index Introduction
Concepts, Techniques and Tools

Risk & Decision Analysis

What should we do under different assumptions?
Set 07 · Level 7 of the Analytics Ladder

Deciding Wisely When the Future Is Uncertain

Traditional planning assumes one future. Risk and decision analysis acknowledges multiple possible futures — and builds decisions that hold up across them.

7Analytics Ladder · Level 07 of 10

Every consequential business decision is made under uncertainty. Revenue forecasts can miss. Costs overrun. Competitors act unexpectedly. The techniques in this set do not eliminate that uncertainty — they make it visible, quantifiable, and manageable.

The key insight: the goal is not to predict the future accurately. It is to make decisions that perform well across the range of futures that could plausibly occur — and to know which assumptions matter most.

A good decision under uncertainty is not one that turned out right. It is one that was well-reasoned given what was known at the time — with the key risks explicitly identified and managed.
7
Techniques
3
Tools Covered
10K+
Monte Carlo
simulations
EV
Expected Value
decision trees
Technique 01

Scenario Analysis

Evaluates how outcomes change when multiple assumptions change simultaneously. Best Case · Base Case · Worst Case. Strategic planning, investment decisions, business continuity.

Technique 02

What-If Analysis

Tests the impact of a single specific hypothetical change. "What if costs increase by 15%?" Fast, simple, ideal for operational decisions and quick stakeholder briefings.

Technique 03

Sensitivity Analysis

Changes one variable at a time to measure its effect on the outcome. Identifies the critical assumptions — those that most influence the result.

Technique 04

Tornado Charts

Visualises sensitivity analysis results as horizontal bars, ranked by impact. The widest bar = the variable that matters most. Executive-friendly and immediately actionable.

Technique 05

Monte Carlo Simulation

Runs thousands of scenarios simultaneously, each with randomly sampled inputs from probability distributions. Produces a probability distribution of outcomes — the most rigorous uncertainty quantification technique.

Technique 06

Decision Trees (Expected Value)

Maps out decision alternatives and their consequences using probability-weighted payoffs. The Expected Value calculation selects the option with the highest probability-weighted outcome.

Technique 07

Risk Matrix

Qualitative/semi-quantitative tool for prioritising risks by Likelihood × Impact. Used for risk registers and rapid risk communication when full quantification is not feasible.

The recommended sequence

These techniques work best in sequence: Scenario Analysis (broad uncertainty exploration) → What-If Analysis (specific event testing) → Sensitivity Analysis (identify key drivers) → Tornado Chart (prioritise for stakeholders) → Monte Carlo (full probability distribution if needed). Each builds on the previous, moving from broad uncertainty to focused action.

Technique 01

Scenario Analysis

Not one future — three. Best Case, Base Case, and Worst Case reveal the range of possible outcomes.

Scenario analysis evaluates how outcomes change when multiple assumptions change simultaneously. Unlike sensitivity analysis (which changes one variable at a time), scenarios reflect the fact that real-world conditions move together. A recession doesn't just reduce revenue — it simultaneously increases costs, tightens credit, and changes competitor behaviour.

Key question for every scenario

Ask: Which scenario worries management most? and Which assumptions drive the largest differences? These questions focus the conversation on what matters — not just the numbers, but the decisions those numbers imply.

The Scenario Development Process

01
Identify key uncertainties
What are the 3–5 variables with the most uncertainty and the most impact? Examples: customer demand, commodity prices, regulatory changes, competitor actions, exchange rates.
02
Define realistic ranges
For each variable, set realistic bounds — not the mathematically extreme but the plausibly possible. "Sales could be 20% above or 30% below the plan" based on historical variance and market intelligence.
03
Build three coherent scenarios
Best Case, Base Case, and Worst Case. Each scenario should be internally consistent — variables should move together in ways that reflect a coherent view of the world, not arbitrary combinations.
04
Evaluate the impact
Calculate the outcome (profit, NPV, cash flow) for each scenario. The spread between Best and Worst reveals the business's exposure to uncertainty.
Business Example
New Product Launch — Scenario Table
VariableBest CaseBase CaseWorst Case
Annual Sales (units)15,00010,0007,000
Selling Price ($/unit)$110$100$95
Unit Cost ($/unit)$55$60$70
Profit$825,000$400,000$175,000

The range is $175K–$825K — a 4.7× spread. This tells management that the investment is profitable in all scenarios, but the level of profitability is highly uncertain. The conversation shifts: "Which scenario is most likely, and what could we do to prevent the worst case?"

