Using Decision Trees in Financial Management

Decision trees are diagrams that show the sequence of interrelated decisions and the expected results of choosing one alternative over the other. Typically, more than one choice or option is available when you're faced with a decision or, in this case, potential outcomes from a risk event. The available choices are depicted in tree form starting at the left with the risk decision branching out to the right with possible outcomes. Decision trees are usually used for risk events associated with time or cost.

Steps in decision tree analysis

Main steps in decision tree analysis are as follows: 1. Identifying the problem and alternatives To understand the problem and develop alternatives, it is necessary to acquire information from different sources like marketing research, economic forecasting, financial analysis, etc. As the decision situation unfolds, various alternatives may arise which are to be identified. There would also be kinds of uncertainties in terms of market size, market share, prices, cost structure, availability of raw material and power, governmental regulation. Technological change, competition, etc. Recognising that risk and uncertainty are inherent characteristics of investment projects, persons involved in analyzing the situation must be encouraged to express freely their doubts, uncertainties, and reservation and motivated to suggest contingency plans and identify promising opportunities in the emerging environment. 2. Delineating the decision tree The decision tree represents the anatomy of decision situation. It illustrates decision points along with the alternative options available for experimentation and action at these decision points chance points where outcomes are dependent on a chance process and the likely outcomes at these points This decision tree diagrammatically reflects the nature of decision situation in terms of alternative courses of action and chance outcomes which have been identified in the first step of the analysis. If myriad possible future events and decisions are considered, it can become very complex and cumbersome. As a result, it would not be a useful tool of analysis. If many elaborate events are taken into account then it may obfuscate the critical issues. Hence it is necessary to simplify the decision tree so that focus can be given on major future alternatives. 3. Specifying probabilities and monetary outcomes After delineating the decision tree, probabilities corresponding with each of the possible outcomes at various chance points and monetary value of each combination of decision alternative and chance outcome have to be gathered. The probabilities of various outcomes can be defined objectively. For instance, based on objective historical data the probability of good monsoon can be defined. On the other hand, probabilities for real life outcomes are somewhat difficult and cannot be obtained. For example, one cannot determine the probabilities for success of a new automobile launch. These have to be defined subjectively and based on experience, judgment, understanding of informed executives and their intuition. Also, it is difficult to assess cash flows corresponding to these outcomes. So again judgment of experts helps in defining these cash flows. 4. Evaluating various decision alternatives The final step in decision tree analysis includes evaluation of various alternatives. This can be done as follows: starting with the right- hand end of the tree and then we calculate the expected monetary value at various chance points that come first as we proceed leftward. Given the expected monetary values of chance points in step 1, evaluate the alternatives at the final stage decision points in terms of their expected monetary values. At each of the final stage decision points, select the alternative which has the highest expected monetary value and truncate the other alternatives. Each decision point is assigned a value equal to the expected monetary value of the alternative selected at that decision point. Proceed backward (leftward) in the same manner, calculating the expected monetary value at chance points, selecting the decision alternative which has the highest expected monetary value at various decision points, truncating inferior decision alternatives, and assigning values to decision points, till the first decision point is reached. Wikipedia A decision tree is a decision support tool that uses a tree-like graph or model of decisions and their possible consequences, including chance event outcomes, resource costs, and utility. It is one way to display an algorithm. Decision trees are commonly used in operations research, specifically in decision analysis, to help identify a strategy most likely to reach a goal. Another use of decision trees is as a descriptive means for calculating conditional probabilities. When the decisions or consequences are modelled by computational verb, then we call the decision tree a computational verb decision tree[1]. In decision analysis, a "decision tree" - and the closely-related influence diagram - is used as a visual and analytical decision support tool, where the expected values (or expected utility) of competing alternatives are calculated. A decision Tree consists of 3 types of nodes:- 1. Decision nodes - commonly represented by squares 2. Chance nodes - represented by circles 3. End nodes - represented by triangles Drawn from left to right, a decision tree has only burst nodes (splitting paths) but no sink nodes (converging paths). Therefore, used manually, they can grow very big and are then often hard to draw fully by hand. Analysis can take into account the decision maker's (e.g., the company's) preference or utility function, for example: The basic interpretation in this situation is that the company prefers B's risk and payoffs under realistic risk preference coefficients (greater than $400K -- in that range of risk aversion, the company would need to model a third strategy, "Neither A nor B").

