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