Industry Applications

IndustryTypical scenario variablesPrimary use
Finance / InvestmentRevenue growth, margins, discount rate, capexDCF valuation, capital allocation
OperationsDemand volume, supplier costs, lead times, capacityCapacity planning, inventory decisions
TelecommunicationsCustomer churn, data usage, network costs, energy costsNetwork expansion, pricing strategy
Human ResourcesHeadcount growth, salary inflation, attrition rateWorkforce and compensation planning
StrategyMarket share, competitor response, regulatory environmentMarket entry, M&A, business continuity
Technique 02

What-If Analysis

What happens if X changes? Fast, specific, and instantly communicable to any audience.

What-if analysis examines the impact of a single, specific hypothetical change to one input variable. It answers the most common question in business planning: "What happens to our result if this one thing changes?"

Unlike scenario analysis (which changes multiple variables simultaneously) or sensitivity analysis (which systematically varies one variable across a range), what-if analysis tests a single specific event — making it the fastest and most accessible of the three techniques.

Business Example
Operational What-If — Cost Increase

Current situation: Revenue = $1,000,000 · Costs = $700,000 · Profit = $300,000

Question: What if operating costs increase by 15%?

New Costs = $700,000 × 1.15 = $805,000
New Profit = $1,000,000 − $805,000 = $195,000

A 15% cost increase reduces profit by 35% (from $300K to $195K). This single calculation reframes the conversation: the business is highly sensitive to cost increases. What cost controls should be in place, and at what cost level does the business break even?

Common Business What-If Questions

DepartmentWhat-If QuestionVariable changed
SalesWhat if sales fall by 10% in Q3?Revenue volume
ProcurementWhat if fuel costs increase by 20%?Input cost
OperationsWhat if supplier delivery times double?Lead time / inventory holding cost
HRWhat if travel expenses increase by 20%?Departmental cost line
FinanceWhat if interest rates rise by 150 basis points?Financing cost
MarketingWhat if customer acquisition cost increases by 30%?Marketing efficiency
Benefits of What-If Analysis

Quick to perform — a single calculation or formula change in Excel. Easy to explain — anyone can follow "if X changes to Y, then Z becomes W." Immediately actionable — the result either crosses a threshold that triggers action or it does not. Use what-if analysis for rapid operational decisions and for setting up the more detailed sensitivity analysis that follows.

Technique 03

Sensitivity Analysis

Change one variable at a time, hold everything else constant, and measure the impact on the outcome.

Sensitivity analysis systematically tests how the outcome changes as each input variable is varied across a defined range — one at a time, holding all others at their base values. This identifies the critical assumptions: those inputs where a small change produces a large change in the outcome.

The one-at-a-time rule

The defining discipline of sensitivity analysis: change only one variable at a time. Keep all other variables at their base case values. This isolates the unique effect of each variable. If you change multiple variables simultaneously, you cannot determine which change drove the result — that is scenario analysis, not sensitivity analysis.

Business Example
Project NPV Sensitivity — Sales Volume

A project has Base Case NPV = $500,000. The analyst tests the sensitivity of NPV to sales volume changes, one level at a time:

Sales Volume ChangeNPVChange from Base
−20%$100,000−$400,000 (−80%)
−10%$300,000−$200,000 (−40%)
Base (0%)$500,000
+10%$700,000+$200,000 (+40%)
+20%$900,000+$400,000 (+80%)

Interpretation: A 10% change in sales volume produces a 40% change in NPV. Sales volume is a highly sensitive variable — management should monitor it closely and build contingency plans if early sales data falls below plan.

Common variables tested in sensitivity analysis

Revenue side

Demand & Price drivers

Revenue · Selling price · Customer demand volume · Market share · Price elasticity · Exchange rates

Cost side

Cost drivers

Labour cost · Material cost · Energy costs · Financing / interest rates · Overhead allocation · Supplier costs

Best practices

Test each variable across a consistent range (typically ±10%, ±20%, ±30%). Document all base-case assumptions clearly before running sensitivity. After completing all sensitivity tests, produce a tornado chart to rank the results by impact. The combination of sensitivity analysis + tornado chart is the standard risk communication package for executive audiences.

Technique 04

Tornado Charts

Which risk matters most? Tornado charts answer this visually — making sensitivity results instantly actionable for any audience.

A tornado chart visualises sensitivity analysis results as horizontal bars ranked from largest impact (top) to smallest (bottom). The resulting shape resembles a tornado — wide at the top, narrowing toward the base. The widest bar at the top is the variable that most influences the outcome. Management should focus attention and mitigation effort there first.

Business Example
Project Profit Sensitivity — Tornado Chart
TORNADO CHART — Impact on Project Profit ($000s) Base Case: $400K Sales Volume −$400K +$400K Selling Price −$250K +$250K Material Cost −$160K +$160K Labour Cost −$90K +$90K Utilities −$30K +$30K Downside (variable ↑) Upside (variable ↓)

Reading the chart: Sales volume has the widest bar — it dominates the outcome. A focus on volume risk mitigation (pipeline monitoring, contingency capacity) delivers far more protection than addressing utilities (narrowest bar). Selling price is the second priority.

