Abstract
Decision-making under risk occurs when there is an uncertainty about the states of nature that can occur, but the probabilities of each of the states of nature occurring have already been determined. We can use these probabilities to determine additional strategies for decision-making. One such strategy is the Expected Monetary Value (EMV) approach for making an optimal decision. In the problem where the company had to decide on the right investment approach, the company had already done research to determine the various possible states of nature for each of the alternatives as well the probabilities of each of these states of nature. The report illustrates the method for using the EMV for decision-making. We calculate the EMV for each of the decision alternatives and make a decision that tries to maximize the resultant EMV. Therefore, the report recommends the company to invest in Just Hats franchise, as it will maximize the EMV.
Keywords: Expected Monetary Value, Probabilities, Decision-making under uncertainty
Introduction and Background
A: Real Estate Development
B: Investment in a retail franchise of Just Hats
C: Investment in Cupcakes and so forth
For each of these alternatives, based on an extensive research, the company arrived at the Net Present Value and the probabilities. Table 1 shows these values.
I have to analyze these alternatives and develop the expected value of each of these so that I would be able to recommend the best investment option for the company.
Expected Monetary Value (EMV)
Any decision analysis of a problem has three elements: 1) a set of strategies or decisions available to the decision-maker, 2) a set of outcomes and their probabilities, and 3) a model that the decision-maker uses to assign values for each of these decision-outcome combinations. Once the decision-maker knows these elements, he or she can select the optimal solution based on the optimality criterion. When the decision-maker starts the process, he or she is unaware of the outcome. Once the decision-maker makes the decision, it will reveal the outcome and the decision-maker will receive the corresponding payoff, which could even be a cost if the payoff is a negative value. The decision-maker has to start by listing all the payoffs for all the decision-outcome pairs. A table that lists such values is a payoff table. Positive values in the payoff table correspond to gains while negative values correspond to losses. The decision-maker must be aware of the difference between a good decision and a good outcome. When decision-making is under uncertainty, the best decision can have less than great result if one is unlucky. Regardless of the decision made, hindsight could make one wish they had made a different decision. Therefore, decision-makers must make decisions based on the information they possess, at the right time, in a rational manner and not second-guess them.
As discussed earlier, there are different criterions for deciding the optimality of the choices. We can analyze the payoff table using either Bayesian techniques or non-Bayesian techniques. The difference between them is that Non-Bayesian techniques ignore probabilities whereas the Bayesian techniques take into account the probabilities. Maximin criterion considers the worst payoff of for each row in a payoff table and chooses the decision (alternative) that has the best value. In other words, it considers the alternative that has the maximum of the minimum value. This is useful for people who are too conservatives as it tends to avoid large losses while ignoring even large rewards. Maximax criterion finds the best payoff in each row and selects the best row as one with the maximum highest value. This is useful for optimistic people and focuses on large gains while ignoring the losses. Such decisions could ultimately bankrupt a company. Minimax Regret criterion uses a regret table or opportunity loss table, which one populates by calculating the difference between the payoff and the best possible payoff for that possible state of future. Then we select the alternative with the lowest maximum regret. However, the best and most widely used method is the Expected Monetary Value criterion.
While the above criterions are the non-Bayesian criterion, the EMV is a Bayesian criterion as it considers the expected probabilities. The EMV is the weighted average of the possible monetary values (generally Net Present Value, NPV) weighted by their respective probabilities. The sum of the products of the payoffs and the probabilities of the states of the nature result in the expected payoff for a decision alternative. We treat each of these decision alternatives as separate with an expected value that we can calculate. This process is also known as “playing the averages”. The following (Equation 1) is the equation for calculating EMV.
Equation 1: Equation for calculating EMV for NPVs
Source:
For each alternative, F is state of the nature calculated by the formula pi*mi. Therefore, F1 is the product of NPV and P for the state of nature high. Similarly, the F2 is the product of the NPV and P for the state of nature medium, and F3 is the product of NPV and P for the state of nature low.
EMV for Real Estate = ∑pi*mi = F1 + F2 + F3 of that row = $33,25,000
EMV for Just Hats = ∑pi*mi = F1 + F2 + F3 of that row = $34,30,000
EMV for Cupcakes = ∑pi*mi = F1 + F2 + F3 of that row = $28,92,000
We tabulate these results as follows in Table 2.
Based on these results, I can recommend that the best investment decision would be to invest in Just Hats franchise, as the resultant payoff would be $34,30,000, which is the maximum, after the completion of ten years from the date of investment. However, we can see that none of the payoffs or the NPVs show a value of $34,30,000. What this signifies is that if the same decision is replayed enough number of times, the figure for the average payoff will approach $34,30,000.
References
Albright, S. C., Winston, W. L., & Broadie, M. (2015). Business analytics: data analysis and decision making (5th ed.). Stamford, CT: Cengage Learning.
Mian, M. A. (2002). Project economics and decision analysis, volume II: Probabilistic models. Tulsa, OK: PennWell Corporation.
Stonebraker, J. (2002). How Bayer makes decisions to develop new drugs. Interfaces, 32(6), 77-90.
Weiers, R. M., Gray, J. B., & Peters, L. H. (2011). Introduction to business statistics (7th ed.). Mason, OH: South-Western Cengage Learning.
