The document discusses several capital budgeting techniques: sensitivity analysis, which examines how changes in assumptions impact NPV; scenario analysis, which considers multiple forecasts simultaneously; and break-even analysis, which determines the sales needed to cover costs. It also discusses real options, noting that NPV underestimates a project's value since managers can adjust in response to changes. Decision trees are presented as a tool to analyze projects with uncertain outcomes.

1. Risk Analysis, Real Options, and Capital Budgeting

2. Chapter Outline 8.1 Sensitivity Analysis, Scenario Analysis, and Break-Even Analysis 8.2 Monte Carlo Simulation 8.3 Real Options 8.4 Decision Trees

3. 8.1 Sensitivity, Scenario, and Break-Even Each allows us to look behind the NPV number to see how stable our estimates are.

4. Sensitivity, Scenario, and Break-Even The projected cash flow often goes unmet in practice, and the firm ends up with a money loser.

5. Sensitivity analysis examines how sensitive a particular NPV calculation is to changes in underlying assumptions . Revenues : Depends on three assumptions - market share , size of jet engine market , and price per engine. Costs: Total cost before taxes = Variable cost + Fixed cost

6. Sensitivity Analysis and Scenario Analysis A table such as Table 8.3 can be used for a number of purposes : It can indicate whether NPV analysis should be trusted It shows where more information is needed

7. Sensitivity Analysis and Scenario Analysis The effect of incorrect estimates on revenues is so much greater than the effect of incorrect estimates on costs, more information on the factors determining revenues might be needed.

8. Sensitivity Analysis and Scenario Analysis However, sensitivity analysis suffers from some drawbacks: It may unwittingly increase the false sense of security among managers; it treats each variable in isolation. Managers frequently perform scenario analysis to minimize this problem.

9. Break-Even Analysis This approach determines the sales needed to break even . It is a useful complement to sensitivity analysis, because it also sheds light on the severity of incorrect forecasts .

10. Break-Even Analysis Accounting Profit (Fixed costs + Depreciation )* (1-T c ) (Sales price-Variable costs)* (1-T c ) Contribution margin: It is the amount that each additional engine contributes to pre-tax profit .

11. Break-Even Analysis EAC = Initial Investment / 5-year annuity factor at 15% (Fixed costs + Depreciation )*(1-T c ) = Fixed costs *(1-T c ) + Depreciation )*( 1-T c ) = Fixed costs *(1-T c ) + 【 Depreciation - Depreciation*T c 】 Fixed costs *(1-T c ) + 【 EAC - Depreciation*T c 】

12. Break-Even Analysis Present Value Break-Even Point: Fixed costs*(1-T c ) + 【 EAC -Depreciation*T c 】 (Sales price-Variable costs)*(1-T c )

13. Break-Even Analysis The EAC of $447.5 million is greater than the yearly depreciation of $300 million , because we implicitly assume that the $1,500 million investment could have been invested at 15%.

14. Break-Even Analysis Depreciation understates the true costs of recovering the initial investment . Thus Companies that break even on an accounting basis are really losing money . They are losing the opportunity cost of the initial investment .

15. 8.3 Real Options NPV analysis ignores the adjustments that a firm can make after a project is accepted. These adjustments are called real options . Thus, NPV underestimates the true value of a project.

16. 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 .

17. Options The Option to Expand Has value if demand turns out to be higher than expected.

18. The Option to Abandon Managers also have the option to abandon existing projects. Abandonment can often save companies a great of money .Thus, the option to abandon increases the value of any potential project. Abandonment options are pervasive in the real world.

19. Timing Options They have value if the underlying variables are changing with a favorable trend.

20. 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. M = NPV + Opt A good example would be comparing the desirability of a specialized machine versus a more versatile machine. If they both cost about the same and last the same amount of time, the more versatile machine is more valuable because it comes with options.

21. 8.4 Decision Trees Two decisions: Whether to develop and test the solar-powered jet engine. Whether to invest for full-scale production following the results of the test.

22. A fundamental problem in NPV analysis is dealing with uncertain future outcomes. Warning : Perhaps a higher discount rate should have been used for the initial test-marketing decision.