Benefits of Tornado Charts

Executive-friendly: A bar chart ranked by size is instantly legible at every level of the organisation. Fast interpretation: The top 2–3 variables are obvious at a glance. Prioritises resource allocation: Management effort should be proportional to bar width — invest heavily in monitoring and mitigating the top 2 variables, less so in the bottom 2.

Technique 05

Monte Carlo Simulation

Instead of three scenarios, run ten thousand. The result is a full probability distribution of possible outcomes.

Monte Carlo simulation replaces fixed input values with probability distributions — each input is described not as a single number but as a range with associated probabilities. The simulation then randomly samples from each distribution thousands of times, calculating the output for each combination. The resulting collection of outputs forms a probability distribution of the outcome.

Instead of "profit will be $400K in the base case," Monte Carlo gives you: "there is an 80% probability that profit will be between $280K and $620K, and a 10% probability that profit will fall below $200K."

The Monte Carlo Process

01
Assign distributions to uncertain inputs
Replace each uncertain variable with a probability distribution: Normal (symmetric uncertainty around a mean) · Triangular (min, most likely, max) · Uniform (equal probability across a range) · Lognormal (naturally bounded at zero — common for costs and prices).
02
Run N iterations (typically 10,000)
In each iteration, randomly sample one value from each input distribution. Calculate the output. Record the result. Repeat 10,000+ times.
03
Analyse the output distribution
Plot the 10,000 outputs as a histogram or cumulative distribution. Read off: the mean, the 10th and 90th percentiles (P10/P90 range), the probability of being below a threshold (e.g. P(profit < $0) = probability of a loss).
04
Communicate with confidence intervals
Present to stakeholders as: "Expected outcome: $X. P10/P90 range: $A to $B. Probability of meeting the target: C%." This is materially more honest and useful than a single-point forecast.
Business Example
New Store Opening — Monte Carlo Output

A retail chain models first-year profit for a new location. Three uncertain inputs are each assigned triangular distributions:

InputMinimumMost LikelyMaximum
Customer Volume (daily)180260340
Average Spend per Visit ($)$22$31$42
Operating Costs (annual $K)$580K$650K$790K

After 10,000 iterations: Mean profit: $418K · P10: $142K · P90: $695K · P(loss): 8.3%

The 8.3% probability of a loss is the number that matters for the board's risk appetite. If the organisation's threshold is "no more than 5% chance of a loss," this project is marginal — and the analysis has quantified exactly how marginal.

Distribution TypeWhen to useParameters
NormalVariables with symmetric uncertainty around a mean; measurement errorsMean, Standard Deviation
TriangularWhen you have expert estimates of min, most likely, and max — most common in businessMinimum, Mode, Maximum
UniformEqual likelihood across a range; when you truly have no information beyond boundsMinimum, Maximum
LognormalVariables bounded at zero (prices, costs, durations); right-skewed distributionsMean and SD of the log
DiscreteWhen the variable takes specific values with known probabilitiesValue-probability pairs
Technique 06 & 07

Decision Trees & Risk Matrices

Mapping choices, probabilities, and payoffs — then choosing the path with the highest expected value.

Decision Trees — Expected Value Analysis

A decision tree maps out decision alternatives, chance events, and their outcomes. Expected Value (EV) is the probability-weighted average payoff: the sum of each outcome multiplied by its probability. Decision-makers choose the option with the highest EV — unless risk tolerance dictates otherwise.

Business Example
Market Entry Decision — Expected Value
DECISION Enter Market? Enter Don't Enter CHANCE High demand (40%) +$800K Mod demand (40%) +$200K Low demand (20%) −$300K $0 (No gain, no loss) EV (Enter) 0.4 × $800K = $320K 0.4 × $200K = $80K 0.2 × (−$300K) = −$60K EV = $340K Decision: ENTER $340K > $0 (don't enter)

Interpretation: EV of entering = (0.4×$800K) + (0.4×$200K) + (0.2×−$300K) = $340K. Since $340K > $0 (don't enter), the expected-value maximising decision is to enter. But note: there is a 20% chance of losing $300K. If the organisation cannot absorb that loss, it might rationally choose not to enter despite the positive EV.

Risk Matrix — Likelihood × Impact

For risks that cannot be fully quantified, a risk matrix provides a structured qualitative assessment. Each risk is rated on Likelihood (1–5) and Impact (1–5). Risk Score = Likelihood × Impact. Risks in the high-score zone require immediate mitigation; low-score risks are accepted or monitored.

