Decision Analysis¶

Why This Matters¶

Every manager makes decisions under uncertainty. The difference between a good leader and a great one is not clairvoyance -- it is a disciplined toolkit for structuring messy problems, quantifying risk, and knowing when additional information is worth paying for. Decision Analysis gives you that toolkit. It bridges the gap between raw quantitative models (Corporate Finance's NPV, Marketing's pricing, Operations' capacity planning) and the behavioral reality that humans are reliably irrational. You will learn to draw a decision tree, compute the expected value of a gamble, update your beliefs when new data arrives, simulate thousands of scenarios in seconds, and -- perhaps most importantly -- recognize when your own brain is sabotaging you.

How It All Connects¶

The course follows a deliberate arc. You begin by structuring decisions (Lessons 1--2), learning to map alternatives, uncertainties, and payoffs into decision trees and compute Expected Monetary Value (EMV). Next, you confront the time value of money (Lesson 3), because most real decisions involve cash flows spread over years -- requiring Net Present Value (NPV) and Internal Rate of Return (IRR). You then apply these tools to real cases (Lesson 4). Before going deeper, the course pauses for a reality check on cognitive biases (Lesson 5) -- the systematic errors your brain commits when estimating probabilities and evaluating risk.

The second block deepens the probability engine. You formalize probability rules (Lesson 6), learn Bayes' Theorem for updating beliefs (Lesson 7), and calculate the value of information (Lesson 8) -- the maximum you should ever pay for a consultant, a market study, or a quality test. Lessons 9--10 apply these ideas to data-driven and risk-attitude contexts.

The third block introduces Monte Carlo simulation (Lessons 11--12), which replaces single-point estimates with probability distributions run thousands of times. You apply simulation to risk management, NPV under uncertainty, joint ventures, and company valuation (Lessons 13--15). Finally, Lessons 16--17 tackle probability models, integration, and decision-making under deep uncertainty -- when the models themselves are unreliable.

Cross-references abound: - Corporate Finance: NPV, IRR, WACC, DCF valuation, and the discount rate appear directly in Lesson 3 and again in Lessons 13--15. - Marketing Management: Anchoring and framing (Lesson 5) are the same biases used in psychological pricing. Sensitivity analysis on sales volume mirrors break-even analysis. - Operations Management: The Critical Fractile (Lesson 1) is the newsvendor problem -- the foundation of inventory management. Monte Carlo simulation (Lessons 11--12) stress-tests capacity decisions.

Lesson 1: Decision Trees -- Structuring the Problem¶

Sessions covered: 1 (Laree Verbindungen) and 4 (Kahrvinger A)

Core Concept¶

A decision tree is a chronological map of your choices and their consequences, drawn left to right. It has two building blocks:

Branches extend from each node. From a square, each branch is an alternative you can pick. From a circle, each branch is a possible state of the world, labeled with its probability.

Building a Tree: The 4-Step Protocol¶

1. List the decisions you face, in chronological order.
2. For each decision, identify the alternatives (branches from squares).
3. For each alternative, identify the uncertainties that follow (circles) and assign probabilities to each branch.
4. Assign payoffs at the terminal nodes (the far right end of each path).

Folding Back (Backwards Induction)¶

You solve a decision tree from right to left:

1. Start at the terminal payoffs.
2. At each uncertainty node, compute the Expected Value (EV) = sum of (probability x payoff) across all branches.
3. At each decision node, pick the branch with the highest EV (or lowest expected cost).
4. Work backward until you reach the initial decision.

Intuition: You cannot decide what to do today without first knowing what the rational response will be at every future fork. Folding back forces you to think through the entire game before committing to the first move.

The Critical Fractile (Newsvendor Problem)¶

When your decision is "produce one more unit or not?" and demand is uncertain, the tree simplifies to a single formula.

Setup: You have already decided to produce q units. Should you produce q + 1?

Formula for incremental EV:

EV(q + 1) = G * P(D > q) - L * P(D <= q)

Produce the extra unit when EV(q + 1) >= 0, which simplifies to:

P(D <= q) <= G / (G + L)

The right-hand side, F_c = G / (G + L), is the Critical Fractile. It depends only on your cost structure, not on demand. If F_c is high (G >> L), you should produce aggressively because the upside of selling far exceeds the downside of waste.

