**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.

**Advantages** of Risk-adjusted Discount Rate:

- 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.

**Disadvantages:**

- 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.