Decision_of_Uncertainty_Paper

Decision of Uncertainty Paper Decision of Uncertainty Paper We are challenged every day with several decisions and the fear of making the wrong decision. Sometimes it is the fear of losing the business. Other times it is the fear of losing the customers. All our decisions involve risk, for that reason, a good statistical tool for analyzing data give us a means of minimizing the risk. A small coffee shop is interesting in growing in demand; this would mean a need to come up with important production strategies decisions. The coffee shop will need a strategy that optimizes the use of existing production resources that include machineries and equipment. One important option may be re-conditioning the equipment and the machinery in order that a more dependable volume and quality of output would be the result. However, after analyzing relevant costs and other factors, the option is not feasible. Normally, cash flows on returns on investment (ROI) are utilized to come up with decisions. To look for other option in increasing demand, the coffee shop use the option to make some data gathering to determine the feasible of purchasing new equipment for use in the production. The coffee shop research team conducted informal interviews among owners of 5 coffee shops that are located in other communities. These coffee shops have been making use of the new equipment that is intended to be bought by the business under study. The highlights of the findings include the following: 1) The use of the new equipment improves production 2) Allow the coffee shop business to cope with the increase of demand 3) The 5 coffee shops had a mean increase of 4% ROI because of the use of the new equipment 4) The probability that the 4% increase in ROI will be attained is .40 or 40% The coffee shop research team allowed a margin of 5%in their estimates (or 95% confidence level). This is to accommodate some uncertainties due to some fluctuations in electricity and other uncontrollable factors. Statistical Analysis The objective of the analysis is to determine whether the purchase of new equipment would result to a 4% increase in ROI (return on investment) for the small coffee shop. The coffee shop, finds out the results in the mini interview and agree to continue with the statistical analysis. Statistics that would be used The Coffee Shop will use the Bayes’ Theorem, Bayes’ theorem also known as Bayes’ rule law, is a result in probability theory that relates conditional probabilities. (Haddick.science. uu.nl) According to Fraser, and Ormiston (2001), Bayes' theorem can also be written neatly in terms of a likelihood ratio Λ and odds O as where O (A|B) are the (posterior) odds of A given B, O (A) are the (prior) odds of A by itself and Λ (A|B) is the likelihood ratio. Note that the odds measured here are the odds for and beside event A, or in other words, the odds for A against Ac. One can more usually consider the odds for any event A1 against any other event A2. This results in the theorem where O (A1:A2 | B) are the posterior odds for A1 against A2 given B, , O (A1:A2) are the prior odds for A1 against A2 , (Fraser and Ormiston 2001) Solution 1. Probability that a 4% increase in ROI will be attained is 0.40. P (ROI) 2. Probability that it will not be attained (negative) is 0.60. P (N ROI) 3. Probability that the data obtained is valid and accurate is 0.95. P (+ ROI) 4. Probability that the data obtained is not accurate is 0.05. P (+N) Probability that an ROI will be achieved: = (.95)*(.40) + (.05)*(.60) = 0.41 This was found by adding the probability that regardless of other information, a true increase in ROI will appear (95% *40%) plus the probability that a false 4% increase in ROI will appear (5% * 60%). Hence, a probability that a 4% increase in ROI P (ROI+) is = (.95) * (.40) / (0.95) * (.40) *(.60) = 0.38/0.41 = 0.9268 Or 92.68% Conclusion It is more likely that the expected return on investment of 4% will be reached (92. 68%) and only 7.32% is the chance that the 4% increase in ROI will not be achieved. The recommendation will be that the small coffee shop may purchase the new equipment in order to manage with additional production requirements resulting from increase in demand. Buying the new equipment will provide a 4% increase in ROI (return on investment). Reference Bayes’ theorem Retrieved January 16th, 2012 from: http://haddock.science.uu.nl/servicesdevel/ATHENA/bayes-1.pdf Cooper, D.R., & Schindler, P.S. (2006). Business Research Methods (9th ed.). Boston, MA: McGraw-Hill/Irwin. Fraser, Lyn and Ormiston, Aileen (2001). Understanding Financial Statements. Prentice – Hall, Inc.