Back-of-napkin: If your margin on a sale is $21 and your loss on unsold inventory is $9, then F_c = 21/30 = 0.70. You keep producing until there is a 70% chance you have already met demand.

Cross-reference -- Operations Management: This is the classic newsvendor model. The same Critical Fractile formula drives how many perishable items (newspapers, fashion items, airline seats) to stock.

Sequential Games and Competitive Dynamics¶

When your tree involves a competitor who will react to your move, you model both players' decisions as alternating decision nodes. Fold back from the rival's last move to determine what they will rationally do, then decide your first move accordingly.

Example (Coke vs. Pepsi): If Coke moves first and chooses "aggressive," Pepsi's best response is "modest" (payoff 5 vs. 4.5). If Coke chooses "modest," Pepsi's best response is "aggressive" (payoff 6.5 vs. 6.0). Knowing Pepsi's rational reactions, Coke folds back and sees: aggressive yields 6.5, modest yields 5.0. Coke goes aggressive.

Lesson 2: Expected Monetary Value, Certainty Equivalent, and Risk Premium¶

Sessions covered: 2 (ScriptBook)

Expected Monetary Value (EMV)¶

EMV is the probability-weighted average of all possible outcomes of a decision.

EMV = SUM over all outcomes of [ P(outcome_i) * payoff_i ]

Decision rule (risk-neutral): Choose the alternative with the highest EMV. Over many repeated decisions, this maximizes long-run wealth.

Caution: EMV works well for repeated, moderate-stakes decisions. For a single, bet-the-company decision, the average is a poor guide -- you need to account for your attitude toward risk.

Utility Functions¶

Humans do not value money linearly. The jump from $0 to $100,000 feels enormous; the jump from $10,000,000 to $10,100,000 feels trivial. A utility function U(x) translates dollar outcomes into personal satisfaction ("utils").

Using utility in decisions: 1. Compute the utility of each outcome: U(payoff_i). 2. Compute the Expected Utility (EU): EU = SUM of [ P(outcome_i) * U(payoff_i) ]. 3. Convert back to dollars using the inverse function.

Certainty Equivalent (CE)¶

The CE is the guaranteed cash amount that makes you exactly indifferent between taking it and playing the risky gamble.

CE = U⁻¹(EU)

Translation: take the expected utility of the gamble and run it through the inverse of your utility function to get a dollar figure.

Risk Premium (RP)¶

The RP is how much expected wealth you sacrifice to eliminate risk entirely.

RP = EMV - CE

Cross-reference -- Corporate Finance: The "risk premium" in discount rates (r = rꜰ + Risk Premium) is the market-level version of this individual-level concept. Both compensate for bearing uncertainty.

Back-of-napkin: If a project has an EMV of $1M but your CE is only $700K, your risk premium is $300K. You would accept a guaranteed $700K over the gamble. If someone offers you $800K to walk away, take it -- it exceeds your CE.

Lesson 3: Net Present Value and Internal Rate of Return¶

Sessions covered: 3 (NPV and IRR lecture), 15 (SkyWest Airlines)

The Time Value of Money¶

A dollar today is worth more than a dollar tomorrow because today's dollar can be invested. To compare cash flows occurring at different times, you need a discount rate (r) that converts future money into present-day equivalents.

Discount rate = rꜰ + Risk Premium

where rꜰ is the risk-free rate (e.g., government bond yield) and the Risk Premium compensates for the project's specific uncertainty.

Present Value (PV)¶

PV = CF₁ / (1 + r)¹ + CF₂ / (1 + r)² + ... + CFₙ / (1 + r)ⁿ

Present Value Tables: Table 1 gives the PV of receiving 1 euro in n years at rate r. Table 2 gives the PV of receiving 1 euro per year for n years (annuity factor).

Example: At r = 12%, 1 euro received in 5 years is worth 0.567 euros today. An annuity of 1 euro/year for 5 years is worth 3.605 euros today.

