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**Base Case and Sensitivity Analysis – “Waterfall and Tornadoes”**

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**We create a model to evaluate alternatives and test the importance of uncertainties.**

Strategy Table Decision Structure Deterministic Analysis Probabilistic Appraisal Initial Situation Iteration Influence Diagram 1 2 3 4 5 Deterministic Model A B C Deterministic Sensitivity Decision Tree Probability Distributions Value of Information Decision Quality Speaker’s Notes: This is the phase that many companies skip because they don’t have an effective language and set of skills for dealing with the uncertainty. But it’s really not that hard! There will be nothing more than simple algebra in this section. 2.05-I • Deterministic & Sensitivity Analysis

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**We will discuss using spreadsheets for deterministic (base case) analysis and sensitivity analysis.**

Base Case Analysis and Waterfall Diagrams Sensitivity Analysis and Tornado Diagrams Using Sensitivity Results for Insight Speaker’s Notes: “This section suggests three different types of analysis once a spreadsheet model has been constructed. The first is “base case” analysis; it is deterministic, and only base case values are used. This analysis will include bar charts, waterfalls, and cash flow plots.” “The second type of analysis—sensitivity analysis—produces tornado diagrams, which show which uncertain variables are the greatest contributors to risk.” 2.05-I • Deterministic & Sensitivity Analysis

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**Base case* analysis gives an initial comparison of each alternative.**

* All variables set at their “base case” values 1 2 3 4 5 A B C Spreadsheet Model Base Case Inputs Base Case Outputs 1 2 3 4 Speaker’s Notes: The slide says it all. The important question is “Why is #3 best?” 2.05-I • Deterministic & Sensitivity Analysis

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**Annual Cash Flow ($ millions)**

Another base case output—the cash flow plot—illustrates cash needs and yields from each alternative under consideration. –60 –50 –40 –30 –20 –10 10 20 30 1 2 3 4 5 6 7 8 9 Year Annual Cash Flow ($ millions) Run Out Moderate Investment Aggressive Investment Speaker’s Notes: This is modified from the original O&G example cited below to reflect a mature products example. “Decision makers often need to see the pattern of cash flows over time. This graph shows that there would be some expenditures in the first year for each strategy. In the ‘Run Out’ strategy these expenditures are to complete the production wells in the field. In the other two strategies the initial investment involved both production and injector wells.” “Notice the increased level of production for the water floods. In the aggressive case the investment is spread over two years.” Note: the plot does not show the break-even point; however the analysis shows that the waterflood will begin to pay back in 3-5 years. The plot shows how moderate or aggressive investment extends mature product life, with economic break-even in 3–5 years. 2.05-I • Deterministic & Sensitivity Analysis

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**Initial evaluation with the model also yields important insights into sources of value and risk.**

Base Case Waterfall of Value Sources of Value 1 2 3 4 5 A B C Spreadsheet Model Uncertainty Range Tornado Diagram Sources of Risk Speaker’s Notes: The slide says it all. 2.05-I • Deterministic & Sensitivity Analysis

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Base case evaluation shows the net value of each alternative, in this case dealing with mature products investment alternatives. Net Present Value ($ millions) 50 100 150 200 250 300 “Run Out” 71 Moderate Investment 291 Aggressive Investment 280 Speaker’s Notes: This is modified from the original O&G example cited below to reflect a mature products example. “This is an oil and gas production example from one of our projects. The made-up name of the oil field is “Seco Valley” (Español for Dry Valley). The field was still being developed (I.e. wells drilled) but it was clear that oil and gas production would decline faster than originally projected. So the operator was considering a “waterflood,” which would inject water into the field to increase production by forcing out more oil and gas. They considered two levels of waterflood; the “aggressive” approach involved drilling twice as many injector wells. The ‘Run Out’ strategy did not include a waterflood.” We show the analysis results here using a horizontal bar chart. A vertical chart would accomplish the same objective. “The deterministic analysis of three alternatives shows that the moderate waterflood was slightly better than the aggressive approach. What do you suppose is causing that result?” Why is the value of the aggressive investment less than the moderate investment? 2.05-I • Deterministic & Sensitivity Analysis

