesting facts about the

DTA model. The main issues to address are how the model estimates and perceives

technological uncertainty, and how the discount rate is estimated and applied. Giving the way

we have implemented the model, the technological uncertainties, or probabilities, are added to

the model through backward induction. The probabilities in each of the clinical phases are

very project specific, and we must assume our estimates to be biased. This somewhat

complicates the practical estimation, at least compared to the DCF model. Furthermore, each

clinical phase is attached with great uncertainty, and the amount of risk that needs to be

compensated for is changing constantly depending on each phase, and how they progress. This

fact makes it difficult to reliably estimate a discount rate for the projects commercialisation

phase and thereby ultimately the total project value. As seen in the case study, an easy and

straightforward assumption is to discount the commercialisation phase with the cost of

capital, or cost of equity in our case.

The overall idea and purpose of the model is intuitively good, and the model is able to value

strategic flexibility and incorporate probabilities in each clinical phase. Compared to the DCF

model, the DTA model offers a more detailed valuation process, but at the same time it is more

complex to implement, and requires a rather detailed insight in the technological challenges

regarding the development of the product. However, the model is evaluated to have a better

match to what we believe is important, when valuing NN9927 and in general pharmaceutical

development projects. Since the input variables in the DTA model have several similarities to

the DCF model, we believe it is necessary to be able to estimate the specific technological

uncertainties within each clinical phase for the DTA model to have superior potential. The

DTA model is lastly assessed to have good potential for the pharmaceutical industry compared

to the other valuation methods.

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5.3 Evaluation of the Binomial and Quadranomial approach

Using the Binomial model to valuate project NN9927 results in a positive value of US$ 132,9

million dollars, which reflects the value of the project and the option, affected by only market

uncertainty. The Quadranomial model estimates the value to US$ 355,5 million dollars, which

reflects the project and the option, influenced by both market and technological uncertainty.

The actual option values were, US$ 130,2 million for the Binomial model, and US$ 173,1

million for the Quadranomial model.

The main critic of both approaches is mostly concerning the estimation of input variables

rather than the intuition of the models, which at first seem appropriate in our industry

context. Because ROA and the resulting option value are only as accurate as the estimated

underlying asset, a critical aspect of both the binomial and the quadranomial approach is the

use of DCF as the underlying asset. The option analysis will only be as accurate as the

estimation of the DCF, meaning that if the underlying asset is miscalculated, then the option

value is also miscalculated. This emphasises the need for strong consideration regarding the

choice of underlying asset and relating volatility. Since volatility is what drives most of the

value in both ROA models it is important to consider the estimation of this. Proving the

importance of the estimation of the volatility is the influence it has on the result. In the

binomial case, changing the volatility by 10 per cent resulted in a US $8,6 million dollars

change in project value. Both models therefore depend on the ability to reliably estimate the

volatility. The complex and difficult estimation process decreases the otherwise appreciated

quality of the models’ ability to valuate strategic flexibility.

The extended quadranomial model further depends on the ability to estimate technological

uncertainties, and the model is more demanding to fully exploit the advantage of, since the

requirements to the input are stronger. As just explained, DTA is also dependent on

technological uncertainty, and the ability to reliably estimate it. But opposite the

quadranomial model, it does not rely on the challenging volatility estimation.

At first, the general impression is that both the binomial and the quadranomial model seem

fitting for valuing product NN9927 and pharmaceutical projects in general. The ability to

valuate and incorporate uncertainties and flexibility is well aligned with, what we find as

characterising the pharmaceutical industry. Though, given the complex practical

implementation, both models are restricted by the complexity of the practical implementation,

we found in the previous chapter.

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Furthermore, through our own research of the industry we believe that the potential of using

ROA is highly dependent on the ability to incorporate the uncertainties regarding the

technological development i.e. clinical phase success rates. The clinical phases are the most

characterising and unique element in the drug development, why a valuation model should be

able to comprehend and incorporate these. When considering this, the explained theory and

practical implementation of the binomial model have shown that it does not have the best fit

to the industry. The binomial model only incorporates market uncertainty. It simply lacks the

ability to comprehend, what is important for determining the value of a pharmaceutical

project, resulting in that the large amount of private risk17 that affects the decisions in all of

the development stages is neglected (Amram & Kulatikala, 2000). The extended quadranomial

approach is evaluated to have a better potential than the binomial model, since it incorporates

this important technological uncertainty. The quadranomial option approach, therefore,

challenges the DTA by using option theory to model the uncertainty in the market, while still

incorporating the success rates of the clinical phases.