Net Present Value (NPV)¶

NPV = F₀ + F₁ / (1 + r)¹ + F₂ / (1 + r)² + ... + Fₜ / (1 + r)ᵀ

where F₀ is typically a negative initial investment.

Decision rule: - NPV > 0: Take the project (it creates wealth). - NPV < 0: Reject the project (it destroys wealth). - NPV = 0: The project earns exactly the required return.

Intuition: An NPV of 8.88 million euros means undertaking this project makes your company exactly 8.88 million euros richer in today's money.

Internal Rate of Return (IRR)¶

The IRR is the discount rate that forces NPV to zero:

0 = CF₀ + CF₁ / (1 + IRR)¹ + CF₂ / (1 + IRR)² + ... + CFₙ / (1 + IRR)ⁿ

Decision rule: - If r < IRR: Take the project. - If r > IRR: Reject the project.

Intuition: An IRR of 25% means the project acts like a machine converting every 100 euros invested today into 125 euros one year later.

IRR Pitfalls -- Two Critical Warnings¶

1. Multiple IRRs: If cash flows alternate between positive and negative (e.g., environmental cleanup costs at the end), the polynomial equation can yield multiple solutions. Which IRR do you compare to r? You cannot -- the metric breaks.

2. Mutually exclusive projects: When choosing between two projects, always use NPV, never IRR. Project A may have a lower IRR than Project B, but a higher NPV at your actual discount rate. NPV measures total wealth; IRR measures percentage efficiency.

Back-of-napkin: To quickly approximate NPV for a level annuity: NPV = -Investment + (Annual CF * Annuity Factor). Look up the annuity factor in Table 2 for your rate and years.

Continuous Discounting¶

When compounding happens at every instant (used in option pricing and portfolio returns):

PV = Q * e^(-r*t)

where e is Euler's number (approx. 2.71828), r is the annual rate, and t is time in years.

Example: 100 euros received in 1 year at 20% continuous discount: PV = 100 * e^(-0.20) = 81.97 euros. Compare to annual discounting: 100/1.20 = 83.33 euros. Continuous discounting is slightly more aggressive.

Cash Flow Types¶

Cross-reference -- Corporate Finance: FCF and ECF are the bread and butter of DCF valuation. The WACC (Weighted Average Cost of Capital) is used as the discount rate for FCF; the cost of equity is used for ECF.

Lesson 4: Applied Decision Analysis -- Integrating Trees and NPV¶

Sessions covered: 4 (Kahrvinger A)

Combining Decision Trees with Financial Analysis¶

Real-world decisions rarely involve a single fork. Kahrvinger demonstrates how to embed NPV calculations within a decision tree: each terminal node's payoff is itself an NPV computed from projected cash flows. The tree structures the strategic choices; the NPV quantifies each path's value.

Protocol: 1. Build the decision tree with all strategic alternatives and uncertainty nodes. 2. At each terminal node, project the cash flows that would result from that specific path. 3. Discount those cash flows to compute the NPV of that terminal outcome. 4. Fold back through the tree using EMV (or expected utility, if risk attitudes matter).

Intuition: The tree tells you which decisions to make and in what order. The NPV tells you how much each path is worth. Together, they give you a complete decision framework.

Sensitivity Analysis at the Tree Level¶

After solving the tree, test your conclusion: - Vary the probabilities at each uncertainty node. At what probability does your optimal decision flip? - Vary the key cash flow assumptions. How much does your best-path NPV change?

Back-of-napkin (Break-Even Probability): If your tree says "launch the product" with an EMV of $2M, and the success branch contributes $10M while the failure branch costs -$3M, then the break-even probability of success is: 0 = p(10) + (1-p)(-3), so p = 3/13 = 23.1%. If you believe success probability exceeds 23%, launch. This quick calculation shows how robust (or fragile) your decision is.

Lesson 5: Cognitive Biases and Intuitive Decision-Making¶

Sessions covered: 5 (Intuitive Decision Survey 1 / UEFA Euro 2008) and 10 (Intuitive Decision Survey 2 / Risk Attitudes)

System 1 vs. System 2 (Kahneman)¶

Your brain operates in two modes:

Most business decisions require System 2, but your brain defaults to System 1 unless you consciously force it to slow down.