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**Net Present Value ($ millions)**

This horizontal “waterfall chart” shows incremental sources of value and cost for each strategy. Net Present Value ($ millions) 200 400 600 800 1,000 Run Out 71 Halo Revenues Product Revenues Key Added Value Promotion SF Reduced Value Moderate 291 Investment Product Revenues Halo Revenues SF Pr. Aggressive Speaker’s Notes: This is modified from the original O&G example to reflect a mature products example. Present the chart. SF = Sales Force, Pr =Promotion This is a horizontal waterfall chart. We usually draw them vertically, but this one has a lot of text to display, and it is easier to read horizontally. More on that later. There is a note at the bottom about subsidence losses. Waterflood would reduce the risk of subsidence, which means the surface collapse that damages wells. Reducing subsidence was originally one of the motivations for the waterflood. The analysis shows that the benefit of reducing subsidence was small. Investment 280 Although typically drawn vertically, this orientation simplifies labeling. 2.05-I • Deterministic & Sensitivity Analysis

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**The waterfall chart can “break out” the base case value added or lost from each major source.**

Business context: Purchase an existing business, add value, then sell. Value from Future Sale Required Investment Net Present Value Contributions to Profit Base Case NPV Market Growth New Products Fixed Costs Current Contribution Speaker’s Notes: Here is a more typical waterfall chart. By the way, we saw McKinsey consultants using the graph very effectively and started using it ourselves. The formal name they give it is “Sources of Change” diagram—informally the “waterfall.” If you imagine water flowing from right to left, it looks like a waterfall. At least as much as a tornado looks like a tornado. The example is from a company that was making equity investments in various businesses. They would make an vestment in the company, and then see various forms of returns. The investment was larger than the current profits of the company, but there were increases in value due to market growth for existing products and from market growth. The investor also believed that the future value of the business (including market growth and new products) would make the company attractive to other investors so that it could be sold at a significant profit. We often use these charts in the first decision board meeting where analytical results are presented. They provide a lot of insight into the sources of value in the business. 2.05-I • Deterministic & Sensitivity Analysis

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**Corresponding Influence Diagram**

The elements of a waterfall correspond to the “value centers” of the influence diagram. Net Present Value NPV Waterfall of Value Corresponding Influence Diagram Service Fixed Overhead Base Case NPV Licensing Required Investment Licensing Contribution Revenues Commission Costs Fixed Overhead Consulting Revenues Service Contribution Installation Costs Speaker’s Notes: By “value centers” we mean the contributors to value in the business. These could be products, business units, geographic regions, etc. These can be identified in an influence diagram and then quantified in the waterfall. It’s a good idea to sketch the waterfalls you’d like to produce before you start modeling. The modeler needs to know which intermediate results will be needed in order to plot the desired waterfalls. It’s best to “sketch” the waterfall in parallel with developing the influence diagram. 2.05-I • Deterministic & Sensitivity Analysis

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**The choice of “value centers” depends on the business context and the strategic decisions.**

Retail chain Existing stores New locations Biotech product company Product #1 Product #2 Upcoming product launch Research pipeline Global expansion opportunity North American contribution Europe Asia/Pacific Other regions Business portfolio Business unit, group, or sector #1 Business unit, group, or sector #2 Speaker’s Notes: The slide says it all. Think of value centers as primary market segments or business centers or components of value, not cost centers. 2.05-I • Deterministic & Sensitivity Analysis

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**The waterfall is a good way to reconcile changes in a strategy’s valuation over time.**

Revised Valuation June 15 Competitor Exits Increase Fixed Overhead Net Present Value Data Revisions Revised Valuation May 27 Initial Valuation Speaker’s Notes: It happens every time. You’ve presented results in an early decision board meeting, and then by the next meeting the results change. Here’s a way to reconcile the numbers. 2.05-I • Deterministic & Sensitivity Analysis

