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**Here are some of the techniques which can handle the risk factor of capital budgeting:- 1.** **Risk-Adjusted Discount Rate 2. Certainty-Equivalent 3. Quantitative Techniques 4. Probability Assignment 5. Standard Deviation 6. Co-Efficient of Variation 7. Sensitivity Analysis 8. Decision Trees.**

**Technique # 1. **

**Risk-Adjusted Discount Rate****:**

Generally, against risk the businessman requires a premium over and above the existing one which is risk-free. As such, the more uncertain will be the future return, the more will be the risk and the greater will be the premium and vice-versa. As a result, the risk premium is being introduced in capital budgeting decisions with the help of discount rate.

In short, if the time preference for money is to be recognized by discounting estimated future cash flows, at some risk-free rate, to their present value, then, to allow for the riskiness, of those future cash flows a risk premium rate may be added to risk-free discount rate.

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Such a composite discount rate will allow for both time preference and risk preference and will be a sum of the risk-free rate and the risk premium rate reflecting the investors’ attitude towards risk. The time- adjusted discount rate is the discount rate which combines time as well as risk preferences of investors.

This discount rate, of course, varies depending on the degree of risk involved. The relatively risky project accounts for relatively high discounts rates and relatively safe project accounts for relatively low discount rates. For example, a very low rate of risk- adjusted discount rate may be considered if investment is made on Govt. bonds where there is no risk of estimated future returns.

On the other hand, a high rate is to be used if the investment is made to a new project, i.e., different risk-adjusted discount rates are used for different types of projects. For example, if the risk-free rate is assumed to be 10%, some extra rate is to be added to it, say 5%, by way of compensation for the aversion of bearing the risk, and the composite 15% rate is to be used for discounted cash flows.

**Acceptance Rule**:

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The risk-adjusted discount rate approach can be used with the help of both the NPV and IRR method If NPV method is followed (as is shown in the above illustration) in order to evaluate the decision, the same should be calculated with the help of risk- adjusted discount rate.

If the NPV is found to be positive (+) the proposal may be accepted and the negative (-) NPV suggests that the project should be rejected. In case of IRR, if IRR exceeds the risk-adjusted rate, the proposal may be accepted and in the opposite case, it should be rejected.

**Advantages**:

(i) It is very simple to calculate and easy to understand;

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(ii) It incorporates the risk-averse attitude of investors; and

(iii) In reality, the companies apply different standards about cost of capital for different projects which reveal operational feasibility Disadvantages

**However, this approach is beset with certain operational and conceptual difficulties which are enumerated below: **

(i) The determination of appropriate risk-adjusted discount rate for different degree of risk for various projects is arbitrary and hence, it does not give any objective result.

(ii) It does not make direct use of the information which is available from the probability distribution of expected future cash. Besides, conceptually it adjusts the wrong element. Practically, it is the future cash flow which is subject to risk and as such, the same is to be adjusted and not the required rate of return.

(iii) It leads to a compounding of risk overtime as the premium is added to the discount rate. That is, it presumes that the risk increases with time, the same may not be correct in all cases.

(iv) This method also presumes that the investors are averse to risk. But there are some investors who prefer to take risk and ready to pay premium for taking risk, i.e., instead of increasing the discount rate, the same should be reduced.

**Technique # ****2. **

**Certainty-Equivalent (or Conservative Forecast)**:

In the previous method i.e., Risk-Adjusted Discount Rate, the riskiness of the project is considered by adjusting the expected cash flows and not the discount rate. This method, however, eliminates the problem which arises out of the inclusion of risk premium in the process of discounting.

In other words, under this method, the estimated cash flows are reduced to a conservative level with the help of a correction factor known as certainly equivalent coefficient. This is nothing but the correction factor in the ratio of riskless/certain cash flow to risky cash flow. It is the relationship between certain (riskless) cash flow and risky (uncertain) cash flows.