The Big Five Biases¶

1. Anchoring You fixate on an initial number (often arbitrary) and insufficiently adjust away from it. - Example: An MSRP of $45,000 on a car makes a "discounted" price of $38,000 feel like a steal, even if the car is worth $35,000. - Defense: Generate your own estimate before seeing any anchor.

2. Overconfidence You systematically overestimate your own abilities and forecasts. Entrepreneurs rate their own chance of success at 81%, but give similar ventures only 59%. - Defense: Track your predictions over time. Build a personal "calibration log."

3. Confirmation Bias You seek out information that supports your existing beliefs and dismiss contradictory evidence. - Defense: Deliberately play devil's advocate. Build a "board of advisors" who will challenge you. Activate the goal of being accurate, not right.

4. Sunk Cost Fallacy You continue investing in a losing project because of money already spent, even though sunk costs are irrelevant to forward-looking decisions. - Defense: Ask: "If I had not already invested $X, would I start this project today?" If no, stop.

5. Law of Small Numbers (Hasty Generalization) You draw sweeping conclusions from tiny samples. Four heads in a row does not mean the coin is biased. - Defense: Always ask "How large is my sample?" The law of large numbers only kicks in with many observations.

Additional Biases to Watch¶

• Framing Effect: Choosing differently depending on whether options are presented as gains vs. losses (e.g., "90% survival rate" vs. "10% mortality rate").
• Availability Bias: Overweighting vivid, recent, or memorable events when estimating probability.
• Loss Aversion: Losses hurt roughly twice as much as equivalent gains feel good. This makes managers reject positive-EMV gambles with even small downside risk.

Cross-reference -- Marketing Management: Anchoring and framing are deliberately used in pricing strategy. Sunk cost fallacy explains why gym members who pay annually attend more in the first months.

Intuition as a Tool¶

Intuition is not magic -- it is a mental model's "visual acuity," sharpened by experience and exposure to effective frameworks. Intuitive decisions work when: - You have genuine expertise in the domain. - The environment provides regular, rapid feedback. - The patterns are stable and learnable.

Intuitive decisions fail when: - The domain is novel or rapidly changing. - Feedback is delayed or noisy. - You mistake confidence for competence.

Lesson 6: Probability -- The Language of Uncertainty¶

Sessions covered: 6 (DAZN / Basic Probability Concepts)

Foundations¶

Probability is a number between 0 (impossible) and 1 (certain) that measures how likely an event is to occur.

Core Rules¶

Key Definitions¶

• Mutually exclusive: P(A and B) = 0. The events cannot happen simultaneously.
• Independent: P(A given B) = P(A). Knowing B does not change your belief about A.
• Collectively exhaustive: The set of outcomes covers all possibilities. Their probabilities sum to 1.

Probability Distributions¶

• Categorical (discrete): A variable that takes a finite set of values (e.g., coin flip: heads or tails). Each value has a specific probability; all probabilities sum to 1.
• Continuous: A variable that can take any value in a range (e.g., sales volume). Described by a probability density function (PDF).

Back-of-napkin: For any event where the outcome is binary (success/fail), quick expected value = P(success) * payoff_success + P(failure) * payoff_failure. If positive, the gamble is favorable.

Cross-reference -- Operations Management: Every demand forecast is a probability distribution. Understanding the shape (normal, skewed, fat-tailed) matters for safety stock calculations.

Lesson 7: Bayes' Theorem -- Updating Your Beliefs¶

Sessions covered: 7 (Bank Score and OilCom)

Why Bayes' Theorem Works¶

You start with a prior belief (e.g., 20% of parts are defective). New information arrives (a quality test), but the test is imperfect. Bayes' Theorem tells you exactly how much to revise your belief based on the reliability of the new evidence.

Intuition: Bayes' Theorem is a belief-revision engine. It prevents two dangerous extremes: ignoring new data entirely (stubbornness) and overreacting to noisy data (panic).

