The direction of a company that I shall name Stygian Chemical Industries. Ltd. . must make up one’s mind whether to construct a little works or a big one to fabricate a new merchandise with an expected market life of 10 old ages. The determination hinges on what size the market for the merchandise will be. Possibly demand will be high during the initial two old ages but. if many initial users find the merchandise unsatisfactory. will fall to a low degree thenceforth. Or high initial demand might bespeak the possibility of a sustained high-volume market. If demand is high and the company does non spread out within the first two old ages. competitory merchandises will certainly be introduced. If the company builds a large works. it must populate with it whatever the size of market demand. If it builds a little works. direction has the option of spread outing the works in two old ages in the event that demand is high during the introductory period ; while in the event that demand is low during the introductory period. the company will keep operations in the little works and do a tidy net income on the low volume. Management is unsure what to make. The company grew quickly during the 1950’s ; it kept gait with the chemical industry by and large.

The new merchandise. if the market turns out to be big. offers the present direction a opportunity to force the company into a new period of profitable growing. The development section. peculiarly the development undertaking applied scientist. is forcing to construct the large-scale works to work the first major merchandise development the section has produced in some old ages. The president. a chief shareholder. is wary of the possibility of big unnecessary works capacity. He favors a smaller works committedness. but recognizes that later enlargement to run into high-volume demand would necessitate more investing and be less efficient to run. The president besides recognizes that unless the company moves quickly to make full the demand which develops. rivals will be tempted to travel in with tantamount merchandises. The Stygian Chemical job. oversimplified as it is. illustrates the uncertainnesss and issues that concern direction must decide in doing investing determinations. ( I use the term “investment” in a wide sense. mentioning to spendings non merely for new workss and equipment but besides for big. hazardous orders. particular selling installations. research plans. and other purposes. )

These determinations are turning more of import at the same clip that they are increasing in complexness. Countless executives want to do them better—but how? In this article I shall show one late developed construct called the “decision tree. ” which has enormous potency as a decision-making tool. The determination tree can clear up for direction. as can no other analytical tool that I know of. the picks. hazards. aims. pecuniary additions. and information demands involved in an investing job. We shall be hearing a great trade about determination trees in the old ages in front. Although a freshness to most business communities today. they will certainly be in common direction idiom before many more old ages have passed. Subsequently in this article we shall return to the job confronting Stygian Chemical and see how direction can continue to work out it by utilizing determination trees. First. nevertheless. a simpler illustration will exemplify some features of the decision-tree attack. Exposing Options

Let us say it is a instead cloud-covered Saturday forenoon. and you have 75 people coming for cocktails in the afternoon. You have a pleasant garden and your house is non excessively big ; so if the conditions permits. you would wish to put up the refreshments in the garden and have the party at that place. It would be more pleasant. and your invitees would be more comfy. On the other manus. if you set up the party for the garden and after all the invitees are assembled it begins to rain. the refreshments will be ruined. your invitees will acquire moist. and you will heartily wish you had decided to hold the party in the house. ( We could perplex this job by sing the possibility of a partial committedness to one class or another and chances to set estimations of the conditions as the twenty-four hours goes on. but the simple job is all we need. ) This peculiar determination can be represented in the signifier of a “payoff” tabular array:

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Much more complex determination inquiries can be portrayed in final payment table signifier. However. peculiarly for complex investing determinations. a different representation of the information pertinent to the problem—the determination tree—is utile to demo the paths by which the assorted possible results are achieved. Pierre Masse . Commissioner General of the National Agency for Productivity and Equipment Planning in France. notes: “The determination job is non posed in footings of an stray determination ( because today’s determination depends on the 1 we shall do tomorrow ) nor yet in footings of a sequence of determinations ( because under uncertainness. determinations taken in the hereafter will be influenced by what we have learned in the interim ) . The job is posed in footings of a tree of determinations. ”1 Exhibit I illustrates a determination tree for the cocktail party job. This tree is a different manner of exposing the same information shown in the final payment tabular array. However. as ulterior illustrations will demo. in complex determinations the determination tree is often a much more limpid agencies of showing the relevant information than is a final payment tabular array.