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**Contributions to Profit**

Create the waterfall by working “backwards,” incrementally turning off sources of value. Value from Future Sale 2 Contributions to Profit Base Case Value 1 Product C 4 NPV Overhead 3 Product B 4 5 Required Investment Product A Step 1 Record base case NPV. Step 2 Change future sales value to zero; record NPV. Step 3 Set fixed and overhead costs to zero; record NPV. Step 4 Switch off product contributions one by one; record each NPV. Step 5 With all products switched off, NPV should equal the required investment. Speaker’s Notes: Here’s the way to compute the numbers for the waterfall. Think of it as starting with the base case result, and systematically “turning off” elements of value. Now you see why the model has to have the right “switches” in it. 2.05-I • Deterministic & Sensitivity Analysis

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**One note about style: use short phrases on a “vertical bar” waterfall.**

sometimes. phrases can tell a powerful story Net Present Value Speaker’s Notes: This slide and the following one encourage participants to think about how much they plan to write on the waterfall… You might be tempted to rotate text to add more words. 2.05-I • Deterministic & Sensitivity Analysis

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**Sideways text is not effective,**

Vertical text is OK in books and handouts, but it’s not effective in presentations. unless lying down! your audience happens to be Sideways text is not effective, Speaker’s Notes: …and choose how they will lay out the slide. 2.05-I • Deterministic & Sensitivity Analysis

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**The horizontal waterfall format accommodates many bars and lots of text.**

Net Present Value Look at all arrows & neat stuff you can write on this waterfall chart now that it’s oriented the “other” way. You run the risk of boring your audience of course, but if you write like Charles Dickens, you might consider this form of waterfall. You can also write in the arrow, or use text to help emphasize direction: Left! Right! And your audience doesn’t have to lie down! In here! Speaker’s Notes: The slide says it all. 2.05-I • Deterministic & Sensitivity Analysis

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**Uncertainties that Increase Value Uncertainties that Decrease Value**

The waterfall shows only base case values—it is equally important to understand which factors drive value higher or lower. Uncertainties that Increase Value Value from Future Sale Contributions to Profit Uncertainties that Decrease Value NPV Product C Product B Overhead Base Case Value Product A Speaker’s Notes: The slide says it all. It’s here because some people get so wrapped up in the contributions to value that they forget about risk. Required Investment 2.05-I • Deterministic & Sensitivity Analysis

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**We will discuss using spreadsheets for deterministic (base case) analysis and sensitivity analysis.**

Base Case Analysis and Waterfall Diagrams Sensitivity Analysis and Tornado Diagrams Using Sensitivity Results for Insight Speaker’s Notes: “This section suggests three different types of analysis once a spreadsheet model has been constructed. The first is “base case” analysis; it is deterministic, and only base case values are used. This analysis will include bar charts, waterfalls, and cash flow plots.” “The second type of analysis—sensitivity analysis—produces tornado diagrams, which show which uncertain variables are the greatest contributors to risk.” 2.05-I • Deterministic & Sensitivity Analysis

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**What do analysts in companies typically do when they encounter uncertainties?**

Ignore them Run three cases: base case, best case, worst case How good is “best?” How bad is “worst?” Make an “assumption” and proceed. The “easy way out” Are these justified? A “tornado” analysis provides the justification you need for leaving variables at their base values versus including their uncertainty explicitly in your analysis. 2.05-I • Deterministic & Sensitivity Analysis

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**Primary Sources of Risk**

Sensitivity (“tornado”) analysis identifies the primary sources of risk, which are then analyzed using probabilistic analysis. Tornado Many Uncertainties Primary Sources of Risk Structure Deterministic Analysis Probabilistic Analysis Appraisal Decision Initial Situation Speaker’s Notes: Try to have participants visualize a difficult situation they’re dealing with. Are there many uncertainties? Do they know which are the primary sources of risk? Iteration We also typically reassess ranges for the top bars in the tornado. 2.05-I • Deterministic & Sensitivity Analysis

