Decision Theory Using Probabilities, MV, EMV, EVPI

Reading 10: Decision Theory – Thompson Lumber Case(File020r reference only)1Decision Theory Using Probabilities, MV, EMV, EVPI and Other TechniquesThompson Lumber is looking at marketing a new product – storage sheds. Mr.Thompson has identified three decision options (alternatives) as he looks at thesituation.1. He can construct a large new plant in which he can manufacture thesheds.2. He can construct a smaller plant in which he can manufacture the sheds.3. He can construct no plant.Mr. Thompson believes that the reception of the new product will be eitherfavorable (high demand) or unfavorable (low demand). These are known as thestates of nature. These are two outcomes over which Mr. Thompson has noeffective control.1. State of Nature – High Demand.2. State of Nature – Low Demand.Mr. Thompson must now determine the profit impact of each of the possibleoptions (alternatives) as they are affected by the states of nature. This is areasonably complex process which is accomplished with the aid of hisaccounting and marketing departments. Sales must be forecasted under allthree alternatives and under both states of nature. Expenses must be projectedunder all three alternatives and under both states of nature. The result of theforecasts will be an anticipated net profit associated with each possible decisionand each state of nature.As a result of this analysis, Mr. Thompson has determine that if he builds a largerplant and the product is favorable received, the net profit will be 200,000, but asmaller plant will result in a net profit of 100,000 because of not being able todeliver the product. These are conditional values because they are dependenton building the larger or smaller plant.The conditional values for anunfavorable market are determined to be a loss of 180,000 and a loss of 20,000 for the larger and smaller plant decisions. Of course, doing nothingresults in a zero for either state of nature.A recap of the information may be expressed in a contingency table. (Table 1)Alternative DecisionsConstruct Large PlantConstruct Small PlantDo NothingStates of NatureFavorable - Unfavorable - 200,000 -180,000 100,000 - 20,000ZeroZero

Reading 10: Decision Theory – Thompson Lumber Case(File020r reference only)2There are three possible environments in which decisions are made – certainty,risk and uncertainty.1)Decisions may be made under certainty.Two investment opportunities exist. Both are guaranteed and have thesame risk. You can invest 1,000 at 6% at the credit union or at 10%in Treasury Bonds.The decision is clear with all things being equal. You invest in theTreasury Bonds.2)Decisions may be made under risk.We know the probability of being dealt a club from a deck of cards is0.2500 while the probability of rolling a 5 with a single, six-side die is1/6 (0.1667). The decision maker will maximize his or her expectedwell being. There are usually two equivalent criteria: maximization ofexpected monetary value and minimization of expected losses.Here we would chose the higher probability if our intent was tomaximize our chance of winning. If however, we attach a monetaryoutcome to the probabilities, we might have a different picture. Let’ssay it costs us 100 if we draw a club from the deck of cards or we geta 5 when rolling a single, six-sided die. Now we want to minimize ourchance of loss, so we select the rolling of the die since that has thesmaller chance of happening. If the 100 is a gain rather than a loss,the opposite would be true. Drawing a club would maximize theprobability to 0.25 rather than 0.16 for rolling a 5 on a single, six-sideddie.Risk is present in either case. In one, minimization of loss is theimportant consideration. In the other case, maximization of profits isthe important consideration.3)Decisions may be made under uncertainty.Decisions under uncertainty occur when the probability is notknowable. For example, the probability of a Democrat being Presidentin 25 years is unknowable. Accessing the probability of the success ofa new product is unknowable. We are uncertain yet some decisionmust be made.Let’s look at the decisions facing Mr. Thompson under all three environments –certainty, risk and uncertainty.

Reading 10: Decision Theory – Thompson Lumber Case(File020r reference only)31. Under Certainty: Look back at Table 1 as you consider the decisions facingMr. Thompson. Clearly Mr. Thompson will make the decision to maximize hisprofits, given there is a 100% probability of one of the states of nature occurring.For example, if Mr. Thompson knows that his product will be well received(favorable state of nature), the decision to be made is clear – build the largeplant. The result of this decision is a 200,000 profit.If however, Mr. Thompson knows the product will not be favorable received(unfavorable state of nature), he should do nothing since this minimizes his loss.However, let us assume he has made the decision to build the new product.Now we only have two options (alternatives) available to us – build the largeplant or build the small plant. Let’s examine the outcomes from Table 1 in light ofhis decision to build the product.Under the condition of unfavorableacceptance, it is quite clear the decision is to minimize the loss, so the smallerplant will be build, thus limiting the loss to - 20,000 (See Table 1).2. Under Risk:Here the decision maker will apply decisions using the estimate probabilitiesassociate with each outcome. Here we will want to select the decision with thehighest expected monetary value (EMV). There are two other possibilities wewill examine – the concept of perfect information and opportunity lost. Thenwe must look at our decision based on analyzing possible changes in our baseassumptions. We do this using the concept of sensitivity analysis.Expected Monetary Value (EMV):The EMV is the weighted sum of possible payoffs for each alternative assumingthe decision can be repeated many times.To assess the EMV, we must use probability. One of the three generallyaccepted methods of probability is that of subjective probability, which is oftenused in business settings. Mr. Thompson uses his best, educated estimate ofthe success of the two possible states of nature. In this instance, Mr. Thompsonbelieves that each state of nature is as likely to occur as the other; therefore, theprobability of a favorable market is 50% (0.50) and the probability of anunfavorable market is also 50% (0.50).Remember the probability of each of the events is measured between 0 and 1and the sum of the probability of all events is equal to 1. This assessment of theprobabilities meets both of these rules.

Reading 10: Decision Theory – Thompson Lumber Case4(File020r reference only)This can be show in tabular format as follows: (Table 2)AlternativeDecisionsConstruct LargePlantConstruct SmallPlantDo NothingProbabilityStates of NatureFavorable - Unfavorable 200,000 -180,000EMV Computed 10,000 100,000 -20,000 40,000Zero0.50Zero0.50Zero1.00We arrive at the EMV (far right column in Table 2) by the following calculations.( 200,000 times 0.50) ( -180,000 times 0.50) 10,000( 100,000 times 0.50) ( -20,000 times 0.50) 40,000(Zero times 0.50) (Zero times 0.50) Zero.The decision is for Mr. Thompson to build a small plant and proceed with the newproduct. The other alternatives yield less expected return given the probabilitiesof 50-50 for the states of nature.If, of course, the probabilities shift in the direction of the unfavorable state ofnature to 40 – 60 or 20 – 80, the decisions remains the same but the strength ofthe decision is lessened ( 28,000 for 60 – 40) and ( 4,000 for 80 – 20). Youmight try to make these calculations using the approach just outlined, but changethe probabilities to 40% for favorable and 60% for unfavorable. Make thecalculation a third time using 20% favorable and 80% unfavorable.Expected Value of Perfect Information (EVPI):Mr. Thompson is not especially c

Expected Monetary Value (EMV): The EMV is the weighted sum of possible payoffs for each alternative assuming the decision can be repeated many times. To assess the EMV, we must use probability. One of the three generally accepted methods of prob