Capital rationing,
sensitivity Analysis and
probability Tree
Instructor: Ms. Zainab Noor
What Is Capital Rationing?
 Capital
rationing is the process
through which companies decide how
to allocate their capital among
different projects, given that their
resources are not limitless. The main
goal is to maximize the return on
their investment.
 Businesses typically face many different investment
opportunities but lack the resources to pursue them all.
 Capital rationing is a way of allocating their available
funds in a logical manner.
 A company will typically attempt to devote its resources
to the combination of projects that offers the highest
total net present value (NPV).
 Companies may also use capital rationing strategically,
forgoing immediate profit to invest in projects that hold
out greater long-term potential for the business as it
positions itself for the future.
Types of Capital Rationing
 There
are two primary types of capital rationing,
referred to as hard and soft.
Hard capital rationing
Hard capital rationing occurs based on external
factors.
For example,
The company may be finding it difficult to raise
additional capital, either through equity or debt. Or, its
lenders may impose rules on how it can use its capital.
These situations will limit the company’s ability to
invest in future projects and may even mean that it
must reduce spending on current ones

Soft capital rationing

Soft capital rationing , also known as internal
rationing, is based on the internal policies of the
company.

A fiscally conservative company, for example,
may require a particularly high projected return
on its capital before it will get involved in a
project—in effect, self-imposing capital rationing.
Examples of Capital Rationing

suppose that based on its borrowing costs and other
factors, ABC Corp. has set 10% as the minimum rate of
return it wants from its capital investments. This is
sometimes referred to as a hurdle rate.

As ABC weighs its various investment opportunities, it
will look at both their likely return and the amount of
capital they require, ranking them according to
what’s known as a profitability index.
For example:

if one project is expected to return 17% and another
15%, then ABC may fund the 17% project first and fund
the 15% one only to the extent that it has capital left
over.

If it still has capital available, it might then consider
projects returning 14% or 13% until its capital has been
fully allocated.

It would be unlikely to fund a project returning below
its hurdle rate unless it has other reasons for doing so,
such as to comply with government requirements.
A
company might also choose to hold onto
its capital if it either can’t find enough
attractive investment opportunities or
foresees difficult times ahead and wants to
keep funds in reserve.
ABC Construction is looking at five possible
projects to invest in, as shown below:

To
determine
which
project
offers the greatest
potential
profitability,
we
compute
each
project using the
following formula:

Profitability = NPV
/ Investment
Capital
Probability tree diagram

Probability tree diagrams are often used to calculate
the number of possible outcomes of an event and the
probability that they could occur.

The design of this diagram also visually organizes these
results into a tree configuration.

This tree has 'branches' and each branch represents a
different probable outcome.

You can figure out the likelihood of a certain series of
events by multiplying probabilities along the branches.

To ensure that your work is accurate, ensure that all
final probabilities add up to 1.0.
How to calculate probabilities with tree
diagrams?
1. Outline the possible outcome
First, establish the answer you're looking for and
outline the possible outcomes.

For example, you're trying to assess if your soccer team, the
Reds, can win their next game. This outcome may depend on who
your opponents are, the Blues, who are highly skilled, or the
Yellows, a team with a lot of novice players.

You first create a dot, then draw two arrows pointing away from
it. As you could play either of these teams, write the 'Blues' and
the 'Yellows' at the ends of these lines. Next, you can write the
probability of each outcome on the arrow's line.
Blue Team
Red
Team
Yellow Team
2. Write the probability of each outcome
 On
average, you play the Yellows about six
times every 10 games, so the probability that
you might play the Yellows today is 0.6.

You next subtract 0.6 from 1 to find the
probability of playing the Blues, which is 0.4.

Now write 0.6 on the arrow that points to the
Blues and on the arrow that points to the
Yellows, write 0.4. Complete a quick tally of
0.6 and 0.4 to make sure they equal 1.0.
Blue Team
Red
Team
Yellow Team
3. Create your next tree branches

Last season against the Yellows, you won eight out of
10 games, which means if you play the Yellows today,
there's a 0.8 probability chance of you winning.

As you lost to the Yellows two out of 10 games last
season, it also means the probability of the Reds
losing is 0.2.

On your tree, create two new arrows branching to the
right from the 'Yellows' branch head. Each one leads
to 'win' and 'lose' outcomes. On the 'win' arrow, write
0.8. On the 'lose' arrow, write 0.2.
 The
games against the Blues last season resulted
in your team winning five out of 10 games.
 This
means that you also lost five out of 10 times.
On your diagram now, create two new arrows
facing the right, leading to 'win' and 'lose';
outcomes after the 'Blues' branch head.

