STOCHASTIC

INVESTMENT ANALYSIS UNDER UNCERTAINTY B-653
3. The Structure of Investment Projects
So far we have introduced three basic concepts for investment analysis: a state
description with its associated event tree, a policy, and a cash flow description for a
project. In terms of these concepts, an investment project can be delineated abstractly
as follows. A policy is given initially which will result in a known cash flow pattern
over the event tree. To be analyzed is an amendment to that policy, called the investment
project, which will result in a new policy and a new cash flow pattern over
the event tree. The project is to be accepted if the new policy with its associated cash
flow pattern is preferred to the old policy. Symbolically, denote the cash flow pattern
for the initial policy, represented by P, by
(2) D(P) = [do; id,); \dti\ ;•••].
In the usual case Z)(P) is the dividend stream for the policy P. Letting P' represent the
new policy,
(3) D(P') = D(P) + C(P)
•D = [do + Co i {di + c! ; [da + c,,) ;•••],
where C{P) is the cash flow description of the investment project, as displayed in (1).
It should be noted that the project cash flow description is defined by the property
C(P) = Z)(P') — D(P); with this understanding, the cash flows cm... can be interpreted
as the net of all effects on cash flows for both the new and old activities, and
thus take account of all dependencies among projects.'
For purposes of analysis, we shall place two restrictions on the set of investment
projects to be considered for adoption. First, the set of available projects must be
known; that is, all deferred projects, as well as the present projects, must be known.
This says that we shall make no provision for investment opportunities that are unknown
at present but which might arise at some future node of the event tree. On the
other hand, since we allow deferred projects, this restriction does not rule out a sequential
investment strategy; for example, one kind of deferred project provides for initiation
of activities at a future point in time only if certain events are obtained in the
interim. The second restriction, imposed in part by the definition of the state description,
is that a project's cash flow description can be calculated for any policy. This
restriction requires that one has available an optimization procedure, or at least some
decision rule, for allocating resources among activities; therefore, for a given policy,
each project has been already optimized with respect to resource allocation before it
is brought up for consideration.
It is worth remarking that some sets of projects may not be feasible to adopt in
total, due perhaps to logical restrictions requiring that one or another of two projects
can be undertaken but not both. For example, one or two new factories can be built
but not both. In this case, one or the other project can be proposed separately, but if
one is already included in the policy then proposal of the second requires deletion of
the first so that only the net effect of the second is considered. It is intended that the
relation (3) embody such considerations, as is implied by the notational dependence
" f the cash flow description upon the policy.
* The notation C(P, P') would be more accurate, but here we shall omit explicit reference to
the dependence upon the new policy.
PART IV. DYNAMIC MODELS REDUCIBLE TO STATIC MODELS