The document discusses various techniques for making investment decisions under risk and uncertainty. The main techniques discussed are: 1) Risk Adjusted Discount Rate (RADR) which adds a risk premium to the risk-free interest rate to calculate the discount rate. 2) Certainty Equivalent Method which adjusts expected cash flows using a certainty equivalent coefficient to account for risk. 3) Statistical methods like standard deviation and coefficient of variation which measure the variability of cash flows. 4) Sensitivity analysis which evaluates cash flows under different assumptions. 5) Simulation and decision tree analysis which use random variables and graphical representations to evaluate investment decisions over multiple time periods and scenarios.

1. Investment Decisions Under Risk

2. Investment Decisions and Risk
• The main function of a finance manager is to allocate various
resources among available investments
• Investment may be long term or short term
• Investment decisions are made on the basis of forecasts.
• Risk will also vary from one investment proposal to another
• Risk is defined as the variability that is likely to occur in
future between the estimated and actual returns

3. Types of Investment Decision
Situations
• Certainty : No risk involved
• Uncertainty : Future loss cannot be foreseen
• Risk : Future loss can be foreseen

4. Techniques of Investment Decisions
1) Risk Adjusted Discount Rate (RADR)
2) Certainty Equivalent method
3) Statistical Method
• Standard Deviation Method
• Coefficient of Variation Method
• Sensitivity Analysis
• Simulation Method
• Probability and expected values method
• Decision tree analysis

5. Risk Adjusted Discount Rate
• RADR is the discount rate which is used to convert future
cash inflow into present values.
• Investors expect a higher rate of return on risky projects as
compared to less risky projects.
Merits :
• It is easy to understand and very simple to calculate
• It gives some premium for risk
RADR = Risk free interest rate + Risk Premium

6. Demerits :
• It assumes that risk increases with time
• There is no proper method for calculate RADR – difficult to
calculate it
• Does not make use of information from probability distribution
expected future cash.

7. Certainty Equivalent Method
• It is a risk incorporation technique which adjusts the
expected cash flows, instead of adjusting discount rate.
• The estimated cash flows are reduced to certain amount
by applying a correction factor known as Certainty
Equivalent Coefficient
CE = Riskless Cash flows
Risky Cash flows

8. • CE Coefficient assumes a value between 0 and 1,and it
varies inversely with risk
Merits :
• It is simple to understand and easy to calculate
• It does not consider the risk increase with increase in time
Demerits :
• Difficult to consider increasing risk capacity
• Difficult and inconvenient to allocate CE Coefficients.

9. Standard Deviation Method
• It is used to compare the variability of possible cash flows of
different projects from their expected values.
• A project having high SD will be more risky
Coefficient of Variation
It is the risk per unit of return
CoV = Standard Deviation * 100
Mean

10. Sensitivity Analysis
• It is concerned with judging the sensitivity of items of
data which are needed to make a decision.
• It provides information about cash flows under three
assumptions :
1) Pessimistic
2) Most likely
3) Optimistic

11. Merits :
• It helps to know the viability of a project by considering
the variables
• It helps to frame alternative plans
Demerits :
• No clarity in results. Values may be inconsistent
• Fails to focus on the interrelationship between variables
• Ignores the chances associated with different values

12. Simulation Method
• It is also known as Method of statistical trails or Monte
Carlo’s Simulation.
• It involves random selection of an outcome for each
variable and combining these outcomes and obtaining one
trial outcome
• It is used to solve problems which cannot be represented
by mathematical models or by analytical method

13. Decision Tree Analysis
• Decision tree is a graphical representation of the
relationship between a present decision and future
events, future decisions, and their consequences in the
form of branches of a tree.
• Evaluation of a project can be done in different stages
and over a period of years with the help of decision
tree.

14. Merits :
• It is easy to understand and very simple
• Clearly brings out the assumptions and calculations
• Give an overview of all the possibilities – helps to keep the
entire picture in mind
• Helps to analyse the assumptions in graphical form
Demerits :
• Time consuming
• Complex
• Difficult to make calculations when tree diagram become more
complicated.