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**Single-variable sensitivity analysis determines the change in model output when one input changes.**

Spreadsheet Model A B 1 INPUT Base Case Low Case 8% -6 High Case 28% 134 2 Market Share 20% NPV ($ MM) 75 OUTPUT 43 44 Swing 140 Speaker’s Notes: This example is from a drug development decision. 2.05-I • Deterministic & Sensitivity Analysis

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**Net Present Value ($ millions)**

A “tornado diagram” graphically depicts the variables’ contributions to uncertainty in NPV. Net Present Value ($ millions) -50 50 100 150 200 Base Value = 75 Price per dose Market Share Doses per Day Prevalence Rate Compliance Treatment Rate Development Cost COGS (%Rev) Uptake curve length Annual Price change $1.50 $6.00 8% 28% 1 3 1.5% 3.0% 30.0% 70.0% 60.0% 140.0 60.0 30% 15% 7 -2% 1% Speaker’s Notes: Pick a variable like Market Share to explain here. I usually explain this chart in the following order: “This is a plot of how various inputs contribute to uncertainty in NPV, which is measured in millions of US dollars across the top. When all variables are at their base values, then the NPV is US$75MM—that’s the base case, which is indicated by the vertical line. Now let’s take Market Share. If we move it to it’s low value of 8%, then the NPV drops to US$ -6 MM. When we put in the high value, the NPV goes up to US$134 MM. These high and low NPV values determine the width of the bar. The bars at the bottom, like COGS show uncertainties that have very small contribution to risk. 2.05-I • Deterministic & Sensitivity Analysis

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The tornado diagram is generated by reevaluating NPV using low and high values for each variable separately. Variable Variable Values Base 10% Low 90% High Price per Dose $3.50 $1.50 $6.00 Market Share 20% 8% 28% Doses per Day 2 1 3 Prevalence Rate 2.0% 1.5% 3.0% Compliance 55% 30% 70% Treatment Rate 50% 60% Development Cost 100 60 140 COGS 25% 15% Uptake curve length 5 7 Annual Price Change 0% -2% 1% Results “Low” “High” Swing -2 171 173 -6 134 140 7 142 135 41 101 14 112 98 22 79 99 51 48 100 62 37 91 56 35 55 86 31 Speaker’s Notes: Explain the slide. The blue arrows at the bottom show what is connected to what—low input and low output for example. We call the inputs low or high depending on whether their numerical value us low or high. We don’t call them “worst” and “best” because often it’s not clear which value will have the highest NPV. (Selling price is a good example—if you lower it, the NPV might go up or down depending on the elasticity of demand for your product.) The quote marks are used for “Low” and “High” outputs because they may not be low and high. Look at COGS for example. Low COGS is good and produces a high NPV. Therefore the “Low” result means the NPV you get when you use the low input. The swing is the difference between the two NPVs. Base Case NPV = $75 MM 2.05-I • Deterministic & Sensitivity Analysis

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**The input may be highly uncertain.**

Uncertain inputs can have a large effect on the output for two reasons. The input may be highly uncertain. Range of Output Range of Input Range of Input The output variable may be highly sensitive to small changes in an input. Range of Output { Speaker’s Notes: The slide says it all. 2.05-I • Deterministic & Sensitivity Analysis

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**Price/Dosing Scenario**

Three of the variables are “coupled” or “dependent.” They tend to vary together. Price/Dosing Scenario “tid”* “bid”* “Once a day” Number of Doses Compliance Price per Dose 3 30% $1.50 2 55% $3.50 1 70% $6.00 We should determine the sensitivity of NPV to joint changes in these variables. Note: These scenarios are obtained by assessing a combination of events that would lead to a low (10th percentile) and a high (90th percentile) outlook. Speaker’s Notes: Someone generally points out that the earlier sensitivity analysis (“single variable sensitivity”) assumes that all the variables are independent. They’re right. What if they’re dependent, as many of them are. Then you need joint sensitivity analysis. In this drug development example, three variables were linked: Number of Doses per day Compliance Price per Dose So we constructed three scenarios, based on the number of doses per day. Compliance and Price per dose values were then assigned that were consistent with the three dosing options. (I.e., given that Dosing is Once a Day, what is a consistent compliance? 70%) The note at the bottom gives the method of determining the scenarios. We want the low and high ends of our joint tornado bar to be 10th and 90th percentiles respectively. *tid: ter in die – three times a day bid: bis in die – twice a day 2.05-I • Deterministic & Sensitivity Analysis