**It may be presented in the following form:**

Certainty-Equivalent Co-efficient = Riskless Cash Flow / Risky Cash Flow.

It should be noted that riskless cash flow means the cash flow which is certain, i.e., the management agrees to accept the cases where no risk is involved. Needless to mention that the same will be lower than the risky one.

For example, a cash flow is expected to generate from a project which amounts to Rs. 40,000. The project is risky but the management expects that at least there will be a cash flow of Rs. 28,000 Certainty equivalent coefficient, in that case, will be as under:

Certainty-Equivalent Coefficient = Rs. 28,000/Rs. 40,000 = 7

It should be remembered that the co-efficient is a fractional amount which lies between 0 and 1. Actually, an inverse relationship lies between the degree of risk and the value of coefficient, the higher the risk, the lower will be the coefficient.

**Present Value Calculations****:**

When expected cash flow is converted into certainty-equivalent, our immediate task is to calculate the present value. The rate of discount is, here, the risk-free rate and/or that rate which reflects the time value of money. The method of computing the present value is the normal course for evaluating capital projects.

**Acceptance Rule**:

If NPV method is used, the proposal should be accepted if NPP of certainty- equivalent cash flows is positive (+), i.e., if NPV is found to be negative (-), the proposal should be rejected.

Similarly, if IRR method is used as decision criterion, the IRR which equates the PV of certainty-equivalent cash inflow with PV of cash inflows should be compared with the riskless discount rate. In other words, if IRR exceeds the riskless rate, the proposal should be accepted, and in the opposite case, it would be rejected.

**Advantages:**

**The certainty-equivalent approach has the following merits:**

1. It is simple to calculate.

2. It recognizes risk by modifying the cash flows which are subject to risk, i.e., conceptually it is superior than the earlier method, viz., time-adjusted discount rate method.

3. It is useful when comparing a number of project appraisals in decision making as it is based on the probability of the combined NPVs occurring.

**Disadvantages**:

**This approach suffers from the following limitations:**

(i) In actual practice, it is very difficult to implement.

(ii) This approach depends on the utility preference to the management and intuitive recognition of the investors since it is a subjective estimate, i.e., it can neither be objective nor be precise and consistent.

(iii) It does not recognise the probability distribution of possible cash flows.

(iv) It is very difficult to calculate and understand.

(v) Sometimes the forecasts are to pass through several levels of management, in that case, the effect may be to exaggerate the original forecast.

Even though this method is not free from snags, it is theoretically superior to the risk-adjusted discount rate method. Because, under the latter, the risk is increased over time when the discount rate is constant which is an appropriate assumption. Using this approach, management fails to consider increasing risk explicitly and hence, may make serious mistakes while measuring risk over time.

In many cases, question of risk will increase with the length of time. In that context, the assumption so made in risk adjusted discount rate is valid although the same is not confirmed by all the projects. For instance, at the initial stage, an investment proposal may be found to be more risky but when it is established, the same may not be a risky one.

Thus, the assumption so made for risk increases with the length of time is not actually valid. However, the management is quite able to specify the degree of risk for a specific future period and at the same time, discounts the cash flow back to the present value applying the time value of money with the help of the Certainty-Equivalent approach, and that is why it is superior to the earlier method viz., risk-adjusted discount rate.

**Technique # ****3. **

**Quantitative Techniques**:

The discussions made so far is the two common techniques of handling risk in capital budgeting decision.

**But they are at best crude attempts. Because, they suffer from the two serious limitations, viz. **

(i) They cannot be consistently applied to various projects over time, and

(ii) Specifying the appropriate degree of risk is beset with operational problems.

That is, in other words, the appropriate method should always possess two fundamental attributes which will actually overcome the said two shortcomings.

**They are:**

(i) It must specify the appropriate degree of risk in precise terms;

(ii) The said specifications must consistently be applied. In other words, the quantitative technique that follows, is the appropriate technique which satisfies the above two requirements.

