Follow the links to the right in order to learn more about the evaluation tool and how to use it. BEWARE, each of these tools has a limitation and should be used with attention to the details.
We have devoted a lot of space on this web domain developing an understanding of some tools to be used in financial decision making in forestry. Now we must be able to define a procedure to use these tools to arrive at decisions that are supportable in terms of what we, or our clients, want.
Russell Ackoff noted in The Art of Problem Solving, that there are 5 fundamental steps to solving a problem. In order they are:
(1) Define the group facing the problemIf you can approach each decision making opportunity with this order of consideration, you will come to the same type of solution that the famous fictional character Sherlock Homes immortalized, "Once you have eliminated the impossible, whatever remains, no matter how improbable, must be the answer."
(2) Determine what variables are present to the problem that you can change
(3) Determine what variables are present to the problem that you cannot change
(4) Define the constraints that you must operate within (real and assumed)
(5) Develop the available solutions
In the forestry world, we will develop
these financial decision making tools into types of analysis that will
be useful to compare projects of different lengths, input and output
different rates of return, and some that are even more difficult to
such as comparing commodity and amenity output projects. There are a
tools that will help us do these things.
1) Net Present Value (NPV)Financial analysis in forestry lends itself to making assumptions and setting certain variables as we see reasonable. This is the skill portion of financial decision making in forestry. However, we need to develop the procedure to follow in order to guarantee that our recommendations are based on the best information available, are affordable decisions (we do not spend all of the profits deciding what to do), and that our decisions are repeatable. That last criteria means that others could look at the same set of facts and come to the same outcome.
2) Equal Annual Equivalent (EAE)
3) Rate of Return
a. Internal Rate of Return (IRR)
b. Composite or Realizable Rate of Return (RRR)
4) Benefit Cost Ratio (B-C ratio)
In order to effectively compare the Investment alternatives it is important to use a systematic procedure for the analysis. Here is a procedure set that will take you down the right road:
1. Define the alternativesI strongly suggest that you become familiar with this series of steps. You will soon start to apply these fundamental steps of logic to your forestlands. This set of steps will be absolutely critical to your success in those ventures. More importantly, it will be integral to your success as a well rounded natural resource professional.
2. Determine the study period
3. Provide estimates of the cash flows for each alternative
4. Specify the time value of money or interest rate
5. Select the measure(s) of effectiveness
6. Compare the alternatives
7. Perform sensitivity analyses
8. Select the preferred alternative
While researching this topic, I stumbled across an article, also posted on the Internet. The author, Robert Harris, is from Vanguard University of Southern California. I am currently seeking his approval to reproduce this wonderful discussion on our web domain. I highly recommend it for an in depth discussion of the topic.
Introduction to Decision Making
What is Decision Making?
A good place to start is with some standard definitions of decision making.
1. Decision making is the study of identifying and choosing alternatives based on the values and preferences of the decision maker. Making a decision implies that there are alternative choices to be considered, and in such a case we want not only to identify as many of these alternatives as possible but to choose the one that best fits with our goals, desires, lifestyle, values, and so on.Kinds of Decisions
2. Decision making is the process of sufficiently reducing uncertainty and doubt about alternatives to allow a reasonable choice to be made from among them. This definition stresses the information gathering function of decision making. It should be noted here that uncertainty is reduced rather than eliminated. Very few decisions are made with absolute certainty because complete knowledge about all the alternatives is seldom possible. Thus, every decision involves a certain amount of risk.
There are several basic kinds of decisions.
1. Decisions whether. This is the yes/no, either/or decision that must be made before we proceed with the selection of an alternative. Should I buy a new TV? Should I travel this summer? Decisions whether are made by weighing reasons pro and con. The PMI technique discussed in the next chapter is ideal for this kind of decision.For example, I have decided to buy that car if I can get it for the right price; I have decided to write that article if I can work the necessary time for it into my schedule.
It is important to be aware of having made a decision whether, since too often we assume that decision making begins with the identification of alternatives, assuming that the decision to choose one has already been made.
2. Decisions which. These decisions involve a choice of one or more alternatives from among a set of possibilities, the choice being based on how well each alternative measures up to a set of predefined criteria.
3. Contingent decisions. These are decisions that have been made but put on hold until some condition is met.
Most people carry around a set of already made, contingent decisions, just waiting for the right conditions or opportunity to arise. Time, energy, price, availability, opportunity, encouragement--all these factors can figure into the necessary conditions that need to be met before we can act on our decision.
