OptionsPort - Real Option Valuation and Optimal Portfolio Strategies, TEKES [662/04]. Industrial partners: Kemira Oyj, Cargotec Oyj, UPM-Kymmene Oyj, Kuntarahoitus Oyj. Publications in this project: Carlsson, Full´er, Heikkil¨a and Majlender [51] and Carlsson, Full´er and Heikkil¨a [58]. My contribution to the project: Using the possibilistic mean value and variance for ranking projects with imprecise future cash flows.
A major advance in development of project selection tools came with the application of options rea-soning to R&D. The options approach to project valuation seeks to correct the deficiencies of traditional methods of valuation through the recognition that managerial flexibility can bring significant value to a project. The main concern is how to deal with non-statistical imprecision we encounter when judging or estimating future cash flows. In our OptionsPort project we developed a model for valuing options on R&D projects, when future cash flows and expected costs are estimated by trapezoidal fuzzy numbers.
Furthermore, we represented the optimal R&D portfolio selection problem as a fuzzy mathematical programming problem, where the optimal solutions defined the optimal portfolios of R&D projects with the largest (aggregate) possibilistic deferral flexibilities. Carlsson, Full´er, Heikkil¨a and Majlender [51] suggested the following algorithm for ordering R&D projects. This paper was Number 1 in Top 25 Hottest Articles Computer Science, International Journal of Approximate Reasoning April to June 2007. (see http://top25.sciencedirect.com/subject/computer-science/7/journal/international-journal-of-approximate-reasoning/0888613X/archive/12/)
Facing a set of project opportunities of R&D type, the company is usually able to estimate the expected investment costs, denoted byX, of the projects with a high degree of certainty. Thus, in the following we will assume that theX is a crisp number. However, the cash flows received from the projects do involve uncertainty, and they are modelled by trapezoidal possibility distributions. Let us fix a particular project of lengthLand maximum deferral timeT with cash flows
cf˜i = (Ai, Bi,Φi,Ψi).
Now, instead of the absolute values of the cash flows, we shall consider theirfuzzy returns on investment
(FROI) by computing the return that we receive on investmentXat yeariof the project as FROIi= ˜Ri =
Ai X,Bi
X,Φi X,Ψi
X
= (ai, bi, αi, βi).
We compute the fuzzy net present value of project by FNPV =
XL i=0
R˜i (1 +r)i−1
×X.
where r is the project specific risk-adjusted discount rate. If a project with fuzzy returns on invest-ments{R˜0,R˜1, . . . ,R˜L}can be postponed by maximum ofT years then we will define the value of its possibilistic deferral flexibility by
DT = (1 +σ( ˜R0))×(1 +σ( ˜R1))× · · · ×(1 +σ( ˜RT−1))×FNPV,
where1 ≤t ≤L. If a project cannot be postponed then its possibilistic flexibility equals to its fuzzy net present value. That is, ifT = 0thenDT = F N P V. The basic optimal R&D project portfolio selection problem can be formulated as the following fuzzy mixed integer programming problem
maximize D=
XN i=1
uiDi
subject to XN
i=1
uiXi+ XN i=1
(1−ui)ci ≤B (7.10)
ui ∈ {0,1}, i= 1, . . . , N.
whereN is the number of R&D projects;B is the whole investment budget;ui is the decision variable associated with projecti, which takes value one if project i starts now (i.e. at time zero) and takes value zero if it is postponed and is going to start at a later time;cidenotes the cost of postponing project i (i.e.
the capital expenditure required to keep the associated real option alive); finally,XiandDistand for the investment cost and the possibilistic deferral flexibility of projecti, respectively,i= 1, . . . , N. In our approach to fuzzy mathematical programming problem (7.10) , we have used the following defuzzifier operator forD,
ν(D) = (E(D)−τ σ(D))×X where0≤τ ≤1denotes the decision makers risk aversion parameter.
I presented the following example atSeminar on New Trends in Intelligent Systems and Soft Com-puting, February 8-9, 2007, Granada, Spain. Let us assume that we have 5 different types of R&D projects with the following characteristics:
Project 1 has a large negative estimated NPV (which is due to the huge uncertainty it involves), and it can be deferred up to 2 years(ν(F N P V)<0, T = 2).
Project 2 includes positive NPV with low risks, and has no deferral flexibility(ν(F N P V)>0, T = 0).
Project 3 has revenues with large upward potentials and managerial flexibility, but its reserve costs (c) are very high.
Deferral
Figure 7.11: Expected cash-flows from projects.
Project 4 requires a large capital expenditure once it has been undertaken, and has a deferral flexibility of a maximum of 1 year.
Project 5 represents a small flexible project with low revenues, but it opens the possibility of further projects that are much more profitable.
Deferral
This project is going to be rejected, because the future (upward) potentials do not seem to
counter-balance its large negative NPV
Figure 7.12: Analysis of Project 1.
Deferral
This project will be abandoned as well, since there are more profitable projects in the
system with higher expected revenues (although it generates some revenues, we
cannot support it, because of our budget constraint)
Figure 7.13: Analysis of Project 2.
Deferral
This project is going to be undertaken now, because its generated revenues are high enough to compensate us for giving up its deferral flexibility (in fact, by delaying the project, we do not expect a significant boost
in its cash flows); furthermore, the first revenues of this project will contribute to
our budget in the near future
Figure 7.14: Analysis of Project 3.
Deferral
This project will be kept alive (and therefore will require a spending on its
”reserve costs”), because it involves huge expected future revenues; however, since we are assumed to pay out a large capital expenditure when entering the project, we
shall use some managerial flexibility (waiting) to learn more about the circumstances of the project, and therefore
reduce the risks associated with the large investment costs
Figure 7.15: Analysis of Project 4.
Deferral
This project is going to be supported, and kept alive, since it can open other project opportunities (thus it involves huge upward potentials), while only implying limited risks
for financial losses (i.e. it represents a starting link of a chain of compounded real
options)
Figure 7.16: Analysis of Project 5.
Deferral