The Formula¶

P(B given A) = [ P(A given B) * P(B) ] / P(A)

The 5-Step Calculation Mechanic¶

Example: 20% of parts are defective. A test correctly identifies good parts 90% of the time and defective parts 80% of the time.

Step 1 -- Map the priors: - P(Good) = 0.80, P(Defective) = 0.20

Step 2 -- Map the likelihoods (conditional probabilities of test results): - P(Test says Good | Good) = 0.90, P(Test says Defective | Good) = 0.10 - P(Test says Good | Defective) = 0.20, P(Test says Defective | Defective) = 0.80

Step 3 -- Compute joint probabilities (prior * likelihood): - P(Good AND Test says Good) = 0.80 * 0.90 = 0.72 - P(Good AND Test says Defective) = 0.80 * 0.10 = 0.08 - P(Defective AND Test says Good) = 0.20 * 0.20 = 0.04 - P(Defective AND Test says Defective) = 0.20 * 0.80 = 0.16

Step 4 -- Compute total probability of each test result: - P(Test says Good) = 0.72 + 0.04 = 0.76 - P(Test says Defective) = 0.08 + 0.16 = 0.24

Step 5 -- Compute posteriors (joint / total): - P(Good | Test says Good) = 0.72 / 0.76 = 0.947 (94.7%) - P(Defective | Test says Good) = 0.04 / 0.76 = 0.053 (5.3%) - P(Good | Test says Defective) = 0.08 / 0.24 = 0.333 (33.3%) - P(Defective | Test says Defective) = 0.16 / 0.24 = 0.667 (66.7%)

Result: Before the test, you believed 80% of parts were good. After a positive test, your confidence jumps to 94.7%. After a negative test, it plummets to 33.3%.

Representation Methods¶

1. Decision tree: Prior as first branch, likelihoods as second branch, joint probabilities at endpoints. Then re-draw with test result first, posteriors second.
2. Probability square: A rectangle divided proportionally by priors (vertical) and likelihoods (horizontal). Joint probabilities appear in each cell.
3. Table: Rows = states of the world, columns = test results, cells = joint probabilities, margins = totals.

Lesson 8: The Value of Information¶

Sessions covered: 8 (Star of the Caribbean) and 9 (Chemical Fusion A)

Core Question¶

Before paying for a consultant, a market study, or a test, ask: "What is the maximum this information is worth?"

Expected Value of Perfect Information (EVPI)¶

EVPI is the maximum you should pay for a test that is 100% accurate -- an oracle that eliminates all uncertainty.

EVPI = EV(decision with perfect information) - EV(best decision without any information)

Calculation: 1. For each state of the world, determine the best decision and its payoff. 2. Weight those payoffs by the probability of each state occurring. 3. Subtract the EMV of your current best decision.

Back-of-napkin: If EVPI is less than the cost of the study, don't bother. No amount of accuracy can make it worthwhile -- and real-world information is always less accurate than perfect.

Expected Value of Imperfect Information (EVII)¶

Real tests are flawed. EVII calculates the actual value of an imperfect signal.

EVII = EV(decision with imperfect information) - EV(best decision without any information)

The Manufacturing Example: - Without the test: ship all parts, expected cost = $50/part (from penalty risk). - With the imperfect test: use Bayesian posteriors to decide ship/rework for each test result. Expected cost drops to $34.07/part. - EVII = $50 - $34.07 = $15.93/part. - If the test costs less than $15.93 per part, use it. If it costs more, fly blind.

Decision Protocol: Should You Buy Information?¶

1. Calculate your baseline EMV (no information).
2. Calculate EVPI (upper bound on information value).
3. If the information source costs more than EVPI, stop -- it is never worth it.
4. If the cost is below EVPI, calculate EVII using the source's actual accuracy (Bayesian updating).
5. If cost < EVII, buy the information. Otherwise, decide without it.

Cross-reference -- Marketing Management: A market research study is an imperfect information source. Before commissioning a $500K study, compute the EVII to see if the potential improvement in your product launch decision justifies the expense.

