Break-even Analysis in Budgeting & LP

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

2. Risk Analysis Approaches

3. 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

4. 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”

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

6. 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?

7. 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

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

9. 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

10. 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?

11. 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

12. 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

13. Break-even Parameter Changes for Parity with Peppers

14. 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