**Technique # ****4. **

**Probability Assignment:**

In capital budgeting decision, the most significant information is the prediction of future cash flows. No doubt, a single figure is desired for a particular period which may be regarded as best estimates/most likely forecast for the period. But if only one figure is considered, certain queries will arise before us. For instance, is it reliable or does it reflect risk on the method and computation of ascertaining such figure?

**Practically, the ‘single figure forecast’ invites the following shortcomings:**

(i) It is not possible to know the uncertainty surroundings, i.e., the probability distribution— the range of the forecast and the probability estimates related to it.

(ii) The terms **“best estimates”** or ‘most likely forecast’ are not so clear, i.e., which measures of central tendency is being applied (i.e…Mean Median or Mode).

Therefore, instead of taking a single figure, it is better to have a range, i.e. a range, of estimates and its related probability.

Probability means he likelihood of the happening of an event. When the event is bound to happen, it may be said that it has a probability of I. And if it is certain that the event will not occur at all it will have a 0 probability.

As such, the probabilities will always lie between 0 and I. It should be remembered that the probability distribution consists of a number of estimates, but the simple form is to consider a few estimates.

The above expected monetary values present a more precise estimate about the likely cash flows as compared to those which do not consider probability assignments. Needless to mention that if the probability assignment lies among the simple three figure forecast (which is shown in the above illustration), it will be a great help on the part of the forecaster about the estimates.

**Objective Probability:**

According to Classical Probability Theory, when the happening or non-happening of an event can be repeatedly performed over a very long period of time under independent and identical conditions, the probability estimates depending on a very large number of observations is called objective probability.

**Subjective Probability:**

The objective probability referred to above is not widely used in capital budgeting decisions since the decisions are non-repetitive and they are hardly performed under independent identical conditions. That is why, at present, another view is being considered which is known as personal or subjective probabilities.

A personal or subjective probabilities based on the personal judgment as there is no larger number of independent and identical observations.

**Technique # ****5. **

**Standard Deviation (An Absolute Measure of Dispersion)**:

The immediate earlier approach, viz., the Probability Assignment Approach, through the calculation of expected monetary value, does not supply a precise value about the variability of cash flows to the decision maker.

In order to overcome this limitation and for a better insight into the risk analysis, we are to find out the dispersion of Cash flows which is nothing but the difference between the expected monetary values and the possible cash flows which may occur. It indicates the degree of risk.

The most widely used measure of dispersion is the Standard Deviation method. It is the square root of squared deviation calculated from the mean. In short, it measures the deviation or variance about the expected cash flows of each possible cash flows.

However, this method is practically used for comparing the variability of possible cash flows from their respective mean or expected values. In this context, it must be remembered that the project having a larger Standard Deviation will be more risky and vice-versa.

**The formula for calculating Standard Deviation is noted below:**

**The following steps must be taken into consideration while calculating Standard Deviation: **

(i) At first, the mean value of possible cash flow should be computed.

(ii) Find out the deviation between the mean value and the possible cash flows.

(iii) Deviations are squared.

(iv) Multiply the squared deviation by the probability assignment in order to find out the weighted squared deviation.

(v) Finally, make a total of the weighted squared deviation and find out this square root which will be known as Standard Deviation.

**Technique # ****6. **

**Co-Efficient of Variation (A Relative Measure of Dispersion)**

Co-efficient of variation is a relative measure of risk. It is defined as Standard Deviation of the probability distribution divided by its expected value and is expressed in terms of percentage.

**The formula is:**

Co-efficient of Variation (C.V.) = Standard Deviation (**Ϭ**)/Mean or Expected cash flows × 100

This is particularly useful where projects involve different cash flows outlay or different expected (mean) values, i.e., where Standard Deviation fails to compare. In other words, the C V. (Co-efficient of variation) is applicable where the Standard Deviation is same but the expected values are different or, where Standard Deviation is different but expected values are same, or where both of them are different.