Decision Making is a Recursive Process
A critical factor that decision theorists sometimes neglect to emphasize is that in spite of the way the process is presented on paper, decision making is a nonlinear, recursive process. That is, most decisions are made by moving back and forth between the choice of criteria (the characteristics we want our choice to meet) and the identification of alternatives (the possibilities we can choose from among). The alternatives available influence the criteria we apply to them, and similarly the criteria we establish influence the alternatives we will consider. Let's look at an example to clarify this.
Suppose someone wants to decide, Should
I get married? Notice that this is a decision whether. A linear
to decision making would be to decide this question by weighing the
pro and con (what are the benefits and drawbacks of getting married)
then to move to the next part of the process, the identification of
(supportive, easy going, competent, affectionate, etc.). Next, we would
identify alternatives likely to have these criteria (Kathy, Jennifer,
Julie, etc.). Finally we would evaluate each alternative according to
criteria and choose the one that best meets the criteria. We would thus
have a scheme like this:
decision whether ... select criteria ... identify alternatives ... make choice
However, the fact is that our decision whether to get married may really be a contingent decision. "I'll get married if I can find the right person." It will thus be influenced by the identification of alternatives, which we usually think of as a later step in the process. Similarly, suppose we have arrived at the "identify alternatives" stage of the process when we discover that Jennifer (one of the girls identified as an alternative) has a wonderful personality characteristic that we had not even thought of before, but that we now really want to have in a wife. We immediately add that characteristic to our criteria. Thus, the decision making process continues to move back and forth, around and around as it progresses in what will eventually be a linear direction but which in its actual workings is highly recursive.
The Components of Decision Making
The Decision Environment
Every decision is made within a decision environment, which is defined as the collection of information, alternatives, values, and preferences available at the time of the decision. An ideal decision environment would include all possible information, all of it accurate, and every possible alternative. However, both information and alternatives are constrained because time and effort to gain information or identify alternatives are limited. The time constraint simply means that a decision must be made by a certain time. The effort constraint reflects the limits of manpower, money, and priorities. (You wouldn't want to spend three hours and half a tank of gas trying to find the very best parking place at the mall.) Since decisions must be made within this constrained environment, we can say that the major challenge of decision making is uncertainty, and a major goal of decision analysis is to reduce uncertainty. We can almost never have all information needed to make a decision with certainty, so most decisions involve an undeniable amount of risk.
The fact that decisions must be made within a limiting decision environment suggests two things. First, it explains why hindsight is so much more accurate and better at making decisions that foresight. As time passes, the decision environment continues to grow and expand. New information and new alternatives appear--even after the decision must be made. Armed with new information after the fact, the hindsighters can many times look back and make a much better decision than the original maker, because the decision environment has continued to expand.
The second thing suggested by the decision-within-an-environment idea follows from the above point. Since the decision environment continues to expand as time passes, it is often advisable to put off making a decision until close to the deadline. Information and alternatives continue to grow as time passes, so to have access to the most information and to the best alternatives, do not make the decision too soon. Now, since we are dealing with real life, it is obvious that some alternatives might no longer be available if too much time passes; that is a tension we have to work with, a tension that helps to shape the cutoff date for the decision.
Delaying a decision as long as reasonably possible, then, provides three benefits:
1. The decision environment will be larger, providing more information. There is also time for more thoughtful and extended analysis.The Effects of Quantity on Decision Making
2. New alternatives might be recognized or created.
3. The decision maker's preferences might change. With further thought, wisdom, maturity, you may decide not to buy car X and instead to buy car Y.
Many decision makers have a tendency to seek more information than required to make a good decision. When too much information is sought and obtained, one or more of several problems can arise.
(1) A delay in the decision occurs because of the time required to obtain and process the extra information. This delay could impair the effectiveness of the decision or solution.The quantity of information that can be processed by the human mind is limited. Unless information is consciously selected, processing will be biased toward the first part of the information received. After that, the mind tires and begins to ignore subsequent information or forget earlier information.
(2) Information overload will occur. In this state, so much information is available that decision-making ability actually declines because the information in its entirety can no longer be managed or assessed appropriately. A major problem caused by information overload is forgetfulness. When too much information is taken into memory, especially in a short period of time, some of the information (often that received early on) will be pushed out. The example is sometimes given of the man who spent the day at an information-heavy seminar. At the end of the day, he was not only unable to remember the first half of the seminar but he had also forgotten where he parked his car that morning.