Uses in teaching

This section requires expansion. Decision trees, influence diagrams, utility functions, and other decision analysis tools and methods are taught to undergraduate students in schools of business, health economics, and public health, and are examples of operations research or management science methods.

[edit] Advantages

Amongst decision support tools, decision trees (and influence diagrams) have several advantages: Decision trees: Are simple to understand and interpret. People are able to understand decision tree models after a brief explanation. Have value even with little hard data. Important insights can be generated based on experts describing a situation (its alternatives, probabilities, and costs) and their preferences for outcomes. Use a white box model. If a given result is provided by a model, the explanation for the result is easily replicated by simple math. Can be combined with other decision techniques. The following example uses Net Present Value calculations, PERT 3-point estimations (decision #1) and a linear distribution of expected outcomes (decision #2):

[edit] Example

Decision trees can be used to optimize an investment portfolio. The following example shows a portfolio of 7 investment options (projects). The organization has $10,000,000 available for the total investment. Bold lines mark the best selection 1, 3, 5, 6, and 7, which will cost $9,750,000 and create a payoff of 16,175,000. All other combinations would either exceed the budget or yield a lower payoff.[2]

Decision Making Tools: Decision Tree Analysis and EMV

Decision Makers' Toolkit

"Decision-making is the cognitive process of selecting a course of action from among multiple alternatives. Every decision-making process produces a final choice." That's what Wikipedia says anyway. What it doesn't say is that some decisions must be made for outcomes that will occur in the future. However, there are a couple of tools that can be put to use in helping make complex decisions, namely, Expected Monetary Value and Decision Tree Analysis.

Expected Monetary Value (EMV)

EMV is a balance of probability and its impact over the range of possible scenarios. If you have to make a decision between two scenarios, which one will provide the greater potential payoff? Scenario 1 Best case provides a 20% probability of making $180,000 BC = 20% X $180,000= $36,000 Worst case provides a 15% probability of loosing [-$20,000] WC = 15% X(-$20,000) =(-$3,000) Most likely case provides a 65% probability of making $ 75,000 MLC = 65% X $75,000 = $48,750 Total Expected Monetary Value 100% $81,750 Scenario 2 Best case provides a 15% probability of making $200,000 BC=15% X $200,000 =$30,000 Worst case provides a 25% probability of making $15,000 WC= 25% X $ 15,000 = $ 3,750 Most likely case provides a 60% probability of making $45,000 MLC=60% X $45,000 = $27,000 Total Expected Monetary Value 100% $60,750 Which scenario do you choose? Number one, because it has the highest EMV, or $81,750

Decision Tree Analysis

In decision tree analysis, a problem is depicted as a diagram which displays all possible acts, events, and payoffs (outcomes) needed to make choices at different points over a period of time. Example of Decision Tree Analysis: A Manufacturing Proposal Your corporation has been presented with a new product development proposal. The cost of the development project is $500,000. The probability of successful development is projected to be 70%. If the development is unsuccessful, the project will be terminated. If it is successful, the manufacturer must then decide whether to begin manufacturing the product on a new production line or a modified production line. If the demand for the new product is high, the incremental revenue for a new production line is $1,200,000, and the incremental revenue for the modified production line is $850,000. If the demand is low, the incremental revenue for the new production line is $700,000, and the incremental revenue for the modified production line is $150,000. All of these incremental revenue values are gross figures, i.e., before subtracting the $500,000 development cost, $300,000 for the new production line and $100,000 for the modified production line. The probability of high demand is estimated as 40%, and of low demand as 60%. The development of a decision tree is a multi step process. The first step is to structure the problem using a method called decomposition, similar to the method used in the development of a work breakdown structure. This step enables the decision-maker to break a complex problem down into a series of simpler, more individually manageable problems, graphically displayed in a type of flow diagram called a decision tree. These are the symbols commonly used: The second step requires the payoff values to be developed for each end-position on the decision tree. These values will be in terms of the net gain or loss for each unique branch of the diagram. The net gain/loss will be revenue less expenditure. If the decision to not develop is made, the payoff is $0. If the product development is unsuccessful, the payoff is - $500,000. If the development is successful, the decision is to build a new production line (NPL) or modify an existing production line (MPL). The payoff for the NPL high demand is ($ 1,200,000 - $500,000 development cost -$300,000 build cost) or $400,000. For a low demand, the payoff is ($700,000 - $500,000 development cost -$300,000 build cost) or -$100,000. The payoff for the MPL high demand is ($850,000 -$500,000 development cost - $100,000 build cost) or $250,000. For a low demand, the payoff is ($720,000- $500,000 development cost - $100,000 build cost) or $120,000. The third step is to assess the probability of occurrence for each outcome: Development Successful = 70% NPL High Demand = 40% MPL High Demand = 40% Development Unsuccessful = 30% NPL Low Demand = 60% MPL Low Demand = 60% Probability Totals* 100% 100% 100% *Probabilities must always equal 100%, of course. The fourth step is referred to as the roll-back and it involves calculating expected monetary values (EMV) for each alternative course of action payoff. The calculation is (probability X payoff) = EMV This is accomplished by working from the end points (right hand side) of the decision tree and folding it back towards the start (left hand side) choosing at each decision point the course of action with the highest expected monetary value (EMV). Decision D2: New Production Line vs. Modified Production Line high demand + low demand = EMV high demand + low demand = EMV (4 0% X $400,000) + (60%X -$100,000) (40% X $250,000)+(60% X $120,000) $100,000 $172,000 Decision Point 2 Decision: Modified Production Line with an EMV of $172,000 Decision 1: Develop or Do Not Develop Development Successful + Development Unsuccessful (70% X $172,000) (30% x (- $500,000)) $120,400 + (-$150,000) Decision Point 1 EMV=(-$29,600) Decision: DO NOT DEVELOP the product because the expected value is a negative number. When doing a decision tree analysis, any amount greater than zero signifies a positive decision. This tool is also very useful when there are multiple cases that need to be compared. The one with the highest payoff should be picked.