Lesson 9: Data-Driven Decisions and Risk Attitudes¶

Sessions covered: 9 (Chemical Fusion A) and 10 (Intuitive Decision Survey 2)

Integrating Data into the Decision Framework¶

Chemical Fusion A demonstrates how to embed real operational data into a decision tree:

1. Frame the decision: What are you choosing between? (e.g., invest in new process vs. status quo)
2. Identify the uncertainties: What data-driven variables are uncertain? (e.g., yield rates, market prices)
3. Assign probability distributions based on historical data or expert judgment.
4. Compute EMV or EU depending on whether risk attitudes matter at the stakes involved.
5. Perform sensitivity analysis to test which variables drive the decision.

Risk Attitudes in Practice¶

Your personal risk attitude determines whether you use EMV (risk-neutral) or expected utility (risk-averse/seeking). For corporate decisions:

• Small, repeatable decisions (inventory orders, pricing adjustments): Use EMV. The law of large numbers smooths out variance.
• Large, one-shot decisions (enter a new market, acquire a company): Use expected utility. A single catastrophic loss can wipe you out regardless of long-run averages.

Measuring Your Risk Tolerance¶

The risk tolerance coefficient (R) parameterizes an exponential utility function:

U(x) = 1 - e^(-x/R)

A higher R means greater tolerance for risk (you need a wider range of outcomes to feel uncomfortable). Companies with deep pockets and diversified portfolios have higher R.

Lesson 10: Sensitivity Analysis¶

Sessions covered: Part of 9 (Chemical Fusion A), 10, and foundational for simulation lessons

What Sensitivity Analysis Does¶

All quantitative analyses involve assumptions. Sensitivity analysis tests whether your conclusion survives reasonable errors in those assumptions.

Break-Even (Indifference) Analysis¶

The simplest form: find the exact value of a key variable where your decision flips.

Example: Should PEAR drop gas-powered engines? Analysis says yes if estimated sales are 50,000 units. Leave sales as unknown X. Set the profit difference between "keep" and "drop" to zero: 2,000,000 - 240X = 0, so X = 8,333. Your decision only flips if sales drop below 17% of your estimate. That is a highly robust conclusion.

Tornado Charts¶

A visual tool for ranking the sensitivity of your output to each input variable:

1. Vary each input one at a time by a standard amount (e.g., +/- 10%).
2. Record the resulting change in your output (NPV, profit, etc.).
3. Plot horizontal bars: widest swing at the top, narrowest at the bottom.
4. The resulting chart resembles a tornado.

Leadership use: The variable at the top of the tornado demands your management attention. If raw material cost dominates, negotiate long-term supply contracts. If labor cost barely moves the needle, stop arguing about minor wage adjustments.

Lesson 11: Monte Carlo Simulation¶

Sessions covered: 12 (Kahrvinger B / Crystal Ball) and 13 (Chemical Fusion C)

Why Simulate?¶

Scenario analysis tests a few discrete states of the world. Sensitivity analysis varies one input at a time. But real projects have multiple uncertain variables moving simultaneously. Monte Carlo simulation handles this complexity.

How It Works¶

1. Model your decision in a spreadsheet (e.g., an NPV model with revenue, cost, and growth assumptions).
2. Replace fixed assumptions with probability distributions. Instead of "sales = 10,000 units," define "sales ~ Normal(mean = 10,000, standard deviation = 2,000)."
3. Run the simulation. The software (Crystal Ball, @RISK, or Python) randomly draws one value from each distribution, computes the output (e.g., NPV), and records the result.
4. Repeat thousands of times (typically 5,000--10,000 iterations).
5. Analyze the output distribution. You now have a histogram of thousands of possible NPVs.

What You Get¶

Instead of "NPV = $5M," you can say: - "There is an 85% probability NPV exceeds zero." - "The median NPV is $4.2M." - "There is a 5% tail risk of losing more than $2M."

Crystal Ball (Oracle)¶

Crystal Ball is an Excel add-in used at IESE for Monte Carlo simulation. Key features: - Assumption cells: Cells where you define probability distributions. - Forecast cells: Cells containing the output you want to analyze. - Sensitivity chart: Shows which assumption variables contribute most to output variance (similar to a tornado chart, but based on simulation data).

