131

APPENDIX: BEHIND THE SCENES

132

Overcoming limitations of traditional financial analysis

DDM versus “ Decision Tree ” method

How to calculate the FlexValue

The DDM approach – an overview

No black box – the math behind DDM

133APPENDIX: BEHIND THE SCENES

Overcoming limitations of traditional financial analysis

Focus: Volatilities instead of a lump-sum risk within the WACC

Figure A.1: NVP calculation

109876543210Terminalvalue as

perpetualannuity

Present value Free cash flow

494

Euro900

800

700

600

500

400

300

200

100

0

6260 59 51 5443 44 43 3543

134

The WACC factor of influence is intended to depict the specific risk of an investment, for example, but in fact reflects only the risk of a certain in-dustry or company in comparison to the market average at a given point in time. In addition, the WACC can prove highly volatile over time.

Using the current market yield as a component of a specific valuation is arbitrary, as this factor also undergoes massive fluctuations with the passing of time.

The consideration of further specific risks, such as those related to a country strategy or technology-driven investments, takes place on the basis of an arbitrarily selected risk premium added to the WACC.

135APPENDIX: BEHIND THE SCENES

Figure A.2: WACC

6,0%

Risk-free

interest1)

Betafactor x

Marketyield –

Risk-free

interest

Intereston

capital

4.5% 1.0 10.5%

1) Average interest rate of long-term federal bonds2) Tax shield considered (35% tax rate)

(10.5% 4.5%)

=+

Cost of capitalCost of

loancapital

WACC

Loan capital share: 30%

=–x+Equity share:

70%

Capital structure:

+ 2.0%

correctedWACC

10.52%

8.52% 2)

Focus: How to overcome the DCF scenario problem

136

Figure A.3: Development and assessment of scenarios

Technologymodel

Worst case

Base case

entsBest caseTechnology

developments

Marketmodel

Worst case

Base case

Best caseMarket

developments

Strategicoption …

Strategicoption 2

Strategicoption 1

Selected corporatestrategies

Financemodel

Worst case

Expected case

Best caseFinancial analysisof selected busi-ness strategies

High uncertainties

regarding

Research & Development status

Economic availability Development of

CAPEX and OPEX

High uncertainties

regarding

Market penetration

Market share

Competitors

Customer requirements

Limitations regarding

Only selected options

No feasibility of execution

High complexity due to the integration of relevant market and financial aspects

Limitations regarding

Quality of financial results

Reduced transparency due to internal and external communication of investment decisions

Management taps one or more experts to provide comprehensive input on technological challenges expected in the future; the results are used to derive technology scenarios.

Market and customer forecasts, closely linked, are frequently only speculative because of the highly complex nature of these two interde-

137APPENDIX: BEHIND THE SCENES

pendent areas. For this reason numerous parameters are required to form meaningful market models.

Based on the two points above, the next step is to map the strategically important business models, as well as overall scenarios that are more or less simple to understand.

Upon reaching the final step, a financial model can be calculated for each scenario. The financial model forms the basis for the decision mak-ing process.

Figure A.4: Limitations of scenarios linked with probabilities

NPV

Worst case scenario

NPV

Probability

Expected case scenario

Best case scenario

Worst case scenario

Expected case scenario

Best case scenario

?

Different scenarioshave different values

Probabilities are assigned toscenarios without reliablecalculation

Scenarios are only special casesof value probability distribution

NPV

Probability

Scenario1

Scenario2

Scenario3

138

DDM vs. “�Decision Tree�” method

The DDM approach – an overview

139APPENDIX: BEHIND THE SCENES

Figure A.5: Development stages leading to the Dynamic Decision Management approach

WACC8%

WACC 10%

Risk

NPV NPV

Probability (P)

Bestcase            

NPV

Probability (P) Probability (P)

TotalValue

Scenariobundle 1

Scenariobundle 2

Scenariobundle 3

NPV

Risk Risk

Value increasethrough

investment decision

Probability of achieving project

values

NPV with risk premium

Scenario-based NPV

NPV with generalized probabilities

NPV with specific

probabilities

TotalValue 1 2 3 4 5NEW NEW

Expected case

Worstcase

Higher risk signifies higher project-specific WACC

Increase in risk results in lower NPV

Opportunities therefore at a disadvantage compared to risks

Differing risks of individual cash flow elements not taken into account

Depiction of uncertain future cash flows through discrete scenarios and sensitivities

Completeness of alternatives or scenarios not given

No statement on the probability of individual scenarios

Discrete scenarios with specific risks are subjectively assigned probabilities

No calculation of probabilities – thus not able to be evaluated

Expected value and volatilities means steady allocation of cash flows and related probabilities

Completeness of all cash flow factors due to analytic methodology rather than intuition

Probability- related risks taken into account 

Consideration of future active management (flexibility)

Optimization of value through active management = by exercising different alternatives

NPV plus value of flexibility = TotalValue

The first

second

140

third

The fourth

The fifth

How to calculate the FlexValue

141APPENDIX: BEHIND THE SCENES

Figure A.6: Distribution curve

Deconstruction Cold Reserve Operations

Probability(P)