Real options analysis: tools and techniques for valuing strategic ...

A By Johnathan Mun https://books.google.co.in/books?id=X47bm9Etd7IC&pg=PA649&lpg=PA649&dq=decision+tree+applications+oil+and+gas&source=bl&ots=W47wkDY2Xt&sig=YwtNvZ8KEDJ-60CEK87Xhodouis&hl=en&ei=Bnz3TP7kMI-srAec-63vDw&sa=X&oi=book_result&ct=result&resnum=2&ved=0CB0Q6AEwATge#v=onepage&q=decision%20tree%20applications%20oil%20and%20gas&f=false pgs.258,474

Remington: the science and practice of pharmacy

https://books.google.co.in/books?id=NFGSSSbaWjwC&pg=PA743&lpg=PA743&dq=decision+tree+applications+pharmaceuticals&source=bl&ots=V64QMimyuo&sig=cdQYBEgEJSf_lON-Alkhv4E6B4E&hl=en&ei=8oT3TLOOLcS3rAfw1azvDw&sa=X&oi=book_result&ct=result&resnum=6&ved=0CDYQ6AEwBTg8#v=onepage&q&f=false pg.740 decision tree analysis the project manager can use ' decision tree analysis' when a decision involves a series of several interrelated decisions. The project manager computes the ' Expected Monetary value' (EMV) of all strategies and chooses the strategy with the highest EMV. Assume that the project manager has four alternative strategies, S1, S2, S3, S4. The resulatant values for each strategy at different probability levels are R1, R2, and R3. Assume that the probability of occurrence of these results is 0.5, 0.2 and 0.3. the payoff matrix for this problem is given in table 18.4. Table 18.4. Payoff Matrix R1 R2 R3 S1 13 10 9 S2 11 10 8 S3 10 12 11 S4 8 11 10 P=0.5The project manager can also represent this problem as a ' decision tree'. Figure 18.3. depicts the decision tree for the given problem. The project manager finally selects strategy S1 as it has the highest value. EMV (A) = 0.5 ( 13)+0.2(10) +0.3(9) = EMV (B) = 0.5(11) +0.2(10) + 0.3(8) = EMV (C) = 0.5(10) +0.2(12) + 0.3(11) = EMV (D) = 0.5(8) +0.2(11) + 0.3(10) = Review of literature

