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4. Sensitivity Analysis Scenario Analysis Monte Carlo Simulation Decision Trees Scenario and Simulation Assessments The Role of Risk in Capital Budgeting > Scenario and Simulation Assessments Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/finance?campaign_content=book_192_section_99&campaign_term=Finance&utm_campaign=powerpoint&utm_medium=dir ect&utm_source=boundless

5. Since variations from the base assumptions are expected, businessmen and women want to know how much their output (eg., revenue) will be affected by the variations. Sensitivity analysis helps find the optimal levels for inputs (eg., raw material prices, number of employees, sales price). Sensitivity analysis is a statistical tool based on seeing how inputs and parameters affect outputs. Generally, each input is changed one at a time to see how it affects output. However, this does not account for interconnectedness between inputs; they may not be independent variables. Sensitivity Analysis Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/finance/textbooks/boundless-finance-textbook/the-role-of-risk-in-capital-budgeting-12/scenario-and-simulation-assessments- 99/sensitivity-analysis-426- 3830?campaign_content=book_192_section_99&campaign_term=Finance&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess Sensitivity of a Variable View on Boundless.com The Role of Risk in Capital Budgeting > Scenario and Simulation Assessments

6. Scenario analysis is designed to see the consequences of an action under different sets of factors. For example, it shows how an investment's NPV would differ under high and low inflation. Scenarios should be feasible enough to provide an accurate picture of the outcomes. A "good" scenario for an investor should not include winning the lottery because, though good, it is neither probable nor realistic for analyzing possible results. Many scenario analyses use 3 scenarios: base case, worst case and best case. However, the number and conditions of the scenarios in each analysis can vary. Scenario Analysis Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/finance/textbooks/boundless-finance-textbook/the-role-of-risk-in-capital-budgeting-12/scenario-and-simulation-assessments- 99/scenario-analysis-427- 7232?campaign_content=book_192_section_99&campaign_term=Finance&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess Scenario Analysis View on Boundless.com The Role of Risk in Capital Budgeting > Scenario and Simulation Assessments

7. The statistical distribution is estimated for each input (eg. inflation rate, market risk). Then, simulations are run to see how constantly changing inputs (based on their distribution) affect the output. The outputs are averaged to find the estimated output. Monte Carlo simulations are great for when there are multiple inputs that can all change and may be unrelated. Monte Carlo simulations can be applied in many areas of business, such as bond pricing, but are especially useful when estimating the "base case" is difficult to do by hand. Monte Carlo Simulation Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/finance/textbooks/boundless-finance-textbook/the-role-of-risk-in-capital-budgeting-12/scenario-and-simulation-assessments- 99/monte-carlo-simulation-428- 3831?campaign_content=book_192_section_99&campaign_term=Finance&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess Monte Carlo Simulation View on Boundless.com The Role of Risk in Capital Budgeting > Scenario and Simulation Assessments

8. Decision trees look similar to flow charts, except they are designed to pick the most optimal strategy. There are three types of nodes on a decision tree: decision nodes, chance nodes, and end nodes. Decision trees are solved from top to bottom in order to determine the most optimal strategy. Sometimes, there may not be an obvious optimal strategy, but the tree is still useful for mapping out the options faced and their costs/benefits. Decision Trees Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/finance/textbooks/boundless-finance-textbook/the-role-of-risk-in-capital-budgeting-12/scenario-and-simulation-assessments- 99/decision-trees-429- 4826?campaign_content=book_192_section_99&campaign_term=Finance&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess Decision Tree View on Boundless.com The Role of Risk in Capital Budgeting > Scenario and Simulation Assessments

9. Free to share, print, make copies and changes. Get yours at www.boundless.com Appendix

10. Key terms analysis A process of dismantling or separating into constituent elements in order to study the nature, function, or meaning. distribution A probability distribution; the set of relative likelihoods that a variable will have a value in a given interval. node A vertex point on a decision tree. Other branches may extend from it; if none do, it is an end node. parameter A variable kept constant during an experiment, calculation, or similar. scenario A set of factors that can affect the consequences of an action. The environment. scenario analysis a process of analyzing possible future events by considering alternative possible outcomes sensitivity analysis the study of how the uncertainty in the output of a mathematical model or system can be apportioned to different sources of uncertainty in its inputs Free to share, print, make copies and changes. Get yours at www.boundless.com The Role of Risk in Capital Budgeting

