Untitled-29

Capital Budgeting under Risk and Uncertainties^135

Given the range and most likely value of basic variables, we can study the impact of

variation in each variable on net present value, holding other variables constant at their

most likely levels. To illustrate the nature of this analysis we shall look at the relationship

between (i) r and NPV, and (iii) P and NPV.

r and NPV The reltionship between r and NPV given the most likely values of other

variables is

NPV =

[ , ( ) , , ](. ) ,

( )

1 600 750 400 120 000 160 000 1 0 6 160 000

1 1

(^5) - - - - +

t= +rt

• 
  


• 
  

  400 000-
  1
  , 5 120 000
  ( )
  ,
  r

  
  

=

272 000

1

400 000

1

5 120 000

1

(^5) ,
( )
,
( )
,

• =

 rt r

t

The net present value for various values of r is shown below. The same relationship

is shown graphically in Table 6.4

r 8% 9% 10% 11%

NPV Rs. 158.080 118.080 79,552 42,700

Figure 6.4: Relationship between r and NPV

P and NPV The relationship between P and NPV, given the most likely values of other

factors, is:

NPV =

[ , ( ) , , ](. ) ,

(. )

,

(. )

1 600 400 120 000 160 000 1 0 6 160 000 , ,

110

400 000

110

5 1 200 000

1

(^5) P
t t

• 
  
  
  
  • 
    
    
    
    • 
      
      
      
      • 
        
        
        
        • 
          
          
          
          • 
            
            
            
            • 
              =
            
            
            
            
          
          
          
          
        
        
        
        
      
      
      
      
    
    
    
    
  
  
  
  

=

640

110

208 000

110

400 000

110

5 1 200 000

1

5

1

(^5) P
t t
t (. ) t
,
(. )
,
(. )

• 
  
  
  
  • 
    
    
    
    • , ,
      = =
    
    
    
    
  
  
  
  

the net present value for various values of P is shown below:

P 600 700 750 800 990 1,000

NPV Rs. 284,384 -41,769 79,552 200,864 443,488 686,112

8 9 10 11

r (Per cent)

NPV

(ë000)

150

100

50