1. Introduction

R and D management, by its very nature, is characterized by uncertainty since effective R and D requires a complex interaction of variables. It is important to balance strategic management (allocate resources and do the right R and D) with operational management (execution of projects) and at the same time take into account issues of people management (leadership, motivation, organisation and teamwork) (Menke, 1994). The strategic aspect of R and D management alone requires the resolution of some very important questions, namely Do we have the right total R and D budget? Are we allocating it to the right business and technology areas? Do we have the right balance of risk and return; of long- and short-term projects; of research vs development; of incremental vs innovation? Are we working on the right projects and programmes with the right effort? It is clear that for success in R and D it is critical to determine what is 'right' for the particular company. The normal process for doing this is through the development of a technology strategy. In practice, the approach used will be that which best fits the operating method of the company but, as Braunstein (1994) has pointed out, the approach is less important than the output, which has to link the corporate goals and strategy to the company's major functional units. Having defined what the business objectives should be for the R and D programme and the overall strategic framework that will define the technology plan, it is then possible to move on to what is probably one of the most problematic parts of technology management, the selection of individual R and D programmes. There is a comprehensive literature of potential methods which can be used (Baker and Pound, 1964; Gear et al., 1971; Souder, 1978). Many of these compare projects with different distributions of possible outcomes and risk, often using relatively complex quantitative methods. There are a number of interdependencies that have to 'come good' before the project finally produces value for the company and it has been argued (Morris et al., 1991) that because many of the major decisions (and many sub-decisions at intermediate milestones) can be taken singly, the overall process is less risky that might initially be thought. Not surprisingly, therefore, Morris goes on to propose that, when choosing R and D projects, there is merit in going for 'long shots' since this is effectively the purchase of 'options' which can be dropped later if the project does not look like bearing fruit. Moreover, the higher risk projects (almost by definition) tend to be the ones that have the highest payback if they are successful (see also Kester, 1984).

2. Decision making under uncertainty

Uncertainty in a business situation is often expressed verbally in terms such as 'it is likely', 'it is probable', 'the chances are', 'possibly', etc. This is not always very helpful because the words themselves are only useful when they convey the same meaning to all parties. It is clear that different people have different perceptions of the everyday expressions which are often used to describe uncertainty. Uncertainty exists if an action can lead to several possible outcomes and an essential, but, challenging aspect of R and D management is to identify the likelihood or probability that these outcomes or events will occur. There are two main interpretations of probability. The first is grounded in the estimation of the probability of an event in terms of relative frequency with which the event has occurred in the past and is usually referred to as 'objective probability'. The second views probability as being the extent of an individual's or group's belief in the occurrence of an event and is usually termed 'subjective probability'. Subjective probability estimates are often included in the models suggested as useful for project selection in R and D planning. Such probabilities might be derived from past experience with similar research projects plus any special features that make the current effort unique or different and alter the past up or down from this base line. A number of tools have been proposed to help in the process of generating probabilities, though they are by no means perfect. Schroder (1975) draws attention to some of the problems that occur in deriving probabilities of technical success and concludes that "subjective probabilities are a rather unreliable predictor of the actual outcome of individual success". He proposes a number of reasons for this which he categorises as either intentional or unintentional (conscious biasing). To decrease the unintentional errors he suggests the following actions: O ensure that risk assessors have sufficient expertise in their field and a comprehension of subjective probabilities. O improve the availability of information and particularly documentation. O fully exploit information systems and attempt to utilize incentive systems which reward accuracy and reliability. O analyse past performance in assessing probabilities to provide valuable insight into potential improvements. O utilise well-tried approaches to help in the subjective probability assessment. It is evident, however, that some confidence levels need to be established and perhaps the most obvious way of achieving this is by the collation over a period of time, of how prior assessments have compared with reality. For this to have genuine value will require a comparison of the assumptions that have been made at each assessment.

3. The use of financial methods for risk analysis

Benefit/cost ratios have been popular for some time, since they are simple and are an attempt to understand the potential gain for the effort required. In performing even a simple benefit/cost analysis, it is necessary for the decision-maker to provide quantitative information in order to ascribe a value to a project. When this has been done, the project can be viewed as a relatively simple financial investment and therefore subject to more standard financial investment tools. The danger of this is that it gives no consideration to the fact that technical programmes are often aimed at a wide range of strategic objectives, a point made by Mitchell and Hamilton (1988) who made a separation into: O exploratory/fundamental type work which is aimed primarily towards the concept of knowledge building. For this type of work, the business impact of which is often poorly defined and wide ranging and here R and D is often best considered as a necessary cost of business. O well understood technical programmes usually associated with incremental improvements of existing products which can be clearly defined. Here the R and D can be seen as an investment and treated accordingly. As usual with two extremes, the difficult part is the mid-ground where neither approach is particularly suitable. Authors have attempted to use techniques borrowed from the financial community which often has to deal with uncertainty. Risk analysis is a key area in financial markets and several of the approaches used in financial analysis are also found in the R and D management area; for example, decision trees and Monte Carlo analysis.

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