Agribusiness Economics and Management - Math Problem Example

Risk Management in Agribusiness Name Institution affiliation Risk Management in Agribusiness Question 1 According to de Barros (2012), the joint probability involves statistical measure where there is a chance of two or more events at the same point in time. The joint probability for the three events that include not infected, slightly infected and seriously infected is given by Joint probabilities P (NSS) = P (N) * P (S) * P (S) P (z1) = 0.4 * 0.7 + 0.6 * 0.4 + 0.2 * 0.2 = 0.56 P (z2) = 0.4 * 0.2 + 0.4 * 0.2 + 0.3 * 0.2 = 0.22 P (z3) = 0.4 * 0.1 + 0.4 * 0.2 + 0.5 * 0.2 = 0.22 Letchford, & Conitzer, (2013) defines Marginal probabilities as collection of random event happening and is thought to be unconditional. In this case the conditional probability is calculated as; P (z1) = 0.56 P (z2) = 0.22 P (z3) = 0.22 According to Cheung & Beck (2010) In Bayesian statistics, posterior probabilities involve random events allocated after relevant background is taken into account. In this case the posterior probability is calculated as; P (z1) = P (A)P(B|A)P(C|A and B) = 0.28 * 0.24 * 0.04 = 0.002688 P (z2) = 0.08* 0.08 * 0.06 = 0.000384 P (z3) = 0.04 *0.08 *0.1 = 0.00032 Type of prediction Joint probabilities Marginal probabilities posterior probabilities Unlikely (z1) 0.56 0.56 0.002688 Possible (z2) 0.22 0.22 0.000384 Probable (z3) 0.22 0.22 0.00032 b) Question 2 Alternative i Interest = principal * rate * time = 500,000 * 2% * 4 Income earned per year = $40,000 Alternative ii Income annually earned from Tomato = 10,500 *0.6 + 13,300 * 0.4 – 10,000 = 1620 * 50 acres = $81,000 Investment in safe money fund Money remaining after planting tomato = wealth – cost per acre * number of acres = $500,000 – 10,000*50 = $0 Interest earned = principal * rate * time = 0 * 2% * 4 = 0 Alternative iii Wheat Income annually = 7,500 * 0.6 + 6,800 *0.4 -6500 = 720 * 50 acres = $36,000 Investment in safe money fund Money remaining after planting wheat = wealth – cost per acre * number of acres = $500,000 – 6500*50 = $325,000 Interest = principal * rate * time = 325,000 * 2% * 4 =$26,000 b) I will select alternative ii because it involves provides more investment income as compared to the other two alternatives. The total yield of alternative ii is the additional income from the investment in wheat and in the safe money fund which is $81,000 + $0 =$ 81,000. This implies that the family used all the money in planting tomato and non-remained for investing in the safe money fund. The income from this alternative is greater than that will be achieved if alternative i was implemented giving $40,000 annually. The income is also greater than that earned in alternative iii that gives a total of $62,000 which is the sum of $36,000 from investing in planting wheat and investment in the safe money fund (King et.al, 2010). Question 3 Hurwicz alpha criterion indicates the compromise that comes between the optimistic and the pessimistic method to the decision making in the event of uncertainty. The index shows the degree of optimism and pessimism. Therefore, the more the index is close to 1, the more the decision maker tends to be optimist. Through the means of the index alpha, the weighted average of the best outcome where weight is the α and the worst payoff involves the weight of 1 – α. In order to make an optimal decision involving various alternatives the maximum criterion for every alternative is calculated, and the alternative that involves the largest weighted average is selected (King et.al, 2010). Alternative 1- Barley = 500 * 0.4 + -200*0.6 = 80 Alternative 2- corn = 300 * 0.4 + 0.6 *-200 = 0 Alternative 3 – potato = 300 *0.4 + 0.6 *-100 = 60 Alternative 4 – wheat = 300 * 0.4 + 0.6 *-200 = 0 A farmer should consider growing Barley in her land and the three states of nature to weather conditions, and this is because Barley is the crop that yields the best payoff among all the four alternatives. Question 4 a) Minimum acceptable return level involves the minimum rate of return that a project or the company is willing to accept before the start of a project given the risk as well as the opportunity cost of preceding the other projects (Mian, 2011).  Minimum acceptable rate of return = value of the project + project risk + rate of inflation change + rate of interest for loans + loan default + expected rate of inflation Rate of return = interest accrued per time unit / principal * 100% = 30,000 / 600,000/*100 = 0.05 *100 = 5 % b) The Roy’s safety first criterion is a method that involves venture decisions that tend to set the lowest required return for the given level of risk. The Roy’s safety first criterion permits the portfolios to be equated centered on the probability that the returns will be less than the minimum desired threshold. According to Roy’s rule, the ideal portfolio involves the one that encompasses minimization of the likelihood that the portfolio’s return will decline below the threshold level. The ideal decision involves selecting the portfolio with the highest safety first ratio (Sadgrove, 2016).  