(3) Selective use of the information will occur. That is, the decision maker will choose from among all the information available only those facts which support a preconceived solution or position.
(4) Mental fatigue occurs, which results in slower work or poor quality work.
(5) Decision fatigue occurs, where the decision maker tires of making decisions. Often the result is fast, careless decisions or even decision paralysis--no decisions are made at all.
A common misconception about decision making is that decisions are made in isolation from each other: you gather information, explore alternatives, and make a choice, without regard to anything that has gone before. The fact is, decisions are made in a context of other decisions. The typical metaphor used to explain this is that of a stream. There is a stream of decisions surrounding a given decision, many decisions made earlier have led up to this decision and made it both possible and limited. Many other decisions will follow from it.
Another way to describe this situation is to say that most decisions involve a choice from a group of preselected alternatives, made available to us from the universe of alternatives by the previous decisions we have made. Previous decisions have "activated" or "made operable" certain alternatives and "deactivated" or "made inoperable" others.
For example, when you decide to go to the park, your decision has been enabled by many previous decisions. You had to decide to live near the park; you had to decide to buy a car or learn about bus routes, and so on. And your previous decisions have constrained your subsequent ones: you can't decide to go to a park this afternoon if it is three states away. By deciding to live where you do, you have both enabled and disabled a whole series of other decisions.
As another example, when you enter a store to buy a VCR or TV, you are faced with the preselected alternatives stocked by the store. There may be 200 models available in the universe of models, but you will be choosing from, say, only a dozen. In this case, your decision has been constrained by the decisions made by others about which models to carry.
We might say, then, that every decision (1) follows from previous decisions, (2) enables many future decisions, and (3) prevents other future decisions. People who have trouble making decisions are sometimes trapped by the constraining nature of decision making. Every decision you make precludes other decisions, and therefore might be said to cause a loss of freedom. If you decide to marry Terry, you no longer can decide to marry Shawn. However, just as making a decision causes a loss of freedom, it also creates new freedom, new choices and new possibilities. So making a decision is liberating as well as constraining. And a decision left unmade will often result in a decision by default or a decision being made for you.
It is important to realize that every
you make affects the decision stream and the collections of
available to you both immediately and in the future. In other words,
have far reaching consequences.
Concepts and Definitions
1. Information. This is knowledge about the decision, the effects of its alternatives, the probability of each alternative, and so forth. A major point to make here is that while substantial information is desirable, the statement that "the more information, the better" is not true. Too much information can actually reduce the quality of a decision. See the discussion on The Effects of Quantity on Decision Making above.For example, when cake mixes first were put on the market, manufacturers put everything into the mix--the highest quality and most efficient solution. Only water had to be added. However, the mixes didn't sell well--they weren't accepted. After investigation, the makers discovered that women didn't like the mixes because using the mixes made them feel guilty: they weren't good wives because they were taking a shortcut to making a cake. The solution was to take the egg and sometimes the milk out of the mix so that the women would have something to do to "make" the cake other than just adding water. Now they had to add egg and perhaps milk, making them feel more useful. The need to feel useful and a contributor is one of the most basic of human needs. Thus, while the new solution was less efficient in theoretical terms, it was much more acceptable. Cake mixes with the new formula became quite popular.
2. Alternatives. These are the possibilities one has to choose from. Alternatives can be identified (that is, searched for and located) or even developed (created where they did not previously exist). Merely searching for preexisting alternatives will result in less effective decision making.
3. Criteria. These are the characteristics or requirements that each alternative must possess to a greater or lesser extent. Usually the alternatives are rated on how well they possess each criterion. For example, alternative Toyota ranks an 8 on the criterion of economy, while alternative Buick ranks a 6 on the same criterion.
4. Goals. What is it you want to accomplish? Strangely enough, many decision makers collect a bunch of alternatives (say cars to buy or people to marry) and then ask, "Which should I choose?" without thinking first of what their goals are, what overall objective they want to achieve. Next time you find yourself asking, "What should I do? What should I choose?" ask yourself first, "What are my goals?" A component of goal identification should be included in every instance of decision analysis.
5. Value. Value refers to how desirable a particular outcome is, the value of the alternative, whether in dollars, satisfaction, or other benefit.
