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Uncertainty Analysis

Uncertainty Analysis. November 13, 2013. Making Confident Decisions in an Uncertain World. If we have probability estimates for different futures, we can undertake risk analysis. Lacking probability estimates, we can try: break-even analysis sensitivity analysis scenario analysis.

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Uncertainty Analysis

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  1. Uncertainty Analysis November 13, 2013

  2. Making Confident Decisions in an Uncertain World If we have probability estimates for different futures, we can undertake risk analysis Lacking probability estimates, we can try: break-even analysis sensitivity analysis scenario analysis

  3. Break-Even Analysis The purpose of break-even analysis is to focus our uncertainty: Rather than ask, ``What is the value of x?’’ we ask ``Is x greater than a threshold x0?’’ That is to say, we set an aspiration level for x

  4. Background to break-even analysis: Profit Variable Costs Royalties, spoilage, packaging, maintenance, direct labour, raw material, direct supplies, direct supervision, sales commissions Fixed Costs Rent, Interest, Research, Insurance, Depreciation, Property Taxes, Advertising Budget, Technical Services, Executive Salaries Selling price of 1 unit

  5. Total Revenue Profit Total Costs Variable Costs Fixed Costs BEP Units sold

  6. Contribution = Selling Price – Variable Cost/Unit So BEP = Fixed Costs/Contribution

  7. Profit Margin The profit margin is an indicator of the health of an organization. Margin = Gross Annual Profit/Fixed Annual Costs or Actual Sales – Break-Even Sales Margin = Break-Even Sales

  8. A pie company has two employees who each earn $30,000 a year, and pays $10,000 rent every year. The ingredients for a pie, including the gas to cook it, cost $10 per pie. If pies are sold at $20 each, the break-even point for the company (calculated pre-tax) is: • 3,500 pies • 4,000 pies • 6,000 pies • 7,000 pies

  9. If the company in the previous question pays taxes at 50%, the (after-tax) breakeven point is: • 7,000 pies • 8,000 pies • 12,000 pies • 14,000 pies

  10. How can this company increase profits? Selling Price Profit Total Cost Volume of Sales

  11. New Selling Price Profit Profit TotalCost Total Cost a) Increase price

  12. Profit Profit Profit TotalCost Total Cost Total Cost b) Increase sales

  13. Profit Profit Profit Profit Total Cost TotalCost Total Cost Total Cost c) Decrease costs and price

  14. Example: A firm makes units that sell for $35,000 each. Variable costs are $20,000/unit and fixed costs are $600,000. The plant can produce 80 units a year, but is currently only working at 60% capacity. The firm is considering reducing selling price by $2,000/unit, adding a feature to each unit that increases variable costs by $1,000, and spending $120,000 on ads to increase sales. If these measures increase sales to 72 units per year, what happens to the BEP and the profit margin? Suppose instead the firm went to 200% capacity and sold the extra units at $25K each, how would this affect gross profits?

  15. Non-Linear Break-Even Analysis The cost of making one more unit is usually not a fixed amount. It typically shows a minimum as production goes from under-utilised to over-utilised. Marginal cost Unit costs No. Produced

  16. Non-Linear Break-Even Analysis As a result, the average variable cost also increases… Marginal cost Unit costs Average variable cost No. Produced

  17. Non-Linear Break-Even Analysis However, the average fixed cost always goes down… Marginal cost Unit costs Average variable cost Average fixed cost No. Produced

  18. Non-Linear Break-Even Analysis So the average total cost of production displays a minimum… Marginal cost Average total cost Unit costs Average variable cost Average fixed cost No. Produced

  19. Non-Linear Break-Even Analysis Similarly, in order to increase sales beyond a certain level, it may be necessary to drop the selling price Revenue and costs Total Revenue = 21000n0.5 n, No. Produced

  20. Non-Linear Break-Even Analysis The fixed costs must be met. Revenue and costs Fixed Costs No. Produced

  21. Non-Linear Break-Even Analysis Including the variable costs, we see there are two break even points Variable costs Revenue and costs BEP BEP No. Produced

  22. Sensitivity Analysis Having solved a problem, we determine the sensitivity of the solution to changes in the problem parameters. Hence we can decide whether and when to do further research. Example: a project has an initial cost of $170,000 and is expected to yield annual receipts of $35,000. There will be a salvage value of $20,000 after ten years, and the annual operating cost will be $3,000. If the MARR is 13%, should the investment be made?

  23. 30,000 20,000 10,000 -30% -20% -10% +10% +20% +30% -10,000 Salvage costs have little effect -20,000 -30,000

  24. 30,000 20,000 10,000 -30% -20% -10% +10% +20% +30% -10,000 Nor do the running costs… -20,000 -30,000

  25. 30,000 20,000 10,000 -30% -20% -10% +10% +20% +30% -10,000 But the solution is sensitive to the worth of the annual receipts… -20,000 -30,000

  26. 30,000 20,000 10,000 -30% -20% -10% +10% +20% +30% -10,000 And to the assumed life of the equipment…. -20,000 -30,000

  27. 30,000 20,000 10,000 -30% -20% -10% +10% +20% +30% -10,000 -20,000 Lastly, the MARR has an effect on the present value. -30,000

  28. Another way of presenting these results is by plotting acceptance-rejection zones. Consider the same proposal, and compare the effect of annual receipts, x, and costs, y, on the EAW: EAW = -130,000(A/P,13,10)+35,000(1+x) -3,000(1+y)+20,000(A/F,13,10) = 1757 +35,000x – 3,000y

  29. y-axis: Disbursements +30% Rejection Zone (EAW < 0) +20% +10% -30% -20% -10% +10% +20% +30% x-axis: Receipts -10% -20% -30%

  30. Isoquants An isoquant is a curve showing what combinations of two parameters would yield the same present worth 15 Accept 10 Life of Asset Reject 5 30,000 35,000 40,000 Annual Receipts

  31. Comparison of Alternatives Based on a ten-year study period, both alternatives look about the same. How sensitive is this conclusion to the length of the study period?

  32. 30,000 Alt. 1 20,000 10,000 Present Worth Alt. 2 5 10 15 20 -10,000 Study Period -20,000 -30,000

  33. Scenario Analysis …also sometimes known as the `Goldilocks’ method…

  34. Scenario Analysis We compare the base case with plausible `best case’ and `worst case’ scenarios:

  35. Scenario Analysis We compare the base case with plausible `best case’ and `worst case’ scenarios:

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