01 Analyzes of risk and uncertainty

Uncertainty = Unknown and non-measurable results

Risks = unknown results, but probabilities can be attributed [zugewiesen]

Methods:

1) Empirical Methods

2) Simulation Methods

3) Methods of decision theory

4) Probabilistic Methods [probabilistisch = der Wahrscheinlichkeit nach]

These are cautious or defensive methods:

A) Reduction of the investment recovery period

—> Shortening the duration of the investment

—>The method is used for all fast investments in technological innovation and relatively low capital intensity.

B) Adjustment of assessment rate [Bemessungssatzes]

—> Adopting a higher rate, including the higher risk

Example:

WACC = 12 %

Risk premium = 5 %

—> Final update rate = 17 %

C) The method of the right equivalent

—> Adopting a certain coefficient of equivalence (0 <α <1 )

—> This one converts the uncertain cashflows into certain cashflows

—> The lower the coefficient, the higher is the risk or the uncertainty

—> The coefficient can decrease over the years, because cashflows in distant future are less certain

It has the task to evaluate the models reaction to changes in variables which are considered more sensitive

A) Sensitivity Analysis

—> Change the profitability of a project in term of modification of an assumption [Annahme]

—> Like the prices per kilometer of our hydrogen fleet

—> Selection of assumptions should focus on those that are decisive [entscheidend] or critical for the viability [Rentabilität] of the investment

B) Scenario Analysis

—> Based on different assumption on external impacts (Market conditions, economic developments, technological trends), different scenarios are made up

—> There should be three scenarios: optimistic, moderate and pessimistic

—> Each scenario gets a specific probability (for example optimistic scenario 50 %)

Those methods are in the context of absolut uncertainty

—> the decision-maker can not predict which state of nature will occur

A) Actions or Strategies:

—> These are the alternative options or strategies that the decision-maker can choose from

—> Calculation of the different VALs

B) Situations or Events (State of Nature):

—> Uncontrollable events or situations that have an impact on the investment

C) Results or Consequences

—> In the end you have as a result a table which shows which action has to follow for the specific state of nature

—> For each situation there is only one adequate action

A) Maximax criterion (Optimistic)

—> best-case-scenario is chosen, because all situations have the same probability to occur

B) Maximini criterion (Pessimistic)

—> Worst-Case-Scenario is chosen; Action with the least loss

—> pessimistic view

C) Minimax regret criterion (minimum losses)

—> it is chosen the action that minimizes the maximal losses

—> that means that the “regrets” are the lowest

—> is used by high uncertainty and no probabilities for the scenarios

D) Criterion of insufficient reason (Laplace)

—> all states of nature are equally likely for that criterion

—> Calculate average payoff of each scenario

—> Choose scenario with highest outcome

The Probabilistic methods have the task to analyze the risk after the sensitivity analyze

A) The decision tree method

—> It is chosen when more decisions have to be taken sequential [aufeinanderfolgend]

—> The tree is made of “decision nodes” [Entscheidungsknoten] and “event nodes” [Ereignisknoten]

—> The probabilities and outcomes are taken into account. The decision-maker can therefor choose a path with the highest probability and highest outcome

B) The average-variance method [Mittelwert-Varianz-Methode]

—> The average and the variance are characterising the risk of specific investment

—> High average of the VAL is good

—> High variance of the VAL is bad (higher risk)

C) The Monte Carlo method

—> This method simulates uncertainties by using random numbers to model different scenarios

—> A probabilistic model is defined for each project variable (e.g. costs, revenues).

—> A large number of simulations are run, using random numbers for each simulation to generate possible outcomes.

—> The results of the simulations are statistically analyzed to better understand risks and probabilities.