The application of ROA in general has some issues that are relevant to address. Since the

development of pharmaceutical drugs are heavily dependent on the approval from

governmental bodies such as the FDA, one thing to reflect upon in the use of real options

theory is who gets to exercise the options. The approval or decision right that such bodies has,

constitutes a large exogenous risk that challenges the use of real option models, especially the

binomial model. The question is, does management actually have options? Early phase of

pharmaceutical drug development may have some of the features of a strategic option—in the

sense that today’s investment creates a set of future decisions – there are no significant

options in later stages, just sudden death of a project (Amram & Kulatikala, 2000 p. 17).

Another thing to consider is managerial behaviour and especially irrational behaviour. Real

Option Analysis is subject to many considerations in the estimation of input. In order to make

useful decisions, managers need to be as objective as possible. But it is widely recognized that

the cognitive biases of managers and analysts tend to affect the analysis, creating more or less

predictable distortions (Triantis, 2005). These biases or irrationalities can have a significant

impact on investment decisions. Likewise, company culture and organisational structure can

affect decisions as well. Compensations schemes that have short-term focus may also have an

affect in early-stage projects (R&D), because it will only produce cash outflows. Investment

17 Private risk is assumed to the same as technological uncertainty and is the uncertainty involved in development of

pharmaceutical drugs.

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managers have less incentive to undertake these investments. Applying ROA requires one to

reflect on this and perhaps incorporate such matters into the model, which we suggest for

possible further research.

5.4 DTA vs. ROA

Based on the above evaluation of each model, summary table 5.1 is showing a comparison of

each model. Each model is evaluated by the previously stated criteria and ranked with low,

medium or high, corresponding to how the model matches our description of the

pharmaceutical industry.

Table 5.1: Evaluation of the investigated models


From the above evaluation and the summary table, it is clear that the DCF model has a low

potential to valuate pharmaceutical projects. We thereby evaluate both the DTA and ROA to

have a potential in valuation of pharmaceutical development projects. The important question

is then, whether the real options approaches have a better potential compared to the simpler

DTA model. Both the Binomial and the Quadranomial model have a lower usability, but a

higher flexibility, which makes the final evaluation of the real option approach difficult.

Since we have determined that the both Decision Tree Analysis and Real Option Analysis are

suitable methods for valuing pharmaceutical drug development projects, the next to consider

is the discussion and choice between them. The choice between the two different approaches

can relatively simply be evaluated through two parameters – characteristics of the underlying

asset and the underlying risk. This is the focus of the following paragraph.

Evaluation of each model

DCF DTA ROA

Concept Low High High

Uncertainty Low Medium Medium

Flexibility Low Medium High

Usability High Medium Low

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First of all, it is important to look more into depth of the underlying risk of the investment. Is

it diversifiable? Generally investment projects are exposed to a variety of different sources of

risk. This ranges from product price, demand risk, state of the world market, interest rates,

and exchange rates to mention but a few. The question is then which particular risk, or group

of risks, that could affect a project’s cash flow to such an extent that it would change

management’s future decisions (Koller et al., 2010). If commodity prices and their fluctuations

are a key part of the future decisions that are to be made then the key underlying risk is not

diversifiable. Investment projects are often affected by both diversifiable and non-diversifiable

risk but are in most cases more dominated by one of them. If the risk of the underlying has a

low correlation with the overall economic activity, then the underlying risk is diversifiable.

For non-diversifiable risk ROA provides the best and most correct value of the investment. If

we apply the DTA approach, when the underlying risk is non-diversifiable, difficulties in

determining the correct discount rate arise, as mentioned earlier. But when the underlying

risk is diversifiable, the DTA approach is a more appropriate method to use. The projects

payoffs can in each scenario be discounted with the cost of capital of the underlying asset. And

as we have already determined, it is an easier model to implement and use, at least compared

to ROA.

Figure 5.1: DTA versus ROA

Source: Koller et al., (2010) and own creation

The other parameter to consider is the characteristic of the underlying asset. Is it a traded

asset? As demonstrated in our practical implementation of, the models the result from both

ROA and DTA are heavily dependent on the variance of the underlying asset, since we accept

DTA vs. ROA

Underlying

Asset

Non-

traded

asset

Traded

asset

Underlying risk

Diversifiable risk Nondiversifiable risk

Decision Tree

Analysis

Decision Tree

Analysis,

Real Option Analysis

Decision Tree

Analysis

Real Option

Analysis

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the MAD assumption. The source of the variance, or volatility, can help determine, which of

the two methods that are the most applicable. If the underlying’s volatility can be derived

from a traded asset, then ROA should be more accurate than DTA, as the key input in the

underlying can be estimated through for example traded commodities. If this is not the case,

the DTA will be the better choice. Since the variance of the underlying asset cannot be derived

from a traded asset, the estimation of it will be largely judgmental and risk of misestimating

the variance is fairly high (Koller et al., 2010).