**Technique # ****7. **

**Sensitivity Analysis:**

This is another measure which expresses risk and is applicable where there are chances of making some estimation errors. It supplies information about the sensitiveness of the estimated projects parameters, viz., the expected cash flow, discount rate, the life of the project, i.e., these are estimation errors. Since the future is itself uncertain, there will always be some estimation errors.

It recognizes these estimation errors by supplying more than one estimate of the future return of a project. In short, under sensitivity analysis, the decision-makers are well-informed about the variability of the outcomes for the purpose of evaluating a project with the help of a number of estimated cash flows. As such, it is superior to one figure forecast, as it presents a more clear idea about the variability of outcomes.

However, this technique, gives us important insight into how the final outcome of an investment decision is likely to be affected by possible variations in the under-laying factors, i.e., via sensitivity analysis, the expected return of the project can be analysed for different values of key factors.

**The sensitivity analysis supplies different cash flow estimates under the following three assumptions:**

(i) The best (i.e., the most optimistic);

(ii The expected (i.e., the most likely); and

(iii) The worst (i.e., the most pessimistic).

Sensitivity analysis expresses how sensitive the cash flows are under the above conditions. The larger the difference between pessimistic and optimistic cash flows the more risky is the project and vice-versa.

**Sensitivity analysis can improve decision making in a number of ways: **

(a) It indicates which variables and assumptions are most critical and tells management where to focus its analytical efforts.

(b) It encourages explicit consideration of uncertainties and risks by managers at different levels.

(c) It identifies areas on which managerial attention should be focused after approval of the project and during implementation.

**Technique # ****8. **

**Decision Trees**:

Decision tree analysis is also another useful technique for tackling risky investment proposals. Under this approach, all probabilistic estimates of potential outcomes and their effects are taken into consideration, i.e., all the possible outcome is weighted in probabilistic terms and are evaluated thereafter.

In short, the approach is particularly applicable where decision at point of time affects the decisions at a subsequent date, i.e., current investment decision has implication against future investment decisions. In other words, this investment decisions involve a sequence of decisions over time.

If Massee’s argument (which is given in footnotes) is accepted, investment expenditure must be viewed not from the standpoint of isolated period commitments, but as links in a chain of present and future commitments. Needless to mention that application of decision tree analysis is to tackle the sequential decisions.

A decision tree is a pictorial representation in tree form which indicates the magnitude, probability and inter-relationship of all possible outcomes’. In other words, it is a graphic display of the relationship between a present decision and possible future events, future decisions and their consequences. The sequence of events is mapped out over time in a format resembling branches of a tree.

Thus, the decision tree reveals the sequential cash flow and the NPV of the proposed projects under different circumstances. It must be remembered in this respect that its outstanding feature is to link events chronologically with forecast probabilities. Therefore, it presents us a systematic appearance of decisions and their forecasted results.

**Construction of a Decision tree:**

**While constructing a decision tree the following steps should carefully be considered:**

**(i) Definition of the Proposal: **

The investment proposals should be defined e.g., to enter a new market or to produce a new product.

**(ii) Identification of Alternatives:**

This decision alternative should be identified, i.e., there may be more than two alternatives. For instance, a company is considering to purchase a plant for manufacturing a new product.

**It may have the following alternatives:**

(a) Purchase large plant,

(b) Purchase a small plant,

(c) Purchase a medium size plant, or

(d) Not to purchase a plant at all.

Each alternative may have different consequences:

**(iii) Graphing the Decision-Tree:**

**The decision-tree is then graphed indicating: **

(a) Decision points,

(b) Decision branches,

(c) Other data.

**(iv) Forecasting Cash Flows:**

The necessary data, viz., projected cash flow, probability distribution total expected present value etc. should be located on the decision tree branches for the purpose of taking up decisions.

**(v) Evaluating Results: **

After ascertaining the expected value for each decisions, the results are analysed. The firm should proceed with the profitable alternative, i.e., the best alternative should be selected.