Untitled-29

142 Financial Management

independent of the cash flow for year i-r. Put differently, there is no relationship

between cash flows from one period to another. In this case the expected net present

value and the standard deviation of net present value are defined as follows:

NPV A

i

i

t

t

n

=

+

• =

( 1 )^1

1

...(8.2)

=













+

s = 
 s









 

  



...(8.3)

where NPV = expected net present value

At = expected cash flow for year t

i = risk-free interest rate

t = initial outlay

s(NPV) = standard deviation of net present value

s 1 = standard deviation of the cash flow for year t.

Note that in the above formulae the discount rate is the risk-free interest rate because

we try to separate the time value of money and the risk factor. This risk of the project,

reflected in s (NPV) is considered in conjunction with NPV computed with the risk-

free discount rate. If

NPV

is computed using a risk-adjusted discount rate and then

if this is viewed along with s (NPV), the risk factor would be doubled counted.

Example: A project involving in outlay of Rs. 10,000 has the following benefits associated

with it.

Year 1 Year 2 Year 3

Net cash flow Probability Net Cash flow Probability Net Cash flow Probabilty

Rs. Rs. Rs. Rs. Rs. Rs.

3,000 0.3 2,000 0.2 3,000 0.3

5,000 0.4 4,000 0.6 5,000 0.4

7,000 0.36 6,000 0.2 7,000 0.3

Calculate

NPV

and s (NPV), assuming that i = 6 per cent

NPV A

i

i

t

t

n

=

+

• =

( 1 )^1

1

I

=

5 000

1 06

4 000

1 06

5 000

1 06

, 2 3 10 000 2 475

(. )

,

(. )

,

(. )

+ + = , = ,

= 


=













+

s = 
 s