Common Probability Distributions for Assumptions¶

Cross-reference -- Operations Management: Monte Carlo simulation is used for capacity planning under demand uncertainty, lead-time variability in supply chains, and quality control processes.

Lesson 12: Risk Management and Disaster Preparedness¶

Sessions covered: 14 (Speed Ventures)

Risk Management Framework¶

1. Identify risks: What variables could alter your expected cash flows? (recession, pandemic, regulatory change, competitor action, supply disruption)
2. Quantify risks: Use probability distributions and simulation to model worst-case, base-case, and best-case scenarios.
3. Manage/hedge risks: Develop strategies to limit damage -- diversification, insurance, hedging, contractual protections.

The Plan B Protocol¶

A Plan B is not a plan to win; it is a plan of minimums designed to: - Contain damage - Preserve reputation, stability, and customer trust - Keep operations moving while Plan A is corrected

Characteristics of a good Plan B: - Simple, fast to activate, easy to understand - Works with limited resources - Has clear triggers for when to activate - Remains aligned with overall strategy (less ambitious, but not directionless)

Guiding principle: "A plan that does not consider its risks and limitations is not incomplete -- it is naive."

Real Options as Risk Management¶

When facing deep uncertainty, structure your strategy as a portfolio:

Real options let you buy information through action: invest a little, observe the outcome, then decide whether to commit fully.

Lesson 13: NPV Applications and Company Valuation¶

Sessions covered: 15 (SkyWest Airlines), 16 (Genzyme-Geltex), 17 (Netscape / Tornado Charts)

NPV Under Uncertainty¶

SkyWest Airlines applies NPV to capital-intensive decisions (fleet expansion, route planning) where cash flows are spread over decades and subject to fuel price volatility, regulatory changes, and competitive dynamics. The key is to: 1. Project FCFs under multiple scenarios. 2. Discount using an appropriate rate (WACC for FCF, cost of equity for ECF). 3. Run Monte Carlo simulation to get a distribution of NPVs. 4. Use tornado charts to identify the variables that matter most.

Joint Ventures¶

Genzyme-Geltex illustrates joint venture valuation: - A joint venture must transfer skills or share activities that fit tightly with the parent company's existing business. - Value the venture using DCF, treating it as a standalone project with its own risk profile. - Structure the deal to align incentives: who contributes what, how are profits shared, what are the exit provisions?

Company Valuation: Two Methods¶

Method 1 -- Discounted Cash Flow (DCF): 1. Project FCFs for a forecast period (typically 5--10 years). 2. Estimate a terminal value (perpetuity growth model or exit multiple). 3. Discount all cash flows at WACC. 4. Enterprise Value = PV of FCFs + PV of terminal value. 5. Equity Value = Enterprise Value - Net Debt.

Method 2 -- Multiples: 1. Identify comparable firms (same industry, similar growth and profitability). 2. Calculate ratios: P/E (Price-to-Earnings), EV/EBITDA, EV/Revenue. 3. Apply the median multiple to your target company's financials.

Netscape and Tornado Charts: Netscape's IPO valuation demonstrates how tornado charts identify which assumptions (subscriber growth, revenue per user, discount rate) most affect the company's estimated value. The widest bar = the variable you must get right.

Cross-reference -- Corporate Finance: These valuation methods are the same ones used in M&A analysis, LBOs, and IPOs. Decision Analysis adds simulation and sensitivity layers on top.

Lesson 14: Probability Models -- College Fund and Gambler's Ruin¶

Sessions covered: 18 (College Fund and Gambler's Ruin)

College Fund Problem¶

A classic Time Value of Money exercise that combines annuity calculations with uncertainty:

Question: How much must you save each year to fund a child's university education in 18 years, given uncertain tuition inflation and investment returns?

Protocol: 1. Estimate the future cost of tuition (use an inflation rate assumption). 2. Calculate the Present Value of that future cost. 3. Determine the annual savings (annuity payment) required to reach that PV at your expected investment return. 4. Run sensitivity analysis on the inflation rate and investment return.

