Christer Carlsson IAMSR / Åbo Akademi University [email protected].

Christer Carlsson

IAMSR / Åbo Akademi [email protected]

FORS 8.05.2003 Christer Carlsson 2

GIGA-INVESTMENTS

Facts and observationsGiga-investments made in the paper- and pulp industry, in

the heavy metal industry and in other base industries, today face scenarios of slow growth (2-3 % p.a.) in their key markets and a growing over-capacity in Europe

The energy sector faces growing competition with lower prices and cyclic variations of demand

Productivity improvements in these industries have slowed down to 1-2 % p.a


GIGA-INVESTMENTS

Facts and observationsGlobal financial markets make sure that capital cannot be

used non-productively, as its owners are offered other opportunities and the capital will move (often quite fast) to capture these opportunities.

The capital markets have learned “the American way”, i.e. there is a shareholder dominance among the actors, which has brought (often quite short-term) shareholder return to the forefront as a key indicator of success, profitability and productivity.


GIGA-INVESTMENTS

Facts and observationsThere are lessons learned from the Japanese industry,

which point to the importance of immaterial investments. These lessons show that investments in buildings, production technology and supporting technology will be enhanced with immaterial investments, and that these are even more important for re-investments and for gradually growing maintenance investments.


GIGA-INVESTMENTS

Facts and observationsThe core products and services produced by giga-

investments are enhanced with lifetime service, with gradually more advanced maintenance and financial add-on services.

New technology and enhanced technological innovations will change the life cycle of a giga-investment

Technology providers are involved throughout the life cycle of a giga-investment


GIGA-INVESTMENTS

Facts and observationsGiga-investments are large enough to have an impact on

the market for which they are positioned:A 300 000 ton paper mill will change the relative competitive

positions; smaller units are no longer cost effectiveA new teechnology will redefine the CSF:s for the marketCustomer needs are adjusting to the new possibilities of the giga-

investment

The proposition that we can describe future cash flows as stochastic processes is no longer valid; neither can the impact be expected to be covered through the stock market


GIGA-INVESTMENTS

The WAENO Lessons: Fuzzy ROV Geometric Brownian motion does not apply Future uncertainty [15-25 years] cannot be estimated

from historical time series Probability theory replaced by possibility theory Requires the use of fuzzy numbers in the Black-Scholes

formula; needed some mathematics The dynamic decision trees work also with fuzzy

numbers and the fuzzy ROV approach All models could be done in Excel


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REAL OPTIONS

Types of options Option to Defer Time-to-Build Option Option to Expand Growth Options Option to Contract Option to Shut Down/Produce Option to Abandon Option to Alter Input/Output Mix


REAL OPTIONS

Table of Equivalences:

INVESTMENT OPPORTUNITY VARIABLE CALL OPTION

Present value of a project’s operating cash flows

S Stock price

Investment costs X Exercise price

Length of time the decision may be deferred t Time to expiry

Time value of money rfRisk-free interest rate

Risk of the project σ Standard deviation of returns on stock


REAL OPTION VALUATION (ROV)

The value of a real option is computed by

ROV =Se −δT N (d1) − Xe −rT N (d2)

whered1 = [ln (S0 /X )+(r −δ +σ2 /2)T] / σ√T

d2 =d1 − σ√T,


FUZZY REAL OPTION VALUATION

• Fuzzy numbers (fuzzy sets) are a way to express the cash flow estimates in a more realistic way

• This means that a solution to both problems (accuracy and flexibility) is a real option model using fuzzy sets


FUZZY CASH FLOW ESTIMATES• Usually, the present value of expected cash

flows cannot be characterized with a single number. We can, however, estimate the present value of expected cash flows by using a trapezoidal possibility distribution of the form

Ŝ0 =(s1, s2, α, β)

• In the same way we model the costs



We suggest the use of the following formula for computing fuzzy real option values

Ĉ0 = Ŝe −δT N (d1) − Xe −rT N (d2)

where

d1 = [ln (E(Ŝ0)/ E(X))+(r −δ +σ2 /2)T] / σ√T

d2 = d1 − σ√T,



• E(Ŝ0) denotes the possibilistic mean value of the present value of expected cash flows

• E(X) stands for the possibilistic mean value of expected costs

• σ: = σ(Ŝ0) is the possibilistic variance of the present value of expected cash flows.



No need for precise forecasts, cash flows are fuzzy and converted to triangular or trapezoidal fuzzy numbers The Fuzzy Real Option Value contains the value of flexibility


SCREENSHOTS FROM MODELS


NUMERICAL AND GRAPHICAL SENSITIVITY ANALYSES


FUZZY OPTIMAL TIME OF INVESTMENT

Ĉt* = max Ĉt = Ŵt e-δt N(d1) – X e-rt N (d2 ) t =0 , 1 ,...,T where

Ŵt = PV(ĉf0, ..., ĉfT, βP) - PV(ĉf0, ..., ĉft, βP) = PV(ĉft +1, ..., ĉfT, βP)

Invest when FROV is at maximum:


OPTIMAL TIME OF INVESTMENT

Ct* = max Ct = Vt e-δt N(d1) – X e-rt N (d2 ) t =0 , 1 ,...,T

How long should we postpone an investment?Benaroch and Kauffman (2000) suggest:Optimal investment time = when the option value Ct* is atmaximum (ROV = Ct*)

Where

Vt = PV(cf0, ..., cfT, βP) - PV(cf0, ..., cft, βP) = PV(cft +1, ...,cfT, βP),


FUZZY OPTIMAL TIME OF INVESTMENT

We must find the maximising element from the set {Ĉ0, Ĉ1, …, ĈT}, this means that we need to rank the trapezoidal fuzzy numbers

In our computerized implementation we have employed thefollowing value function to order fuzzy real option values, Ĉt = (ct

L ,ctR ,αt, βt), of the trapezoidal form:

v (Ĉt) = (ctL + ct

R) / 2 + rA · (βt + αt) / 6

where rA > 0 denotes the degree of the investor’s risk aversion


EXTENSIONS

Fuzzy Real Options support system, which was built on Excel routines and implemented in four mutlinational corporations as a tool for handling giga-investments.

Possibility vs Probability: Falling Shadows vs Falling Integrals [FSS accepted]

On Zadeh’s Extension Principle [FSS submitted]

Christer Carlsson IAMSR / Åbo Akademi University [email protected].

Documents

Transcript of Christer Carlsson IAMSR / Åbo Akademi University [email protected].