160 Financial Management
At= expected cash flow for year t
rk = risk adjusted discount rate for project k
Example The expected cash flows of a project, which involves an investment outlay
of Rs. 1,000,000, are as follows:
Year Cash flow
Rs.- 200,000
2 300,000 - 400.000
- 500.000
- 200,000
The risk-adjusted discount rate for this project is 18 per cent. Is the project worthwhile?
The net present value of the project, using the risk-adjusted discount rate is:
NPV =200 000
118300 000
118400 000
118300 000
114200 000
118, 2 3 4 5 1 000 000
(. ),
(. ),
(. ),
(. ),
(. )+ + + + - , ,= -Rs. 129,440
Since the net present value is negative the project is not worthwhile.
The risk-adjusted discount rate is commonly employed in practice. Firms use different
discount rates, presumably related to the factor risk, for different types of investment
projects. The discount rate is generally low for routine replacement investments, moderate
for expansion investments, and high for new investments.
Despite its popularity, the risk-adjusted discount rate method suffers from two serious
limitations: (i) It is difficult to estimate dk consistently-often it is determined in an
extremely ad hoc and arbitrary manner. (ii) This method assumes that risk increases
with time at a constant rate. This assumption may not be very valid.Certainty Equivalent Method
Before describing the certainty equivalent method let us understand the concept of
certainty equivalent coefficient. Suppose someone presents you with a lottery the
outcome of which has the following probability distribution.
Outcome Probability
Rs. Rs.
1,000 0.3
5,000 0.7
You are further asked: How much of a certain amount would you accept in lieu of this
lottery? Let us say that your reply is: Rs. 3,000. This amount, Rs. 3,000 represents the
certainty equivalent of the above lottery which has a expected value of Rs. 3,800 (Rs.
1,000 ◊ 0.3 + Rs 5,000 ◊ 0.7) and a given distribution. The factor 3,000/3,800 (=0.79)