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Capital Budgeting under Risk and Uncertainties^161

is called the certainty coefficient. It reflects primarily two things: variability of outcomes

and your attitude towards risk. Certainty equivalent coefficients transform expected

values of uncertain flows into their certainty equivalents.

Under the certainty equivalent method, the net present value is calculated as follows:

NPV = 


=

 a -





  

 

...(8.8)

where NPV = net present value

At^ = expected cash flow for the year t

a 1 = certainty equivalent coefficient for the cash flow of year t

i = risk free interest rate

I = initial investment (about which it is assumed that there is no uncertainty)

Example: Vazeer Hydraulics Limited is considering an investment proposal involving

an outlay of Rs. 4,500,000. The expected cash flows and certainty equivalent coefficients

are:

Year Expected Cash Flow Certainty Equivalent Coefficient

(Rs.)

1 1000000 0.90

2 1500000 0.85

3 2000000 0.82

4 2500000 0.78

The risk-free interest rate is 5 per cent. Calculate the net present value of the proposal.

The net present value is equal to:

100000

1 05

1500000 0 85

1 05

2000000 0 82

1 05

2500000

1 05

2 3 4 4500000

(. )

(. )

(. )

(. )

(. ) (. )

+ + + -

= Rs. 534570

The value of the certainty equivalent coefficient usually ranges between 0.5 and 1. A

value of 1 implies that the cash flow is certain or the management is risk neutral. In

industrial situations, however, cash flows are generally uncertain and managements

usually risk-adverse. Hence the certainty equivalent coefficients are typically less than

1. An illustrative table of certainty equivalent coefficients for different types of
   investments is shown here.
   Certainty Equivalent
   Coefficient
   Year 1 Year 2 Year 3 Year 4
   Replacement Investments 0.92 0.87 0.84 0.80
   Expansion Investment 0.89 0.85 0.80 0.75
   New Product Investment 0.85 0.80 0.74 0.68
   R & D Investment 0.75 0.70 0.64 0.58