6. Preferences. These reflect the philosophy and moral hierarchy of the decision maker. We could say that they are the decision maker's "values," but that might be confusing with the other use of the word, above. If we could use that word here, we would say that personal values dictate preferences. Some people prefer excitement to calmness, certainty to risk, efficiency to esthetics, quality to quantity, and so on. Thus, when one person chooses to ride the wildest roller coaster in the park and another chooses a mild ride, both may be making good decisions, if based on their individual preferences.
7. Decision Quality. This is a rating of whether a decision is good or bad. A good decision is a logical one based on the available information and reflecting the preferences of the decision maker.The important concept to grasp here is that the quality of a decision is not related to its outcome: a good decision can have either a good or a bad outcome. Similarly, a bad decision (one not based on adequate information or not reflecting the decision maker's preferences) can still have a good outcome.8. Acceptance. Those who must implement the decision or who will be affected by it must accept it both intellectually and emotionally.
For example, if you do extensive analysis and carefully decide on a certain investment based on what you know about its risks and your preferences, then your decision is a good one, even though you may lose money on the investment. Similarly, if you throw a dart at a listing of stocks and buy the one the dart hits, your decision is a bad one, even though the stock may go up in value.
Good decisions that result in bad outcomes should thus not be cause for guilt or recrimination. If you decide to take the scenic route based on what you know of the road (reasonably safe, not heavily traveled) and your preferences (minimal risk, prefer scenery over early arrival), then your decision is a good one, even though you might happen to get in an accident, or have a flat tire in the middle of nowhere. It is not justified to say, "Well, this was a bad decision."
In judging the quality of a decision, in addition to the concerns of logic, use of information and alternatives, three other considerations come into play:A. The decision must meet the stated objectives most thoroughly and completely. How well does the alternative chosen meet the goals identified?
B. The decision must meet the stated objectives most efficiently, with concern over cost, energy, side effects. Are there negative consequences to the alternative that make that choice less desirable? We sometimes overlook this consideration in our search for thrills.
C. The decision must take into account valuable byproducts or indirect advantages. A new employee candidate may also have extra abilities not directly related to the job but valuable to the company nonetheless. These should be taken into account.Acceptance is a critical factor because it occasionally conflicts with one of the quality criteria. In such cases, the best thing to do may be to choose a lesser quality solution that has greater acceptance.
Thus, the inferior method may produce
results if the inferior one has greater support. One of the most
considerations in decision making, then, is the people factor. Always
a decision in light of the people implementation.
A decision that may be technologically brilliant but that is sociologically stupid will not work. Only decisions that are implemented, and implemented with thoroughness (and preferably enthusiasm) will work the way they are intended to.
Approaches to Decision Making
There are two major approaches to decision making in an organization, the authoritarian method in which an executive figure makes a decision for the group and the group method in which the group decides what to do.
1. Authoritarian. The manager makes the decision based on the knowledge he can gather. He then must explain the decision to the group and gain their acceptance of it. In some studies, the time breakdown for a typical operating decision is something like this:There are two types of group decision making sessions. First is free discussion in which the problem is simply put on the table for the group to talk about. For example, Joe has been offered a job change from shift supervisor to maintenance foreman. Should he take the job?
make decision, 5 min.; explain decision, 30 min.; gain acceptance, 30 min.
2. Group. The group shares ideas and analyses, and agrees upon a decision to implement. Studies show that the group often has values, feelings, and reactions quite different from those the manager supposes they have. No one knows the group and its tastes and preferences as well as the group itself. And, interestingly, the time breakdown is something like this:group makes decision, 30 min.; explain decision, 0 min.; gain acceptance, 0 min.Clearly, just from an efficiency standpoint, group decision making is better. More than this, it has been shown many times that people prefer to implement the ideas they themselves think of. They will work harder and more energetically to implement their own idea than they would to implement an idea imposed on them by others. We all have a love for our own ideas and solutions, and we will always work harder on a solution supported by our own vision and our own ego than we will on a solution we have little creative involvement with.
Developmental discussion (1) insures systematic coverage of a topic and (2) insures that all members of the group are talking about the same aspect of the problem at the same time.