The tree is made up of a series of nodes and subdivisions. At the first node on the left. the host has the pick of holding the party inside or outside. Each subdivision represents an alternate class of action or determination. At the terminal of each subdivision or alternate class is another node stand foring a opportunity event—whether or non it will rain. Each subsequent alternate class to the right represents an alternate result of this opportunity event. Associated with each complete alternate class through the tree is a final payment. shown at the terminal of the rightmost or terminal subdivision of the class. When I am pulling determination trees. I like to bespeak the action or determination forks with square nodes and the chance-event forks with unit of ammunition 1s. Other symbols may be used alternatively. such as single-line and double-line subdivisions. particular letters. or colourss. It does non count so much which method of separating you use so long as you do use one or another. A determination tree of any size will ever unite ( a ) action picks with ( B ) different possible events or consequences of action which are partly affected by opportunity or other unmanageable fortunes. Decision-event ironss

The old illustration. though affecting merely a individual phase of determination. illustrates the simple rules on which larger. more complex determination trees are built. Let us take a somewhat more complicated state of affairs: You are seeking to make up one’s mind whether to O.K. a development budget for an improved merchandise. You are urged to make so on the evidences that the development. if successful. will give you a competitory border. but if you do non develop the merchandise. your rival may—and may earnestly damage your market portion. You sketch out a determination tree that looks something like the one in Exhibit II.

Your initial determination is shown at the left. Following a determination to continue with the undertaking. if development is successful. is a 2nd phase of determination at Point A. Assuming no of import alteration in the state of affairs between now and the clip of Point A. you decide now what options will be of import to you at that clip. At the right of the tree are the results of different sequences of determinations and events. These results. excessively. are based on your present information. In consequence you say. “If what I know now is true so. this is what will go on. ” Of class. you do non seek to place all the events that can go on or all the determinations you will hold to do on a topic under analysis. In the determination tree you lay out merely those determinations and events or consequences that are of import to you and hold effects you wish to compare. ( For more illustrations. see the Appendix. ) Appendix

Adding Financial Data
Now we can return to the jobs faced by the Stygian Chemical direction. A determination tree qualifying the investing job as outlined in the debut is shown in Exhibit III. At Decision # 1 the company must make up one’s mind between a big and a little works. This is all that must be decided now. But if the company chooses to construct a little works and so finds demand high during the initial period. it can in two years—at Decision # 2—choose to spread out its works.

But allow us travel beyond a au naturel lineation of options. In doing determinations. executives must take history of the chances. costs. and returns which appear likely. On the footing of the informations now available to them. and presuming no of import alteration in the company’s state of affairs. they ground as follows: * Selling estimations indicate a 60 % opportunity of a big market in the long tally and a 40 % opportunity of a low demand. developing ab initio as follows:

* Therefore. the opportunity that demand ab initio will be high is 70 % ( 60 + 10 ) . If demand is high ab initio. the company estimates that the opportunity it will go on at a high degree is 86 % ( 60 ? 70 ) . Comparing 86 % to 60 % . it is evident that a high initial degree of gross revenues alterations the estimated opportunity of high gross revenues in the subsequent periods. Similarly. if gross revenues in the initial period are low. the opportunities are 100 % ( 30 ? 30 ) that gross revenues in the subsequent periods will be low. Therefore the degree of gross revenues in the initial period is expected to be a instead accurate index of the degree of gross revenues in the subsequent periods. * Estimates of one-year income are made under the premise of each alternate result: 1. A big works with high volume would give $ 1. 000. 000 yearly in hard currency flow. 2. A big works with low volume would give merely $ 100. 000 because of high fixed costs and inefficiencies. 3. A little works with low demand would be economical and would give one-year hard currency income of $ 400. 000. 4. A little works. during an initial period of high demand. would give $ 450. 000 per twelvemonth. but this would drop to $ 300. 000 annually in the long tally because of competition. ( The market would be larger than under Alternate 3. but would be divided up among more competitors. )

5. If the little works were expanded to run into sustained high demand. it would give $ 700. 000 hard currency flow yearly. and so would be less efficient than a big works built ab initio. 6. If the little works were expanded but high demand were non sustained. estimated one-year hard currency flow would be $ 50. 000. * It is estimated farther that a big works would be $ 3 million to set into operation. a little works would be $ 1. 3 million. and the enlargement of the little works would be an extra $ 2. 2 million. When the foregoing informations are incorporated. we have the determination tree shown in Exhibit IV.

Bear in head that nil is shown here which Stygian Chemical’s executives did non cognize before ; no Numberss have been pulled out of chapeaus. However. we are get downing to see dramatic grounds of the value of determination trees in puting out what direction knows in a manner that enables more systematic analysis and leads to break determinations. To sum up the demands of doing a determination tree. direction must: 1. Identify the points of determination and options available at each point. 2. Identify the points of uncertainness and the type or scope of alternate results at each point. 3. Estimate the values needed to do the analysis. particularly the chances of different events or consequences of action and the costs and additions of assorted events and actions. 4. Analyze the alternate values to take a class.