Safety-first ratio for the crops = E (r) – Threshold return / standard deviation SF (Banana) = 14 – 5/ 8.50 = 1.0588 SF (Capsicum) = 12- 5 / 6.66 = 1.0511 SF (Corn) = 9 – 5/ 3.20 = 1.25 SF (Potato) = 10 – 5/ 5.30 = 0.9434 SF (Tomato) = 16 – 5 / 9.30 = 1.1828 Corn is best among the crops, and this is because it gives the highest SF ratio as compared to other crops. c) Telser’s rule involves a measure for the calculation of the risk-adjusted return. The rule encompasses the creation of a portfolio on the basis of a minimum level of portfolio returns. Through setting the minimum acceptable return, the company can be able to alleviate the risk of not attaining its investment objective. The rule will select Corn, and this is because the rule aims at creating a margin of safety that may be helpful in the creation of a portfolio. This is achieved through maximization of the objective function where the expected return that is employed for use in the security market line equation tends to be reduced to reflect the margin of safety (Saita, 2010).  Ratio = investment – (risk-free rate) / standard deviation (investment) Banana = 600,000 – 15% / 8.50 (600,000) = 599,999.85 / 5,100,000 = 0.1176 Capsicum = 600,000 – 15% / 6.66 (600,000) = 599,999.85 / 3,996,000 = 0.1501 Corn = 600,000 – 15% / 3.20 (600,000) = 599,999.85 / 1920000 = 0.3125 Potato = 600,000 – 15% / 5.30 (600,000) = 599,999.85 / 3180000 = 0.1887 Tomato = 600,000 – 15% / 9.30 (600,000) = 599,999.85 / 5580000 = 0.1075 The company should select tomato as the crop that it is going to grow next season. The ratio of tomato is low as compared to those of the other crops, and this implies that the fund investment is less risky. Deciding to grow to tomato the company will be able to enjoy higher returns as compared to the benefits that it could have gained if it decided on growing the other crops and therefore it is only good for an investment if the higher returns are not associated with the excess of the additional risk (Bodie, Kane, & Marcus, 2014). d) According to Tesler’s rule, the expected return for the optimum crop should be greater than the risk adjusted return to reduce the risk and maximize the yield. This can be accomplished over and done with maximization of the objective function wherever the expected return that is employed for use in the security market line equation is reduced to reflect the margin of safety. Question 5 a) The E- V rule involves the approved budget that contains the work that is completed by a particular date. In the rule indicates that in case a project is completed the earned value will tend to indicate the value of that the project has produced. The E-V rule also encompasses the value of work that is performed and expressed in terms of the approved budget that is assigned to work for an activity (Usmani et al., 2017). To determine the Earned Value of the three investments we multiply the outcome per hectare by the probability of every crop. Corn E- V = 200000 * 0.2 + 400000 * 0.3 + 600000 * 0.4 + 800000 *0.1 = 480,000 Potato E-V = 200000 * 0.2 + 400000 * 0.4 + 600000 * 0.2 + 800000 *0.2 = 480,000 Wheat E – V = 200,000 * 0.1 + 400,000 * 0.3 + 600,000 * 0.4 + 800,000 *0.2 = 480,000 The farmer can consider investing in any of the three alternative investment crops and this is because the Earned value of the three investments is the same meaning that any project that the farmer selects will have the same Earned Value (EV) as the rest. b) The graph below presents the CDFs for the three investments (Knoke et. al , 2008) References Bodie, Z., Kane, A., & Marcus, A. J. (2014). Investments, 10e. McGraw-Hill Education. Cheung, S. H., & Beck, J. L. (2010). Calculation of posterior probabilities for Bayesian model class assessment and averaging from posterior samples based on dynamic system data. Computer‐Aided Civil and Infrastructure Engineering, 25(5), 304-321. De Barros, J. A. (2012, December). Joint probabilities and quantum cognition. In AIP Conference Proceedings (Vol. 1508, No. 1, pp. 98-107). AIP. Earle, T. C. (2010). Trust in risk management: a model‐based review of empirical research. Risk analysis, 30(4), 541-574. King, R. P., Boehlje, M., Cook, M. L., & Sonka, S. T. (2010). Agribusiness economics and management. American Journal of Agricultural Economics, 92(2), 554-570.Letchford, J., & Conitzer, V. (2013, July). Solving Security Games on Graphs via Marginal Probabilities. In AAAI. Knoke, T., Hildebrandt, P., Klein, D., Mujica, R., Moog, M., & Mosandl, R. (2008). Financial compensation and uncertainty: using mean-variance rule and stochastic dominance to derive conservation payments for secondary forests. Canadian journal of forest research, 38(12), 3033-3046. Mian, M. A. (2011). Project economics and decision analysis: deterministic models (Vol. 1). PennWell Books. Sadgrove, K. (2016). The complete guide to business risk management. Routledge. Saita, F. (2010). Value at risk and bank capital management: risk adjusted performances, capital management, and capital allocation decision making. Academic Press. Usmani, F., Sarma, M., Usmani, F., & Usmani, F. et al. (2017). Planned Value (PV), Earned Value (EV) & Actual Cost (AC) in Project Cost Management. PM Study Circle - A PMP Exam Preparation Blog. Retrieved 4 August 2017, from https://pmstudycircle.com/2012/05/planned-value-pv-earned-value-ev-actual-cost-ac-analysis-in-project-cost-management-2/ Read More