Some Decision Making Strategies
As you know, there are often many solutions to a given problem, and the decision maker's task is to choose one of them. The task of choosing can be as simple or as complex as the importance of the decision warrants, and the number and quality of alternatives can also be adjusted according to importance, time, resources and so on. There are several strategies used for choosing. Among them are the following:
1. Optimizing. This is the strategy of choosing the best possible solution to the problem, discovering as many alternatives as possible and choosing the very best. How thoroughly optimizing can be done is dependent onQuiz shows exploit the uncertainty many people feel when they are not quite sure whether to go with a maximax strategy or a maximin one: "Okay, Mrs. Freen, you can now choose to take what you've already won and go home, or risk losing it all and find out what's behind door number three."A. importance of the problem2. Satisficing . In this strategy, the first satisfactory alternative is chosen rather than the best alternative. If you are very hungry, you might choose to stop at the first decent looking restaurant in the next town rather than attempting to choose the best restaurant from among all (the optimizing strategy). The word satisficing was coined by combining satisfactory and sufficient. For many small decisions, such as where to park, what to drink, which pen to use, which tie to wear, and so on, the satisficing strategy is perfect.
B. time available for solving it
C. cost involved with alternative solutions
D. availability of resources, knowledge
E. personal psychology, valuesNote that the collection of complete information and the consideration of all alternatives is seldom possible for most major decisions, so that limitations must be placed on alternatives.
3. Maximax. This stands for "maximize the maximums." This strategy focuses on evaluating and then choosing the alternatives based on their maximum possible payoff. This is sometimes described as the strategy of the optimist, because favorable outcomes and high potentials are the areas of concern. It is a good strategy for use when risk taking is most acceptable, when the go-for-broke philosophy is reigning freely.
4. Maximin. This stands for "maximize the minimums." In this strategy, that of the pessimist, the worst possible outcome of each decision is considered and the decision with the highest minimum is chosen. The Maximin orientation is good when the consequences of a failed decision are particularly harmful or undesirable. Maximin concentrates on the salvage value of a decision, or of the guaranteed return of the decision. It's the philosophy behind the saying, "A bird in the hand is worth two in the bush."
Example: I could put my $10,000 in a
engineering company, and if it creates and patents a new bacteria that
helps plants resist frost, I could make $50,000. But I could also lose
the whole $10,000. But if I invest in a soap company, I might make only
$20,000, but if the company goes completely broke and gets liquidated,
I'll still get back $7,000 of my investment, based on its book value.
Example: It's fourth down and ten yards to go on your twenty yard line. Do you go for a long pass or punt? Maximax would be to pass; Maximin would be to punt.
Decision Making Procedure
As you read this procedure, remember our discussion earlier about the recursive nature of decision making. In a typical decision making situation, as you move from step to step here, you will probably find yourself moving back and forth also.
1. Identify the decision to be made together with the goals it should achieve. Determine the scope and limitations of the decision. Is the new job to be permanent or temporary or is that not yet known (thus requiring another decision later)? Is the new package for the product to be put into all markets or just into a test market? How might the scope of the decision be changed--that is, what are its possible parameters?And of course, don't forget to implement the decision and then evaluate the implementation, just as you would in a problem solving experience.When thinking about the decision, be sure to include a clarification of goals: We must decide whom to hire for our new secretary, one who will be able to create an efficient and organized office. Or, We must decide where to go on vacation, where we can relax and get some rest from the fast pace of society.2. Get the facts. But remember that you cannot get all the facts. Get as many facts as possible about a decision within the limits of time imposed on you and your ability to process them, but remember that virtually every decision must be made in partial ignorance. Lack of complete information must not be allowed to paralyze your decision. A decision based on partial knowledge is usually better than not making the decision when a decision is really needed. The proverb that "any decision is better than no decision," while perhaps extreme, shows the importance of choosing. When you are racing toward a bridge support, you must decide to turn away to the right or to the left. Which way you turn is less important than the fact that you do indeed turn.As part of your collection of facts, list your feelings, hunches, and intuitive urges. Many decisions must ultimately rely on or be influenced by intuition because of the remaining degree of uncertainty involved in the situation.3. Develop alternatives. Make a list of all the possible choices you have, including the choice of doing nothing. Not choosing one of the candidates or one of the building sites is in itself a decision. Often a non decision is harmful as we mentioned above--not choosing to turn either right or left is to choose to drive into the bridge. But sometimes the decision to do nothing is useful or at least better than the alternatives, so it should always be consciously included in the decision making process.
