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Break-even Analysis in Budgeting & LP AEC 851 – Agribusiness Operations Management Spring, 2006

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Risk Analysis Approaches Risk Preferences UnknownKnown Proba- bilities missing Break-even - Budgets - Programming (LP) Scenario analysis Minimax, safety-first, etc. Proba- bilities present Risk efficiency (stochastic dominance) LP sensitivity w/ probability Stochastic budgeting Risk programming - Quadratic programming-QP - MOTAD, chance-constraind Generalized stochastic dominance

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Simplest level: Assumptions for Variants of Enterprise Budgeting Static, single period analysis –No major investments required to compare –Data adjusted to “typical” year –Investments where cash flow varies over time are best evaluated with NPV or other capital budgeting Known parameters, except for those being varied

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Single-enterprise Break-even Budgets Notation –VC = Variable Cost per unit resource (eg, land) –TC = Total Cost per unit resource –Y = Output per unit resource –P = Price per unit product –OC = Opportunity cost (PY-TC) –Alternative enterprises: D = “Defender” C = “Challenger”

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Single commodity break-even levels How to calculate a break-even value? Short-run Break-even Price of Y: Long-run Break-even Price:

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Comparing alternative enterprises Break-even price for “challenger”: Break-even output for “challenger”: How does the equation underlying these break- even rule differ from the single BE one?

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Accounting for Risk in Budgets: Certainty Equivalents Certainty equivalent (CE) = Value that leaves decision maker indifferent between a value for certain and a risky choice Break-even (or enterprise) budgets: –In comparing less risky enterprise (grow soy beans) to more risky one (grow navy beans), elicit CE for added risk and add CE to costs

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Sensitivity Analysis Sensitivity Analysis with Break-even values: –Given a BE value, what is the likelihood that it is met or not met?

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Risk Analysis in LP Sensitivity (post-optimality) analysis –Max cx, s.t. Ax b Objective function Ranging ( c j ) RHS Bounding ( b i ) Technical parameter changes ( a ij ) Individual parameters or groups for scenarios Parametric programming –Identifies when changes in a given parameter change the activity mix in optimal solution Risk programming

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From LP Sensitivity Analysis to LP Break-even How much change in parameter would maintain optimal obj. function level? –Price change –Productivity change –Resource availability change How feasible would such a change be? Is change within manager’s control?

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Florida Vegetable Data Example Excel Solver for Sensitivity Analysis Key questions –To what parameters is the solution most sensitive? –How much would those parameters have to change in order to change the solution? –How much would the solution change? Pushing beyond standard sensitivity analysis

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Ways to Analyze Changes in other parameters needed in order to reach parity with a given enterprise –Break-even parameter change Objective function responses to standard percentage changes in key parameters –Parametric programming measures response rate

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Break-even Parameter Changes for Parity with Peppers Parameter Break-even Change (%)

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Breakeven LP for Risk Mgt No knowledge of probabilities needed Informs risk management decisions by: –Where (manageable) risk matters most Resource levels Prices –Potential payoff to reducing uncertainty –Second best alternatives

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