1. Capital Budgeting Risk Analysis 1Finance - 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 2Finance - 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) 3Finance - Pedro Barroso

4. Example Inputs:Cash Flows Sales (ton)1,800 Year 0Year 1Year 2Year 3 Price per ton5Sales revenues9,000 Variable cost per ton3Variable costs5,400 Fixed cost1,000Fixed costs1,000 CAPEX6,000Depreciation2,000 Life3EBIT600 Tax rate30%Taxes180 Discount rate8%Net income420 OCF2,420 Investment-6,000 Total cash flow-6,0002,420 NPV237 IRR10.17% 4Finance - Pedro Barroso

5. Sensitivity Analysis: Example Calculate NPV (or IRR) with one input varied while keeping all other inputs constant Annual salesVariable costs 237 1,500-8462.51,860 1,8002373.0237 2,0009583.5-1,387 PriceFixed costs 237 4.5-1,387800597 5.02371,000237 5.51,8601,200-124 5Finance - 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 Variable cost Price 2372.534 4.5237-1,387-3,011 51,860237-1,387 5.53,4841,860237 Scenario Summary Current Values:PessimisticExpectedOptimistic Changing Cells: Sales1,8001,5001,8002,000 Price54.555.5 Variable_cost33.532.5 Fixed_cost1,0001,2001,000800 Result Cells: NPV237-3,9132374,927 6Finance - 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 7Finance - Pedro Barroso

8. Break-Even Analysis: Example Break-even sales (ton): Break-even price: 8Finance - 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) 9Finance - 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 10Finance - 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 11Finance - 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 12Finance - Pedro Barroso

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

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

15. Option to Abandon: Example When we include the value of the option to abandon, drilling project should proceed: 15Finance - 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) Year (t)CostPVNPV t NPV 0 020,00025,0005,000 118,00025,0007,0006,364 217,10025,0007,9006,529 316,92925,0008,0716,064 416,76025,0008,2405,628 16Finance - 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 17Finance - Pedro Barroso

18. Decision Trees Do not study Study finance Squares represent decisions to be made (work backward). Circles represent receipt of information, e.g., a test score. The lines leading away from the squares represent the alternatives “C” “A” “B” “E” “D” 18Finance - 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% 19Finance - Pedro Barroso

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

21. Decision Tree: Example Do not test Test Failure Success Do not invest Invest NPV = 3,433.75 NPV = 0 NPV = –91.46 21Finance - 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 22Finance - Pedro Barroso