Break-even Analysis in Budgeting

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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 Risk Preferences
Unknown Known
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 BudgetsCertainty
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 (? cj)
• RHS Bounding (? bi)
• Technical parameter changes (? aij )
• 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 managers 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