Returning focus to the choice between ROA and DTA, the objective is now to relate the

development of pharmaceutical drugs to the above and answer the research question. We start

with examining the first parameter – whether the underlying risk is diversifiable or not. The

technological uncertainty enfolded in developing a new drug and the outcome of each of the

clinical phases in the development is not correlated with the overall economy, or at least a

very low correlation. The success rate in a given clinical phase is not correlated with for

example exchange rates, interest, or any commodity in general. And since the main driver in

investing in a new pharmaceutical drug is the uncertainty of the success in the clinical phases

(technological risk), and not really if the economy is in a favourable trend (market risk) when

the drug if successful is launched, the risk must be assumed to be diversifiable. All this

indicates that the underlying risk in developing a new drug is diversifiable. In relation to

figure 5.1 we position our self in left side of the figure.

The other parameter is relatively easy to determine. Since pharmaceutical drugs are not

traded, as mentioned previously, the variance in the underlying asset can be difficult to

determine. This indicates that, from the above framework, DTA is the most suitable method to

use. This is aligned with our own findings, which have indicated that DTA encompasses many

features that match our short review and walkthrough of the pharmaceutical industry, such

as the stringent division of the clinical phases, the length and cost of each phase, and the

success rates. When everything is taking into consideration, we believe that out of the

methods described and reflected upon in this thesis, using DTA in the valuation of a

pharmaceutical development project will provide the best result. From this we answer our

final research question. We find that real options theory, more specifically the quadranomial

approach, to have adequate potential, but we also find that DTA in overall provide a better

practical potential.

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5.5 Future research

Based on the research questions and the above findings of this thesis, some recommendations

for future research are stated in the following.

This thesis has taken an external point of view analysing different valuation models based on

the industry and publicly available data. Another interesting problem statement would be a

future research taking an internal point of view and analyse the DTA and Quadranomial

approach. In this perspective, it would be possible to include management and project specific

data in the case study. By taking this point of view, several aspects of the volatility and

technological uncertainty could be tested in relation to the difficulties of the practical

implementation. The potential of each method is dependent on the availability of data, since it

affects the different methods and the underlying assumptions. An internal point of view would

be an interesting case study in relation to the delimitations of this thesis, but is difficult to

achieve, since the pharmaceutical industry has a high level of confidential regarding R&D

data.

In relation to the internal point of view, it would be further interesting to analyse the

influence of debt financing. The study should thereby analyse the influence of the interest tax

shield in each of the valuation methods and how this would affect the theoretical potential of

each model. Considering debt financing would furthermore include a more in depth discussion

of WACC and a discussion of, whether the leverage-ratio would increase or decrease the total

value of the pharmaceutical development project.

To support our findings of this thesis, a future case study could expand the study and analyse

several different pharmaceutical development projects in different phases. By analysing

different pharmaceutical projects in different phases, it is possible to discuss the influence of

the time parameter. We have previously discussed whether strategic options exist in the later

part of the development process.

In continuation of the findings of this thesis, another interesting focus would be on a

qualitative research study, formulating hypotheses about, why practitioners do not implement

or consider the Real Option approach. The hypotheses would have to be verified or rejected

based on preferably a large field study. More specifically it could be based on interviews, or

questionnaires send out to practitioners. The study could furthermore investigate, how the

Real Option approach is practically implemented by the practitioners, who have experience

and chosen to use these theories.

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6 Conclusion

In order to answer our research question and investigate the optimal valuation method for the

pharmaceutical industry and drug development projects, we first studied the pharmaceutical

industry. The pharmaceutical industry consists of companies that primarily use chemical-

based synthetic processes to develop new drugs. Many large pharmaceutical companies

typically also use biotechnology in the development process, why we did not separate the two

terms and used the term pharmaceutical industry to cover both pharmaceutical companies

and biotechnology firms. R&D, innovation, and patents are terms greatly associated with the

industry and form, what makes it unique and complex. The development process, which

consists of several clinical phases and approvals, likewise characterises a complex and

uncertain business environment. Based on in depth research of the industry we found the

following result. Industry measures on the success rate for developing a successful drug is

around 17 per cent and cost measures range anywhere from US$ 86 to 2.558 million,

depending on the size of operations and therapeutic class. We found that developing new

pharmaceutical drugs are time-lengthy processes with the average time spend on developing

new drugs being 11 years.