Choosing Course of Action
We are now ready for the following measure in the analysis—to compare the effects of different classs of action. A determination tree does non give direction the reply to an investing job ; instead. it helps direction determine which alternative at any peculiar pick point will give the greatest expected pecuniary addition. given the information and options pertinent to the determination. Of class. the additions must be viewed with the hazards. At Stygian Chemical. as at many corporations. directors have different points of position toward hazard ; hence they will pull different decisions in the fortunes described by the determination tree shown in Exhibit IV. The many people take parting in a decision—those supplying capital. thoughts. informations. or determinations. and holding different values at risk—will see the uncertainness environing the determination in different ways. Unless these differences are recognized and dealt with. those who must do the determination. wage for it. provide informations and analyses to it. and unrecorded with it will judge the issue. relevancy of informations. demand for analysis. and standard of success in different and conflicting ways.

For illustration. company shareholders may handle a peculiar investing as one of a series of possibilities. some of which will work out. others of which will neglect. A major investing may present hazards to a in-between manager—to his occupation and career—no affair what determination is made. Another participant may hold a batch to derive from success. but small to lose from failure of the undertaking. The nature of the risk—as each person sees it—will affect non merely the premises he is willing to do but besides the scheme he will follow in covering with the hazard. The being of multiple. unexpressed. and conflicting aims will surely lend to the “politics” of Stygian Chemical’s determination. and one can be certain that the political component exists whenever the lives and aspirations of people are affected.

Here. as in similar instances. it is non a bad exercising to believe through who the parties to an investing determination are and to seek to do these appraisals: * What is at hazard? Is it net income or equity value. endurance of the concern. care of a occupation. chance for a major calling? * Who is bearing the hazard? The shareholder is normally bearing hazard in one signifier. Management. employees. the community—all may be bearing different hazards. * What is the character of the hazard that each individual bears? Is it. in his footings. unique. once-in-a-lifetime. consecutive. insurable? Does it impact the economic system. the industry. the company. or a part of the company? Considerations such as the foregoing will certainly come in into top management’s thought. and the determination tree in Exhibit IV will non extinguish them. But the tree will demo direction what determination today will lend most to its long-run ends. The tool for this following measure in the analysis is the construct of “rollback. ” “Rollback” construct

Here is how rollback works in the state of affairs described. At the clip of doing Decision # 1 ( see Exhibit IV ) . direction does non hold to do Decision # 2 and does non even know if it will hold the juncture to make so. But if it were to hold the option at Decision # 2. the company would spread out the works. in position of its current cognition. The analysis is shown in Exhibit V. ( I shall disregard for the minute the inquiry of dismissing future net incomes ; that is introduced later. ) We see that the sum expected value of the enlargement option is $ 160. 000 greater than the no-expansion option. over the eight-year life staying. Hence that is the alternate direction would take if faced with Decision # 2 with its bing information ( and believing merely of pecuniary addition as a criterion of pick ) .

Readers may inquire why we started with Decision # 2 when today’s job is Decision # 1. The ground is the undermentioned: We need to be able to set a pecuniary value on Decision # 2 in order to “roll back” to Decision # 1 and compare the addition from taking the lower subdivision ( “Build Small Plant” ) with the addition from taking the upper subdivision ( “Build Big Plant” ) . Let us name that pecuniary value for Decision # 2 its place value. The place value of a determination is the expected value of the preferable subdivision ( in this instance. the plant-expansion fork ) . The expected value is merely a sort of norm of the consequences you would anticipate if you were to reiterate the state of affairs over and over—getting a $ 5. 600 1000 output 86 % of the clip and a $ 400 1000 output 14 % of the clip.

Stated in another manner. it is deserving $ 2. 672 1000 to Stygian Chemical to acquire to the place where it can do Decision # 2. The inquiry is: Given this value and the other informations shown in Exhibit IV. what now appears to be the best action at Decision # 1? Bend now to Exhibit VI. At the right of the subdivisions in the top half we see the outputs for assorted events if a large works is built ( these are merely the figures in Exhibit IV multiplied out ) . In the bottom half we see the little works figures. including Decision # 2 place value plus the output for the two old ages prior to Decision # 2. If we cut down all these outputs by their chances. we get the undermentioned comparing: Build large works: ( $ 10 ? . 60 ) + ( $ 2. 8 ? . 10 ) + ( $ 1 ? . 30 ) – $ 3 = $ 3. 600 thousand Build little works: ( $ 3. 6 ? . 70 ) + ( $ 4 ? . 30 ) – $ 1. 3 = $ 2. 400 1000