Formula (annual savings for a future target): Annual Payment = FV / [ ((1 + r)ⁿ - 1) / r ] where FV = future value needed, r = investment return, n = number of years.

Gambler's Ruin¶

A probability model proving that a player with finite wealth playing a fair game against an opponent with infinite wealth will eventually go bankrupt with certainty.

Business implications: - A startup with limited cash runway competing against an incumbent with deep pockets is in a Gambler's Ruin scenario. - Even in a "fair" market (50/50 odds on each trade), a small fund will eventually be wiped out by the variance of returns. You cannot survive infinite volatility with finite capital. - Lesson: Size of bankroll relative to bet size matters enormously. Do not confuse "fair odds" with "survivable."

Random Walk Theory¶

Asset prices follow a random walk -- each step (price change) is independent of the previous one. Implications: - Past price movements do not predict future price movements. - Technical analysis (chart patterns) is fundamentally unreliable. - The best forecast of tomorrow's price is today's price.

Lesson 15: Applied DA -- Geopolitical Risk and Integration¶

Sessions covered: 19 (OceanTrans), 20 (Give and Take / How Will You Measure Your Life), 21 (Complexity and Uncertainty)

Geopolitical Risk (OceanTrans)¶

OceanTrans applies decision analysis to shipping and geopolitical uncertainty: - Political risk, regulatory changes, and macroeconomic shocks are modeled as uncertainty nodes in decision trees. - Scenario analysis becomes essential when probability distributions are hard to estimate (deep uncertainty). - Build supply chain resilience: evaluate whether your network is robust or fragile under disruption scenarios.

Integration: How Will You Measure Your Life?¶

Clayton Christensen's framework asks you to apply the same analytical rigor to personal decisions as to business ones: - Strategy is not just about companies -- it is about allocating your finite resources (time, energy, talent) across competing priorities. - The sunk cost fallacy applies to careers: do not stay in a path simply because of past investment. - Overconfidence bias applies to personal risk assessment: people consistently underestimate the probability of negative life events.

Decision-Making Under Deep Uncertainty¶

When you cannot assign reliable probabilities to outcomes: 1. Scenario planning replaces expected-value calculations. Build 3--5 distinct, internally consistent stories about how the future might unfold. 2. Robustness over optimality: Instead of finding the single "best" strategy, find the strategy that performs acceptably across all scenarios. 3. Real options: Preserve flexibility. Delay irreversible commitments until uncertainty resolves. 4. Plan B readiness: Have a clearly defined fallback that is simple, fast to activate, and culturally feasible.

Quick Reference¶

Decision Rules at a Glance¶

Formula Card¶

Expected Monetary Value:

EMV = SUM of [ P_i * X_i ]

Risk Premium:

RP = EMV - CE

Net Present Value:

NPV = F₀ + Σ from t=1 to T of [ Fₜ / (1 + r)ᵗ ]

Internal Rate of Return:

Solve for r: 0 = F₀ + Σ from t=1 to T of [ Fₜ / (1 + r)ᵗ ]

Continuous Discounting:

PV = Q × e⁻ʳᵗ

Critical Fractile:

Fc = G / (G + L)

Bayes' Theorem:

P(B|A) = P(A|B) * P(B) / P(A)

EVPI:

EVPI = EV(with perfect info) - EV(without info)

EVII:

EVII = EV(with imperfect info) - EV(without info)

Annuity Present Value Factor:

PV of annuity = Annual CF * [ 1 - (1 + r)^(-n) ] / r

Mental Math Shortcuts¶

1. Rule of 72: An investment doubles in approximately 72/r years (at rate r%). At 8%, money doubles in ~9 years.
2. Quick EVPI check: If the cost of the study exceeds EVPI, skip it immediately -- no need to compute EVII.
3. NPV sign-check: If the undiscounted sum of all cash flows is negative, NPV is definitely negative (discounting only makes it worse).
4. Break-even probability: For a binary gamble, the break-even probability of success = |Loss| / (|Gain| + |Loss|).
5. 10% discount shorthand: At r = 10%, the annuity factor for 5 years is ~3.79, for 10 years is ~6.14, for 20 years is ~8.51.

Glossary¶