On the 'win' arrow, write 0.5 and on the 'lose'
arrow, you can also write 0.5. Note the sum of 0.5
and 0.5 to still adds up to 1.0.
Blue Team
lose
Red
Team
Win
Yellow Team
lose
4. Calculate the overall probabilities




Your objective is to figure out if your team might win the game.
You now have the data to calculate the overall probabilities by
multiplying each branch of the tree along the way.
First, multiply the probability that you play the Yellows, 0.6, by
the probability that you win against the Yellows, 0.8.
The result gives you 0.48 of winning against the Yellows in
today's game.
Next, multiply the probability that you play the Blues, 0.4, by
the probability that you win against the Blues, 0.5. This gives
you a 0.20 chance of winning against the Blues in today's game.
Win= 0.20
Blue Team
Lose= 0.20
Red
Team
Win= 0.48
Yellow Team
Lose= 0.12
5. Add the relevant probabilities
To predict the general likelihood that you can win
today's game, you can add the probabilities in the
'column' of the tree to calculate your final result.
 By adding 0.48, the chance you win against the
Yellows, with 0.20, the chance you win against the
Blues, gives you a result of 0.68.
 This indicates the overall probability that you might
win the game. To see how this translates to a
percentage chance of winning, multiply 0.68 by 100.
This concludes that the Reds have a 68% chance of
winning today's soccer game

Win= 0.20
Blue Team
Lose= 0.20
Red
Team
Win= 0.48
Yellow Team
Lose= 0.12
Using Decision Trees for
Real Option Analysis
Real options represent actual decisions a
company may make, such as whether to expand
or contract operations.
For example,
 an oil and gas company can purchase a piece of
land today, and if drilling operations are
successful, it can cheaply buy additional lots of
land. If drilling is unsuccessful, the company will
not exercise the option and it will expire
worthless. Since real options provide significant
value to corporate projects, they are an integral
part of capital budgeting decisions.

Sensitivity Analysis
What Is Sensitivity Analysis?
 Sensitivity
analysis determines how
different values of an independent variable
affect a particular dependent variable
under a given set of assumptions.
 In other words, sensitivity analyses study
how various sources of uncertainty in a
mathematical model contribute to the
model's overall uncertainty
How Sensitivity Analysis Works

Sensitivity analysis is a financial model that determines
how target variables are affected based on changes in
other variables known as input variables. It is a way to
predict the outcome of a decision given a certain range of
variables.

By creating a given set of variables, an analyst can
determine how changes in one variable affect the
outcome.
ABC company is planning to initaite a new plant: following are the estimated cost
assossiacted with the project.
Key variables
Range
Pessimistic
Expected
Optimistic
Investment
24000
20,000
18000
sales
15000
18000
21000
VC as % of sales
70%
66.66%
65%
FC
1300
1000
800
Assume Discount Rate: 12%
Project life 10 years
Tax rate 33.33%
Expected Scenario(20,000)
sales
18,000
less: Variable Cost
-12,000
Less: Fixed cost
-1000
Less: Depreciation
-12000
Pre-Tax profit
3000
Less; Taxes
-1000
Profit After Taxes
2000
Cash Flow from Operations
4000
NPV
2600
ABC company is planning to initaite a new plant: following are the estimated cost
assossiacted with the project.
Key variables
Range
Pessimistic
Expected
Optimistic
Investment
24000
20,000
18000
sales
15000
18000
21000
VC as % of sales
70%
66.66%
65%
FC
1300
1000
800
Assume Discount Rate: 12%
Project life 10 years
Tax rate 33.33%
Expected
Scenario(20,000)
Pessimistic
(24000)
sales
18,000
18,000
less: Variable Cost
-12,000
-12000
Less: Fixed cost
-1000
-1000
Less: Depreciation
-12000
-2400
Pre-Tax profit
3000
2600
Less; Taxes
-1000
867
2000
1733
Cash Flow from Operations
4000
4133
NPV
2600
-649
Profit After Taxes
ABC company is planning to initaite a new plant: following are the estimated cost
assossiacted with the project.
Key variables
Range
Pessimistic
Expected
Optimistic
Investment
24000
20,000
18000
sales
15000
18000
21000
VC as % of sales
70%
66.66%
65%
FC
1300
1000
800
Assume Discount Rate: 12%
Project life 10 years
Tax rate 33.33%
Expected
Scenario(20,000)
Pessimistic
(24000)
Optimistic
(1800)
sales
18,000
18,000
18,000
less: Variable Cost
-12,000
-12000
-12000
Less: Fixed cost
-1000
-1000
-1000
Less: Depreciation
-12000
-2400
-1800
Pre-Tax profit
3000
2600
32000
Less; Taxes
-1000
867
1067
Profit After Taxes
2000
1733
2133
Cash Flow from Operations
4000
4133
3933
NPV
2600
-649
4221