Deconstruction

Switch into Operations

Cold Reserve

Value Period 1 (31.12. 2009)

Probability(P)

Value Period 1 (31.12. 2009)

Switch into Operations

Cold Reserve

6.0%

5.5%

5.0%

4.5%4.0%

3.5%

3.0%2.5%

2.0%1.5%

1.0%

0.5%0.0%

6.0%

5.5%

5.0%

4.5%4.0%

3.5%

3.0%2.5%

2.0%1.5%

1.0%

0.5%0.0%

-10,000 0 10,000 20,000 30,000 40,000 50,000 60,000 70,000 80,000

-10,000 0 10,000 20,000 30,000 40,000 50,000 60,000 70,000 80,000

142

143APPENDIX: BEHIND THE SCENES

Figure A.7: FlexValue – example calculation

Results

NVP Baseline = EUR 0.45 mn FlexValue = (Sum of discounted, probability weighted difference values) EUR 0.19 mnTotalValue 2009 = EUR 0.64 mn

NPV Baseline: EUR 0.45 mn

20%

30%

50%

Price ofExcecution

Option

Option Value FlexValue

Probability of continuing operations: 30%Time value of future cash flows: EUR 2 mn

Probability of continuing operations: 50%Time value of future cash flows: EUR 0.5 mn

Probability of continuing operations: 20%Time value of future cash flows:EUR -2.0 mn

Price to shutdown operations: EUR -1 mn

Price to shutdown operations: EUR -1 mn

Price to shutdown operations: EUR -1 mn

No shutdown – Option value = EUR 0

No shutdown –Option value = EUR 0

Not applicable

Not applicable

Value = EUR 0.19 mn EUR 1.0 mn x 20% / (1+0.03 risk-free rate)t

144

No black box – the math behind DDM

stochastic values or value distributions

stochastic.

Figure A.8: Cash flows and probabilities (1/2)

2016 Dec 31: Cash Flow0 50 100 150 200 250 300

6.0%

5.5%

5.0%

4.5%

4.0%

3.5%

3.0%

2.5%

2.0%

1.5%

1.0%

0.5%

0.0%

Prob

abili

ty

Cash flows in the period ending Dec. 31, 2016Mean, i.e. the expected value in the period ending Dec. 31, 2016

145APPENDIX: BEHIND THE SCENES

Figure A.8: Cash flows and probabilities (continuance 2/2)

2016 Dec 31: Cash Flow0 50 100 150 200 250 300

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%Pr

obab

ility

Ban

d

50

62

71.5

81.0 101.5

114.5

132

160

High and low end values of this probability bandMean, i.e. the expected value in the period ending Dec. 31, 2016

146

Stochastic calculus is elegant but gets extremely complex as soon as we try to apply it to anything other than the most basic decision option constellations, i.e. Real Options. Stochastic calculus, for example, the Black-Scholes model and its extensions, is mainly used to valuate finan-cial options such as calls and puts on stock indexes. Stochastic calculus is very challenging and complex when applied to most real investment problems found in the realm of corporate finance.

Monte Carlo simulation runs a valuation repeatedly (thousands to mil-lions of times), using random input values for every run and statistically analyzing the results. The Monte Carlo simulation as a method is very flexible and widely applicable but rather cumbersome to set up. Run-ning a simulation of anything but the most simple of valuations takes substantial know how and requires lengthy calculation periods, even on very fast computers.

Binomial models are based on binomial trees that generate the required distributions. Discrete binomial models are quite easy to understand and implement. They can be applied to almost any decision structure including options. Unfortunately, classic binomial models based on bino-mial trees have two drawbacks:

− The amount of value probability pairs is very small in early periods, potentially leading to substantial option valuation errors in early periods.

147APPENDIX: BEHIND THE SCENES

− The binomial tree expands greatly for values with multiple volatility changes or for combined values based on cash flows consisting of mul-tiple components. Even when considering only modest-sized real world problems, billions or even trillions of value/probability pairs have to be calculated and processed. This far exceeds the memory and processing capabilities of desktop computers.

148

Figure A.9: Diffusion of probabilities

Time

Value

Gauss-WienerOrnstein-Uhlenbeck

150

GLOSSARY

Key terminology of Dynamic Decision Management

» Shows a strategy’s value based on clearly defined as-sumptions; does not presuppose further management action in terms of modifying strategy

» Shows the potential deviations in a strategy’s value when the assumptions change

151GLOSSARY

» Shows the value of strategic alternatives that are possible because of a pro-active management of the “�baseline�”

» Shows the total value of a strategic decision

A holistic process of assessing and calculating the

uncertainties and flexibility of strategic decisions, gener-

ating a quantitative value as the basis for decision making.

152

REFERENCES

153REFERENCES

154

ACKNOWLEDGEMENTS

155ACKNOWLEDGEMENTS

156

157ACKNOWLEDGEMENTS

158

AUTHORS

Jochen Gerber

Hanjo Arms

159AUTHORS

Mathias Wiecher,

Christian Danner