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Joint sensitivity analysis determines the sensitivity of NPV to simultaneous changes in coupled* variables Variable Values Variable Doses per Day Compliance Price per Dose Low 3 30% $ 1.50 Base Case High 2 55% $ 3.50 1 70% $ 6.00 Base Case NPV = $75 MM Results “Low” “High” Swing - 13 87 100 Speaker’s Notes: We then make one more sensitivity run of the model, using the low and high scenarios. * Coupled, or dependent, uncertainties are likely to vary together—either positively or negatively correlated. 2.05-I • Deterministic & Sensitivity Analysis

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**Net Present Value ($ millions)**

The updated tornado diagram focuses our attention on the most significant sources of risk. Net Present Value ($ millions) -50 50 100 150 200 Base Value = 75 Market Share 8% 28% Prevalence Rate 1.5% 3.0% Treatment Rate 30.0% 60.0% Development Cost 140.0 60.0 COGS (%Rev) 30% 15% Uptake curve length 7 3 Annual Price change -2% 1% TID BID Dose/Pricing Scenario Sensitive Insensitive Speaker’s Notes: Here’s the updated tornado diagram. These variables can now be treated as mutually independent. Normally we would draw a line and include the ones above the line in our probabilistic analysis. Possible question: Are the big bars always the tall bars on a waterfall? No. A variable that has a huge impact on mfg. cost in chemical industry is the cost of rubber. But it has very low uncertainty. “How much risk do you think Market Share and Prevalence Rate together contribute?” Note for instructor: their contributions are not proportional to the width of the bars, but rather to the square of the risk of the bars. See next slide. We suggest re-assessing the uncertainty in the most sensitive uncertain variables and including them in probabilistic analysis. 2.05-I • Deterministic & Sensitivity Analysis

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**Cumulative Contribution Contribution to Total Uncertainty***

Uncertainties with the greatest “swing” are crucial to capturing the uncertainty in overall value. 31 Price Change TOTAL 35 Uptake Curve 37 COGS 48 Dev Costs 79 Treatment Rate 100 Dose/Pricing Scen 101 Prevalence Rate 140 Market Share Individual Swing Uncertainty 961 50526 1225 1369 2304 6241 10000 10201 18225 Variance (swing)2 100% 2% 98% 96% 3% 93% 4% 89% 12% 77% 19% 58% 20% 38% Cumulative Contribution Contribution to Total Uncertainty* Speaker’s Notes: Note that the four top bars in this case contribute 89% of the variance in NPV. This calculation assumes that all variables are independent. They do not have to be normally (or symmetrically) distributed. * The uncertainty in the model output (e.g., NPV) is proportional to the sum of the squares of individual input variable swings, if the variables are independent. 2.05-I • Deterministic & Sensitivity Analysis

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**We will discuss using spreadsheets for deterministic (base case) analysis and sensitivity analysis.**

Base Case Analysis and Waterfall Diagrams Sensitivity Analysis and Tornado Diagrams Using Sensitivity Results for Insight Speaker’s Notes: “This section suggests three different types of analysis once a spreadsheet model has been constructed. The first is “base case” analysis; it is deterministic, and only base case values are used. This analysis will include bar charts, waterfalls, and cash flow plots.” “The second type of analysis—sensitivity analysis—produces tornado diagrams, which show which uncertain variables are the greatest contributors to risk.” 2.05-I • Deterministic & Sensitivity Analysis

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**Does the base case match the waterfall (and spreadsheet) base case?**

