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Capital Budgeting Risk Analysis

Capital Budgeting Risk Analysis. Sensitivity, Scenario, and Break-Even. Allows us to look behind the NPV number to see how stable our estimates are

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Capital Budgeting Risk Analysis

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  1. Capital BudgetingRisk Analysis Finance - Pedro Barroso

  2. Sensitivity, Scenario, and Break-Even • Allows us to look behind the NPV number to see how stable our estimates are • When working with spreadsheets, try to build your model so that you can adjust variables in a single cell and have the NPV calculations update accordingly Finance - Pedro Barroso

  3. Example • Projected annual sales: 1,800 ton • Price: 5 per ton • Variable costs: 3 per ton • Fixed costs: 1,000 per year • Initial investment (fixed assets) of 6,000 with life of 3 years and salvage value of 0 • No investment in working capital • Inflation: 0% • Discount rate: 8% • Tax rate: 30% (losses can be offset elsewhere in firm) Finance - Pedro Barroso

  4. Example Finance - Pedro Barroso

  5. Sensitivity Analysis: Example • Calculate NPV (or IRR) with one input varied while keeping all other inputs constant Finance - Pedro Barroso

  6. Scenario Analysis: Example • A variation on sensitivity analysis is scenario analysis • Calculate NPV (IRR) with more than one input varied while keeping all other inputs constant Finance - Pedro Barroso

  7. Break-Even Analysis: Example • Another way to examine variability in our forecasts • What is the minimum (maximum) input value such that NPV is at least zero (IRR = discount rate)? • Break-even analysis: • Annual sales (min): 1,734 ton • Price (min): 4.927 • Variable cost (max): 3.073 • Fixed cost (max): 1,131 Finance - Pedro Barroso

  8. Break-Even Analysis: Example • Break-even sales (ton): • Break-even price: Finance - Pedro Barroso

  9. Real Options • One of the fundamental insights of modern finance theory is that options have value • Because corporations make decisions in a dynamic environment, they have options that should be considered in project valuation • Traditional NPV does not include options value (always zero or positive) Finance - Pedro Barroso

  10. Real Options • Option to Expand • Has value if demand turns out to be higher than expected • Option to Abandon • Has value if demand turns out to be lower than expected • Option to Delay • Has value if the underlying variables are changing with a favorable trend Finance - Pedro Barroso

  11. Discounted CF and Options • We can calculate the market value of a project as the sum of the NPV of the project without options and the value of the managerial options implicit in the project: NPV + Options Example: Comparing a specialized machine versus a more versatile machine; if they both cost about the same and last the same amount of time, more versatile machine is more valuable because it comes with options Finance - Pedro Barroso

  12. Option to Abandon: Example • Suppose we are drilling an oil well. The drilling rig costs $300 today, and in one year the well is either a success or a failure • Outcomes are equally likely. Discount rate is 10% • PV of the successful payoff at time one is $575 • PV of the unsuccessful payoff at time one is $0 Finance - Pedro Barroso

  13. Option to Abandon: Example Traditional NPV would indicate rejection of project: Finance - Pedro Barroso

  14. Success: Payoff = 500 Sit on rig; stare at empty hole: Payoff = 0 Drill Failure Do not drill Sell the rig; salvage value = 250 Option to Abandon: Example Traditional NPV analysis overlooks the option to abandon. Firm has two decisions to make: drill or not, abandon or stay Finance - Pedro Barroso

  15. Option to Abandon: Example • When we include the value of the option to abandon, drilling project should proceed: Finance - Pedro Barroso

  16. Option to Delay: Example • Project can be undertaken in any of the next 4 years; discount rate is 10% • Regardless when the time the project is launched it generate a cash flow of 2,500 forever • NPV at the time of launch steadily rises; best time to launch the project is in year 2 (highest NPV when judged today) Finance - Pedro Barroso

  17. Decision Trees • Allow us to graphically represent the alternatives available to us in each period and the likely consequences of our actions • This graphical representation helps to identify the best course of action Finance - Pedro Barroso

  18. “A” “B” “C” “D” “E” Decision Trees Squares represent decisions to be made (work backward). Circles represent receipt of information, e.g., a test score. Study finance The lines leading away from the squares represent the alternatives Do not study Finance - Pedro Barroso

  19. Decision Tree: Example • Stewart Pharmaceuticals Corp is considering investing in the development of a drug that cures the common cold • A corporate planning group has recommended that the firm should go ahead with the test and development phase • This preliminary phase will last one year and cost $1,000; There is a 60% chance that tests will prove successful • If initial tests are successful, Stewart Pharmaceuticals can go ahead with full-scale production. This investment phase will cost $1,600. Production will occur over the following 4 years with a cash flow of $1,588 • If initial tests are unsuccessful, annual cash flow is $475.9 • Discount rate is 10% Finance - Pedro Barroso

  20. Decision Tree: Example • NPV following successful test: • NPV following unsuccessful test: Finance - Pedro Barroso

  21. Invest Decision Tree: Example Invest NPV = 3,433.75 Success Do not invest Test NPV = 0 Failure Do not test NPV = –91.46 Finance - Pedro Barroso

  22. Decision Tree: Example • Decision to invest: • Test successuful (probability 60%): Invest as NPV = 3,433.75 > 0 • Test unsuccessuful (probability 40%): Not invest as NPV = -91.46 < 0 • Decision to test: • Expected payoff at year 1: • NPV of testing at year 0: • NPV is positive, so we should make the test Finance - Pedro Barroso

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