Corporate
Finance FIN 622
VU
Lesson
14
SINGLE
AND MULTI PERIOD CAPITAL
RATIONING
Following
topics will be discussed in this hand
out:
Single
period capital
rationing
Multi-period
capital rationing
Linear
programming
ONE-PERIOD
CAPITAL RATIONING:
When
limits are placed on the
availability of finance for
positive NPV projects for
one year only and
capital
is freely
available in all the rests of
periods.
There
are some additional
assumptions in single period
rationing which are very
important to consider
here:
i)
If a
firm does not undertake a
project `now' the period of capital
scarcity, the opportunity is lost.
In
other words, the project cannot be
deferred until the capital is
available.
ii)
The outcome of each
project is known with certainty so
that the choice between the
projects is not
affected
by considerations of risk.
iii)
The projects are
divisible it means that we
can undertake 50% of project A and 50% of
project B.
The
basic approach will be to
rank the projects in such a
way that NPV can be
maximized from the use
of
available
finances.
Ranking the
projects using NPV will be
incorrect in this scenario because NPV
basis will lead to select
the
`big'
projects, each of which has
a high individual NPV but
which have a lower NPV than
a large number of
smaller
projects with lower
individual NPVs. Therefore, ranking
should be made in terms of
Profitability
Index.
There
are some issues with the PI
method as well and should be
outlined. This approach
would only be
feasible
if projects are divisible. If projects
are not divisible, which is
normally the case in reality; a
decision
should be
made by considering the absolute
NPV of all possible combinations of
all positive projects
within
the constraint of
limited capital.
This
method is of little use when
project have different cash
flow patterns.
PI method
ignores the absolute size of
individual projects. A project
with a high index might be
very small
and
therefore only generate a small
NPV.
MULTI-PERIOD
CAPITAL RATIONING:
When
capital is in limited availability in
more than one period
and selection of projects cannot be
made by
ranking
projects according to PI, this
situation is known as multi-period
capital rationing.
Capital
constraints are imposed in
more than one period to
restrict the acceptance of positive
NPV projects.
Other
techniques like linear programming tools
can be used.
In
mathematics, linear
programming (LP)
problems are optimization
problems in which the objective
function
and the constraints are all
linear.
Open
problems
· Does
LP admit a polynomial algorithm in the
real number (unit cost) model of
computation?
· Does
LP admit a strongly polynomial algorithm?
· Does
LP admit a strongly polynomial algorithm to
find a strictly complementary
solution?
· Does
LP admit a (strongly or weakly) polynomial
pivot algorithm (may be a non-simplex
pivot
algorithm,
e.g., a criss-cross or arrangement
method)?
· Is the
polynomial diameter conjecture
true for polyhedral
graphs?
· Does
LP admit a (strongly or weakly) polynomial
simplex pivot algorithm?
· Is the linear
diameter (Hirsch) conjecture true
for polyhedral
graphs?
Here
we will discuss the graphical
approach to LP. This involves
only two variables and if
there are more
than
two variables then simplex
method is used.
When
we are confronted with TWO
projects (only) we can use
graphical method to select the one
best fit
project.
First
step is to define the variables or
project by assigning them symbols
like x & y, a & b etc.
The
second step is the key issue
where we establish the constraints
like availability of capital in
period 1, 2
and so
on. For example, if we have
two projects x and y and
project x need 30 million of investment
and
project
y requires 25 million of investment and
we have only 40 million
available, then the constraint can
be
expressed
as:
45
Corporate
Finance FIN 622
VU
30x +
25y <= 40
Last
step is to form an objective function.
The objective function is to maximize the
investment return.
When
we have translated the constraints
and objective function in equation we
plot these on a graph
to
work
out the feasible
solution.
46