# Risk Adjusted Discounted Rate, Decision Tree

#### Risk Adjusted Discounted Rate

Under this method, the cut off rate or minimum required rate of return [mostly the firm’s cost of capital] is raised by adding what is called ‘risk premium’ to it. When the risk is greater, the premium to be added would be greater.

For example, if the risk free discount rate [say, cost of capital] is 10%, and the project under consideration is a riskier one, then the premium of, say 5% is added to the above risk-free rate.

The risk-adjusted discount rate would be 15%, which may be used either for discounting purposes under NPV, or as a cut off rate under IRR.

• It has a great deal of intuitive appeal for risk adverse decision-makers.
• It is easy to understand and simple to operate.
• It incorporates an attitude towards uncertainty.

• A uniform risk discount factor used for discounting all future returns is unscientific as the degree of risk may vary over the years in future.
• There is no easy way to derive a risk-adjusted discount rate.
• It assumes that investors are risk averse. Though it is generally true, there do exist risk-seekers in real world situation that may demand premium for assuming risk.

The Ramakrishna Ltd., in considering the purchase of a new investment. Two alternative investments are available (X and Y) each costing Rs. 150000. Cash inflows are expected to be as follows:

Cash Inflows

 Year Investment X Rs. Investment Y Rs. 1 60,000 65,000 2 45,000 55,000 3 35,000 40,000 4 30,000 40,000

The company has a target return on capital of 10%. Risk premium rate are 2% and 8% respectively for investment X and Y. Which investment should be preferred?

Solution

The profitability of the two investments can be compared on the basis of net present values cash inflows adjusted for risk premium rates as follows:

 Investment X Investment Y Year Discount Factor10% + 2% = 12% Cash Inflow Rs. Present Value Rs. Discount Factor 10% + 8%=18% Cash Inflow Rs. Present Values 1 0.893 60,000 53,580 0.847 85,000 71,995 2 0.797 45,000 35,865 0.718 55,000 39,490 3 0.712 35,000 24,920 0.609 40,000 24,360 4 0.635 30,000 19,050 0.516 40,000 20,640 1,33,415 1,56,485

Investment X

Net present value = 133415 – 150000

=  – Rs. 16585

Investment Y

Net present value = 156485 – 150000

=  Rs. 6485

As even at a higher discount rate investment Y gives a higher net present value, investment Y should be preferred.

#### Decision Tree

The decision-tree approach is useful analytical technique in capital budgeting to evaluate risky investment proposal involving sequential decisions. The technique enables the decision maker to study the various decisions points in relation to subsequent chance, events and choose, from among the alternatives, in an objective and consistent manner. Since the format of the problem of the investment decision has an appearance of a tree with branches, the method is known as decision-tree method.

The decision-tree shows the magnitude, probability and inter-relationship of all possible out-comes of an investment proposal. In a nut-shell, a decision-tree is a graphic display of the relationship between a present decision and future events, future decisions and their consequences. It contains squares and circles. The square represent decision points and the circles represent chance events modes.

Steps involved in decision tree analysis

The following are the important steps involved in constructing and using a decision- tree in capital budgeting:

(i) To identify and define the investment proposal.

(ii) To identify the decision alternatives. For example, if a company is considering setting up a plant, it has the option of setting up a large plant, a medium size plant or a small plant initially and expand it later on or no plant at all.

(iii) To draw various branches of the tree showing the decision points, chance events and other data.

(iv) To enter on the decision-tree branches the relevant data such as the projected cash-flows, probabilities and the expected payoffs.

(v) To analyze the result and by backward induction determine optimal decisions at various decision points and eliminate alternative branches on the basis of dominance.

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