The tornado diagram helps identify potential problems with the assessments and the model. Net Present Value Too symmetric? Are experts biased? Are these really the most sensitive, or are the ranges too wide? Low cost, high NPV! Cost: High Low “Floating” bar— are the values right? Are these really low/zero swings, or is there a mistake? Speaker’s Notes: Example for a real floating bar (the Love Boat?): Selling price. The base case selling price might be the best one. A lower price could cut into profits, while a higher price might reduce units sold more than it increases profits per unit. Any variable where there is a non-linear (especially parabolic) relationship between the variable and NPV could potentially have a floating bar. Does the base case match the waterfall (and spreadsheet) base case? 2.05-I • Deterministic & Sensitivity Analysis

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**Waterfall and tornado analyses provide tools to “mine” for NPV insights.**

• What are the primary sources of value? What drives the uncertainty in net present value? What uncertainties have the greatest effect on decisions? Which variables are dependent? Which risk factors might we be able to control? Is any strategy clearly most attractive? - How can we revise the strategy to capture more value? - How can we help focus the attention of company management? Where should the analysis be refined? Speaker’s Notes: The slide says it all. 2.05-I • Deterministic & Sensitivity Analysis

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**Change Log Version Date Changes**

01 08/06/27 First version for DAF - SDG LS (modified by M Seidler from DCW DSA v2.16) 02 08/08/15 Minimal changes after first DAF (Aug 2008) 03 08/12/15 Created Drug Development example to replace old Real Estate one (I Garrido) 04 09/30/09 Updated to IMS Template (MC) 07/21/10 Updated with minor revisions 06/07/12 Updated to IMSCG Template (LJ) 2.05-I • Deterministic & Sensitivity Analysis

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**Appendix Speaker’s Notes: The slide says it all.**

2.05-I • Deterministic & Sensitivity Analysis

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There is another form of sensitivity—decision sensitivity; it identifies uncertainties that affect decision-making. Example: A Drug Development investment decision Uncertainties Prevalence Market Share Price/dosing scenario Invest Don’t Invest $ 0 How important is each uncertainty—enough to change our decision? 2.05-I • Deterministic & Sensitivity Analysis

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The tornado identifies uncertainties that affect our choice between investing or not; this is called “decision sensitivity.” Net Present Value Best Decision, Given: Low Input High Input 50 100 150 Variable Market Share 8% 28% Don’t Invest Invest Invest Prevalence Rate 1.5% 3.0% Don’t Invest Dose/Pricing Scan TID BID Invest Invest Treatment Rate 30.0% 60.0% Invest Invest Development Cost 140 60 Invest Invest COGS (%Rev) 30% 15% Speaker’s Notes: Note that if we learned that our drug will have a three times a day dosing (tid), or we expected to reach a market share of up to 8%, then we would not invest. Base Value: 75 We could change our decision based on the outcome Market Share and Dose/Pricing Scenario alone. These two are “decision sensitive.” 2.05-I • Deterministic & Sensitivity Analysis

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**Judge the quality of available information before plunging into evaluation.**

Meaningful, Reliable Information: 0% “Blissful ignorance” Don’t know how much we know Ignoring uncertainty Ignoring “intangibles” 50% “Informed about uncertainty” Know information gaps Know what’s important Quantified uncertainty Interdependence not explored 100% “Knowledgeable and ready” Information correct and explicit Important gaps filled Know limits of knowledge 4 Clear Values and Trade-offs 5 Logically Correct Reasoning 6 Commitment to Action 0% 100% Decision Quality 1 Appropriate Frame 2 Creative, Doable Alternatives 3 Meaningful, Reliable Information Speaker’s Notes: As before, this gives some guidance that project teams have found useful. If we’ve done our first tornado, without considering interdependencies, we’re at 50%. 2.05-I • Deterministic & Sensitivity Analysis

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Chapter 7 ©2001 South-Western College Publishing Pamela S. Lewis Stephen H. Goodman Patricia M. Fandt Slides Prepared by Bruce R. Barringer University.

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