In order to assess the theoretical differences we constructed four criteria: ‘Concept’ that

assesses conceptual differences, ‘Uncertainty’ evaluates the perception and measure of

uncertainty, ‘Strategic flexibility’ examines the methods ability to incorporate decisions to

future events, and finally ‘Usability’ helps evaluate, how usable and user friendly the methods

are. We conducted a case study of an early stage pharmaceutical drug project to evaluate the

practical implementation of the methods as well. The overall goal of this case study was not a

numerical valuation but an evaluation of the different methods and assumptions of each

valuation method. Each method was implemented through a five-step model. The steps

ensured a systematic walkthrough of the methods. The implementation required certain

assumptions, such as a division of the development phase and the commercialisation phase, in

which the developed drug is sold. Doing so makes it easier to implement all the methods,

especially the more complex methods. We found that the quadranomial model provides the

highest value, while the DCF models provides the lowest value.

The Discounted Cash Flow model’s key concept is to assess potential future cash flows of an

asset and discounting these cash flows to present value using an appropriate discount rate.

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The DCF model perceives uncertainty as risk, thereby also meaning that a more uncertain

environment increases the discount rate and thus decreases the valuation value. The model

base its conclusion on today’s expectations of the future and assumes that management acts

passively through the investment period and because of this not having the possibility of

incorporating future events i.e. lacking the possibility of valuing strategic flexibility. The

relative simplicity of the model makes it, from a theoretical standpoint, uncomplicated to

implement, and the result is easily understood and communicated through an organisation.

Compared to the other valuation models, the DCF model only perceives uncertainty through

the estimation of beta in the cost of equity and does not integrate any technological

uncertainty of any kind. The ability to estimate a correct and reliable beta value is thereby

highly important in the valuation of pharmaceutical projects. We evaluated the DCF model to

have a low potential in valuating pharmaceutical drug development projects.

Decision Tree Analysis is a slightly more complicated model. The basic idea is to create a

decision tree consisting of events and decisions, and the concept revolves around discounting

the contingent cash flows with appropriate discount rates. When using the DTA framework,

uncertainty is perceived as both risk and opportunities. In the context of the pharmaceutical

industry, we modelled uncertainty as technological uncertainty. More specifically the success

rates in the clinical phases. In DTA future events and decisions are incorporated in the model,

enabling management actions during the life of the investment. The main issues to address

are the estimation of the technological uncertainty, and how the discount rate is estimated

and applied. The probabilities in each of the clinical phases are very project specific, which

make them difficult to estimate accurately for a specific project. The overall idea and intention

of the model is intuitively good. Compared to the DCF model, the DTA model offers a more

detailed valuation process, but at the same time it is more complex to implement and requires

a rather detailed insight in the technological challenges regarding the development of the

product.

The most complex model investigated is Real Option Analysis. The concept is to use option-

pricing theory to determine the value of a project. The value is based on the progression of an

underlying asset, which we assume to be the commercialisation DCF valuation in the

acceptance of the MAD assumption. By using backward induction we determined the value of

the project. We investigated two types of real option models; the binomial- and quadranomial

model. In the latter, two sources of uncertainty is separated and incorporated – market- and

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technological uncertainty, whereas in the binomial model only market uncertainty is

modelled. The degree of strategic flexibility is relatively high and can be seen in the broad

variety of different options, such as the option to grow, abandon, or wait. The idea and thought

of incorporating strategy in to the valuation through option theory seems at first appealing

but is let down by its complex and occasionally difficult estimations. The main critic is also

mostly concerning the estimation of input variables rather than the intuition of the models.

We found that the potential of using ROA is highly dependent on the ability to incorporate a

reliable volatility of the underlying asset and the technological uncertainties in the clinical

phases.

Through our investigation of the industry and evaluation of the models, we subsequently

found that both DTA and ROA have features that match the pharmaceutical industry. As we

have determined, the industry is faced with great uncertainty, stringent legislation and

regulations, and an ever-changing environment, which makes the simplicity of the DCF

without real potential. Moreover from our research, the most important and significant

characteristic of the industry is the clinical phases. Therefore an optimal valuation method

must incorporate these, why we advocate the use of DTA or the quadranomial real option

approach, which explicit include the success rates in the clinical phases. In order to single out

one method in particular, we looked more in depth of assumptions behind the models. Based

on a framework examining tradability and underlying risk, we reached the conclusion that

DTA is the best valuation method for valuating pharmaceutical drug development projects.

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