11. Sensitivity of a Variable Sensitivity analysis determines how much an output is expected to change due to changes in a variable or parameter. In this case, the output (y-axis) decreases exponentially with an increase in the input (x-axis). This is mapped out for each input. Free to share, print, make copies and changes. Get yours at www.boundless.com Flickr. "All sizes | exponential curve data | Flickr - Photo Sharing!." CC BY-SA http://www.flickr.com/photos/rlodan01/4387091613/sizes/m/in/photostream/ View on Boundless.comCC BY-SAhttp://www.flickr.com/photos/rlodan01/4387091613/sizes/m/in/photostream/View on Boundless.com The Role of Risk in Capital Budgeting

12. Decision Tree This decision tree highlights the outcomes of different investing strategies. Next to the terminal nodes is blue text with the yield and gain. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia. "Investment decision Insight." Public domain http://en.wikipedia.org/wiki/File:Investment_decision_Insight.png View on Boundless.comPublic domainhttp://en.wikipedia.org/wiki/File:Investment_decision_Insight.pngView on Boundless.com The Role of Risk in Capital Budgeting

13. Scenario Analysis This scenario analysis shows how changes in factors like yield and transport cost can affect profits. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikimedia. "Sensitivity-analysis." CC BY-SA http://commons.wikimedia.org/wiki/File:Sensitivity-analysis.png View on Boundless.comCC BY-SAhttp://commons.wikimedia.org/wiki/File:Sensitivity-analysis.pngView on Boundless.com The Role of Risk in Capital Budgeting

14. Monte Carlo Simulation By running many simulations based on the probability or distribution of an input (x), the analyst can see the average output (y). This is done for multiple inputs at once to find out how they affect the output. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikimedia. "File:Spurious regression.svg - Wikimedia Commons." CC BY-SA http://commons.wikimedia.org/w/index.php?title=File:Spurious_regression.svg&page=1 View on Boundless.comCC BY-SA http://commons.wikimedia.org/w/index.php?title=File:Spurious_regression.svg&page=1View on Boundless.com The Role of Risk in Capital Budgeting

15. Free to share, print, make copies and changes. Get yours at www.boundless.com The Role of Risk in Capital Budgeting Which of the following is a characteristic of sensitivity analysis? A) Sensitivity analysis normally accounts for all interactions between inputs. B) Generally, sensitivity analysis allows you to change multiple variables at a time. C) All of these answers. D) All of the inputs and parameters are connected via an algorithm to produce the output.

16. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ The Role of Risk in Capital Budgeting Which of the following is a characteristic of sensitivity analysis? A) Sensitivity analysis normally accounts for all interactions between inputs. B) Generally, sensitivity analysis allows you to change multiple variables at a time. C) All of these answers. D) All of the inputs and parameters are connected via an algorithm to produce the output.

17. Free to share, print, make copies and changes. Get yours at www.boundless.com The Role of Risk in Capital Budgeting Which of the following is a characteristic of scenario analysis? A) Scenario analysis is a strategic process of analyzing decisions by considering alternative outcomes. B) It is a predictive mechanism. C) Most scenario analyses consider two different scenarios: best and worst case. D) All of these answers.

18. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ The Role of Risk in Capital Budgeting Which of the following is a characteristic of scenario analysis? A) Scenario analysis is a strategic process of analyzing decisions by considering alternative outcomes. B) It is a predictive mechanism. C) Most scenario analyses consider two different scenarios: best and worst case. D) All of these answers.

19. Free to share, print, make copies and changes. Get yours at www.boundless.com The Role of Risk in Capital Budgeting Which of the following is a characteristic of Monte Carlo simulations? A) Only significant factors are assigned a probability. B) The Monte Carlo method only requires that you run one simulation. C) The Monte Carlo method is able to handle multiple moving inputs. D) All of these answers.

20. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ The Role of Risk in Capital Budgeting Which of the following is a characteristic of Monte Carlo simulations? A) Only significant factors are assigned a probability. B) The Monte Carlo method only requires that you run one simulation. C) The Monte Carlo method is able to handle multiple moving inputs. D) All of these answers.

21. Free to share, print, make copies and changes. Get yours at www.boundless.com The Role of Risk in Capital Budgeting A company is setting up a decision tree and wants to record an event. This event will result in one of three possibilities. What occurs will be determined by whether market interest rates increase or decrease. This event should be signified by ____. A) a Decision node. B) an End node. C) a Chance node. D) an Initial node.

22. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ The Role of Risk in Capital Budgeting A company is setting up a decision tree and wants to record an event. This event will result in one of three possibilities. What occurs will be determined by whether market interest rates increase or decrease. This event should be signified by ____. A) a Decision node. B) an End node. C) a Chance node. D) an Initial node.

23. Attribution Wikibooks. "Operations Research/Sensitivity analysis." CC BY-SA 3.0 http://en.wikibooks.org/wiki/Operations_Research/Sensitivity_analysisCC BY-SA 3.0 http://en.wikibooks.org/wiki/Operations_Research/Sensitivity_analysis Wikipedia. "Sensitivity analysis." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Sensitivity_analysisCC BY-SA 3.0http://en.wikipedia.org/wiki/Sensitivity_analysis Wikipedia. "Sensitivity analysis." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Sensitivity_analysisCC BY-SA 3.0http://en.wikipedia.org/wiki/Sensitivity_analysis Wiktionary. "parameter." CC BY-SA 3.0 http://en.wiktionary.org/wiki/parameterCC BY-SA 3.0http://en.wiktionary.org/wiki/parameter Wikipedia. "Monte Carlo methods in finance." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Monte_Carlo_methods_in_financeCC BY-SA 3.0http://en.wikipedia.org/wiki/Monte_Carlo_methods_in_finance Wikipedia. "Monte carlo simulation." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Monte_carlo_simulation#Finance_and_businessCC BY-SA 3.0http://en.wikipedia.org/wiki/Monte_carlo_simulation#Finance_and_business Wikipedia. "Monte Carlo methods for option pricing." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Monte_Carlo_methods_for_option_pricingCC BY-SA 3.0 http://en.wikipedia.org/wiki/Monte_Carlo_methods_for_option_pricing Wiktionary. "distribution." CC BY-SA 3.0 http://en.wiktionary.org/wiki/distributionCC BY-SA 3.0http://en.wiktionary.org/wiki/distribution Wikipedia. "Decision tree." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Decision_treeCC BY-SA 3.0http://en.wikipedia.org/wiki/Decision_tree Boundless Learning. "Boundless." CC BY-SA 3.0 http://www.boundless.com//physics/definition/nodeCC BY-SA 3.0http://www.boundless.com//physics/definition/node Wikibooks. "Future/Scenario." CC BY-SA 3.0 http://en.wikibooks.org/wiki/Future/ScenarioCC BY-SA 3.0http://en.wikibooks.org/wiki/Future/Scenario Wikipedia. "Scenario analysis." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Scenario_analysisCC BY-SA 3.0http://en.wikipedia.org/wiki/Scenario_analysis Wikipedia. "Scenario analysis." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Scenario_analysisCC BY-SA 3.0http://en.wikipedia.org/wiki/Scenario_analysis Boundless Learning. "Boundless." CC BY-SA 3.0 http://www.boundless.com//marketing/definition/analysisCC BY-SA 3.0http://www.boundless.com//marketing/definition/analysis Wiktionary. "scenario." CC BY-SA 3.0 http://en.wiktionary.org/wiki/scenarioCC BY-SA 3.0http://en.wiktionary.org/wiki/scenario Free to share, print, make copies and changes. Get yours at www.boundless.com The Role of Risk in Capital Budgeting