Also as part of your collection of facts, consult those who will be affected by and who will have to implement your decision. Input from these people not only helps supply you with information and help in making the decision but it begins to produce the acceptance necessary in the implementers because they feel that they are part of the decision making process. As Russell Ackoff noted in The Art of Problem Solving, not consulting people involved in a decision is often perceived as an act of aggression.Also be sure to think about not just identifying available alternatives but creating alternatives that don't yet exist. For example, if you want to choose which major to pursue in college, think not only of the available ones in the catalog, but of designing your own course of study.4. Rate each alternative. This is the evaluation of the value of each alternative. Consider the negative of each alternative (cost, consequences, problems created, time needed, etc.) and the positive of each (money saved, time saved, added creativity or happiness to company or employees, etc.). Remember here that the alternative that you might like best or that would in the best of all possible worlds be an obvious choice will, however, not be functional in the real world because of too much cost, time, or lack of acceptance by others.Also don't forget to include indirect factors in the rating. If you are deciding between machines X, Y, and Z and you already have an employee who knows how to operate machine Z, that fact should be considered. If you are choosing an investigative team to send to Japan to look at plant sites and you have very qualified candidates A, B, and C, the fact that B is a very fast typist, a superior photographer or has some other side benefit in addition to being a qualified team member, should be considered. In fact, what you put on your hobbies and interests line on your resume can be quite important when you apply for a job just because employers are interested in getting people with a good collection of additional abilities.5. Rate the risk of each alternative. In problem solving, you hunt around for a solution that best solves a particular problem, and by such a hunt you are pretty sure that the solution will work. In decision making, however, there is always some degree of uncertainty in any choice. Will Bill really work out as the new supervisor? If we decide to expand into Canada, will our sales and profits really increase? If we let Jane date Fred at age fifteen, will the experience be good? If you decide to marry person X or buy car Y or go to school Z, will that be the best or at least a successful choice?Risks can be rated as percentages, ratios, rankings, grades or in any other form that allows them to be compared. See the section on risk evaluation for more details on risking.6. Make the decision. If you are making an individual decision, apply your preferences (which may take into account the preferences of others). Choose the path to follow, whether it includes one of the alternatives, more than one of them (a multiple decision) or the decision to choose none.
Remember also that very few decisions are irrevocable. Don't cancel a decision prematurely because many new plans require time to work--it may take years for your new branch office in Paris to get profitable--but don't hesitate to change directions if a particular decision clearly is not working out or is being somehow harmful. You can always make another decision to do something else.
Because making decisions involves a
of risk, it would be helpful to examine risk and risk analysis in this
chapter in order to gain an understanding of what is involved. Risk and
uncertainty create anxiety, yet they are necessary components of an
General Comments on Risk Taking
1. Only the risk takers are truly free. All decisions of consequence involve risk. Without taking risks, you cannot grow or improve or even live.The same is true of all risks. Make the opportunity as familiar as possible and learn as much about it as you can before you release the security of the old. Find out about the new job, its location, the lifestyle of those who live there, and so on.
2. There is really no such thing as permanent security in anything on earth. Not taking risks is really not more secure than taking them, for your present state can always be changed without action on your part. If you don't take the risk of dying by driving to the store, your house could collapse on you and kill you anyway.
3. You are supposed to be afraid when you risk. Admit your fears--of loss, of rejection, of failure.
4. Risking normally involves a degree of separation anxiety--the anxiety you feel whenever you are removed from something that makes you feel secure. Many children feel this when they first leave their parents for school. Some college students feel this when they go off to college. Travelers sometimes feel it when they get homesick. The way to overcome separation anxiety is to build a bridge between the familiar and secure and the new. Find out what the new place--school or country--is like and how its elements compare to familiar and secure things at home. Take familiar things with you--books, teddy bear, popcorn popper, whatever.
The Orthodox Theory of Risk Evaluation
The traditional strategy for evaluating
risks is to use an expected value calculation, based on the simple idea
that the expected value of a risk is the value of the possible outcome
discounted by the probability of its realization. The formula is EV=P*R
or expected value equals prize times risk (or chance). Thus, if you
one chance in a million of winning a million dollars, your expected
is one dollar (which is one millionth of a million dollars). Expected
calculations are often used when comparing an amount of money to be
with the probable payoff. (Note: if the risk is, for example, one in
you can divide the prize by twenty, which is the same as multiplying
prize by one twentieth.)
Let's take a typical state lottery, for example. The investment for a ticket is a dollar. The usual prize is about $6,500,000 and the chance of winning is about one in 14,800,000. By discounting the possible outcome by the chance of winning (dividing $6.5 million by 14.8 million), we discover that the expected value of the lottery ticket is about 43.9 cents. Since a ticket costs $1.00 (more than twice as much as its expected value), we would conclude that this is a poor risk. Only when the expected value meets or exceeds the required expense is the risk considered worth taking, according to this theory.
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