The pick which maximizes expected entire hard currency output at Decision # 1. therefore. is to construct the large works ab initio. Accounting for Time
What about taking differences in the clip of future net incomes into history? The clip between consecutive determination phases on a determination tree may be significant. At any phase. we may hold to weigh differences in immediate cost or gross against differences in value at the following phase. Whatever criterion of pick is applied. we can set the two options on a comparable footing if we discount the value assigned to the following phase by an appropriate per centum. The price reduction per centum is. in consequence. an allowance for the cost of capital and is similar to the usage of a price reduction rate in the present value or discounted hard currency flow techniques already good known to business communities. When determination trees are used. the discounting process can be applied one phase at a clip. Both hard currency flows and place values are discounted. For simpleness. allow us presume that a price reduction rate of 10 % per twelvemonth for all phases is decided on by Stygian Chemical’s direction.

Using the push back rule. we once more begin with Decision # 2. Taking the same figures used in old exhibits and dismissing the hard currency flows at 10 % . we get the informations shown in Part A of Exhibit VII. Note peculiarly that these are the present values as of the clip Decision # 2 is made. Now we want to travel through the same process used in Exhibit V when we obtained expected values. merely this clip utilizing the discounted output figures and obtaining a discounted expected value. The consequences are shown in Part B of Exhibit VII. Since the discounted expected value of the no-expansion option is higher. that figure becomes the place value of Decision # 2 this clip. Having done this. we go back to work through Decision # 1 once more. reiterating the same analytical process as before merely with discounting. The computations are shown in Exhibit VIII. Note that the Decision # 2 place value is treated at the clip of Decision # 1 as if it were a ball amount received at the terminal of the two old ages.

The large-plant option is once more the preferable 1 on the footing of discounted expected hard currency flow. But the border of difference over the small-plant option ( $ 290 1000 ) is smaller than it was without dismissing. Uncertainty Options

In exemplifying the decision-tree construct. I have treated uncertainness options as if they were distinct. chiseled possibilities. For my illustrations I have made usage of unsure state of affairss depending fundamentally on a individual variable. such as the degree of demand or the success or failure of a development undertaking. I have sought to avoid unneeded complication while seting accent on the cardinal interrelatednesss among the present determination. future picks. and the intervening uncertainnesss. In many instances. the unsure elements do take the signifier of distinct. single-variable options. In others. nevertheless. the possibilities for hard currency flow during a phase may run through a whole spectrum and may depend on a figure of independent or partly related variables subject to opportunity influences—cost. demand. output. economic clime. and so forth. In these instances. we have found that the scope of variableness or the likeliness of the hard currency flow falling in a given scope during a phase can be calculated readily from cognition of the cardinal variables and the uncertainnesss environing them. Then the scope of cash-flow possibilities during the phase can be broken down into two. three. or more “subsets. ” which can be used as distinct opportunity options. Decision

Peter F. Drucker has compactly expressed the relation between present planning and future events: “Long-range planning does non cover with future determinations. It deals with the future of present determinations. ”2 Today’s determination should be made in visible radiation of the awaited consequence it and the result of unsure events will hold on future values and determinations. Since today’s determination sets the phase for tomorrow’s determination. today’s determination must equilibrate economic system with flexibleness ; it must equilibrate the demand to capitalise on net income chances that may be with the capacity to respond to future fortunes and demands. The alone characteristic of the determination tree is that it allows direction to unite analytical techniques such as discounted hard currency flow and present value methods with a clear portraiture of the impact of future determination options and events.

Using the determination tree. direction can see assorted classs of action with greater easiness and lucidity. The interactions between present determination options. unsure events. and future picks and their consequences go more seeable. Of class. there are many practical facets of determination trees in add-on to those that could be covered in the infinite of merely one article. When these other facets are discussed in subsequent articles. 3 the whole scope of possible additions for direction will be seen in greater item. Surely the decision-tree construct does non offer concluding replies to directions doing investing determinations in the face of uncertainness. We have non reached that phase. and possibly we ne’er will. However. the construct is valuable for exemplifying the construction of investing determinations. and it can likewise supply first-class aid in the rating of capital investing chances. 1. Optimum Investing Decisions: Rules for Action and Criteria for Choice ( Englewood Cliffs. New Jersey. Prentice-Hall. Inc. . 1962 ) . p. 250. 2. “Long-Range Planning. ” Management Science. April 1959. p. 239. 3. We are anticipating another article by Mr. Magee in a extroverted issue.


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