Untitled-29

Capital Budgeting under Risk and Uncertainties^143

=

2 400 000

1 06

1 600 000

1 06

2 400 000

1 06

2 4 6 2 258

1 2

, ,

(. )

, ,

(. )

, ,

(. )

. ,

/

L + +

N

M

O

Q

P=Rs

Perfectly Correlated Cash Flows

If cash flows are perfectly correlated, the behaviour of cash flows in all periods is alike.

This means that if the actual cash flow in one year is a standard deviations to the left

of its expected value, cash flows in other years will also be a standard deviations to

the left of their respective expected values. Put in other words, cash flows of all years

are linearly related to one another. The expected value and the standard deviation of

net present value, when cash flows are perfectly correlated, are as follows:

(^) NPV =
A
i
t
t
t
n
( 1 )
1
1 +

• =

...(8.3)

s(NPV) = 


=













+

 s

 



  ...(8.4)

Example: An investment project involves a current outlay of Rs 10,000. The mean

and Standard Deviation of cash flows which are perfectly correlated, are as follows:

Year  ssssst

1 5000 1500

2 3000 1000

3 4000 2000

4 3000 1200

Calculate  

 and s(NPV), assuming a risk-free interest rate of 6 per cent.

NPV A

i

i

=
t= 1 ( 1 +)t- 1

4

I

=

5 000

1 06

4 000

1 06

5 000

1 06

3000

1 06

, 2 3 4 10 000 3121

(. )

,

(. )

,

(. ) (. )

+ + + = , =

= s(NPV) = 


=

-

+

a-





  

 

=  

















+ + + =

Standardising the Distribution

Knowledge of NPV and s(NPV) is very useful for evaluating the risk characteristics

of a project. If the NPV of a project is approximately normally distributed, we can

calculate the probability of NPV being less than or more than a certain specified value.