Risk Score (L×I)ZoneAction required
15–25🔴 CriticalImmediate action — mitigation or contingency plan required before proceeding
8–14🟡 HighActive monitoring and mitigation plan. Escalate to senior management
4–7🔵 MediumStandard monitoring. Include in risk register. Review quarterly
1–3🟢 LowAccept and document. Review if circumstances change
Tool Guide 🟢 Start Here

Microsoft Excel

Scenario Manager, Data Tables, Goal Seek — everything you need for risk analysis without any add-ins.

🟢 Start HereScenario Manager

The Scenario Manager stores multiple named scenarios (Best/Base/Worst) with different input values and produces a summary table comparing all outcomes at once.

01
Build your base case model
Create a spreadsheet with clearly labelled input cells (e.g. B2 = Sales Volume, B3 = Price, B4 = Cost) and formula cells that calculate outputs (e.g. B8 = Profit = (B2×B3)−(B2×B4)). Use cell references in all formulas — no hard-coded numbers.
02
Open Scenario Manager
Data → What-If Analysis → Scenario Manager → Add
03
Add Base Case scenario
Scenario name: "Base Case". Changing cells: select all input cells (e.g. B2:B4). Click OK → enter the base case values → OK.
04
Add Best Case and Worst Case
Click Add again. Name: "Best Case". Enter the optimistic values for each cell. Repeat for "Worst Case" with pessimistic values.
05
Generate the summary
Click Summary → Result cells: select your output cell(s) (e.g. B8 = Profit) → OK. Excel creates a new sheet with all three scenarios side by side in a formatted table.
Output
A formatted table showing input values and output results for each scenario — ready to paste into any presentation or report.
🟢 Start HereData Tables — One-Way & Two-Way Sensitivity

Data Tables calculate how a formula result changes across a range of input values automatically — far faster than manually changing inputs one at a time.

01
One-Way Data Table (one variable)
Set up a column of input values (e.g. sales volumes: 7000, 8000, 9000, 10000, 11000). In the cell one row above and one column to the right of the first input, place a reference to your output formula. Select the entire range (inputs + blank cell above + formula cell) → Data → What-If Analysis → Data Table → Column Input Cell: enter the cell reference of the input being varied → OK.
02
Two-Way Data Table (two variables)
Set up row headers (one variable range) and column headers (another variable range). Place the output formula at the intersection. Select the full table → Data → What-If Analysis → Data Table → Row Input Cell: first variable cell, Column Input Cell: second variable cell → OK.
Use case for two-way table
Price (rows) × Volume (columns) → Profit — shows profit for every combination simultaneously. Add conditional formatting (green = profitable, red = loss) for instant visual impact.
🟢 Start HereGoal Seek

Goal Seek finds the input value needed to achieve a specific target output. The reverse of a normal calculation: "What sales volume do we need to break even?"

01
Open Goal Seek
Data → What-If Analysis → Goal Seek
02
Configure
Set cell: your output formula cell (e.g. B8 = Profit). To value: your target (e.g. 0 for break-even). By changing cell: the input you want Excel to adjust (e.g. B2 = Sales Volume) → OK.
Business use
"At what sales volume do we break even?" · "What price do we need to achieve a 15% margin?" · "What cost reduction gets us to $500K profit?"
🟢 Start HereTornado Chart (Manual in Excel)
01
Prepare the data
Create a table: Variable | Downside Impact | Upside Impact. Sort by the absolute value of total range (Downside + Upside), largest first.
02
Insert a Bar Chart
Select Variable column and both impact columns → Insert → Bar Chart → Clustered Bar
03
Format as tornado
Set the downside series to negative values (multiply by −1). Both series share the same axis, creating bars extending left (downside) and right (upside) from the base case. Format downside bars red, upside bars green.
Tool Guide 🔵 Full Power

Python — Scenario, Sensitivity & Monte Carlo

Automate all risk analysis techniques — from scenario tables to full Monte Carlo simulations with thousands of runs.

🔵 Full PowerScenario & Sensitivity Analysis
# Scenario Analysis import pandas as pd import numpy as np import matplotlib.pyplot as plt # Base model function def profit(sales, price, unit_cost): return sales * (price - unit_cost) # Scenario table scenarios = { 'Best Case': {'sales': 15000, 'price': 110, 'unit_cost': 55}, 'Base Case': {'sales': 10000, 'price': 100, 'unit_cost': 60}, 'Worst Case': {'sales': 7000, 'price': 95, 'unit_cost': 70}, } for name, s in scenarios.items(): s['profit'] = profit(**{k:v for k,v in s.items()}) df_scen = pd.DataFrame(scenarios).T print(df_scen) # Sensitivity Analysis — vary each input ±20% one at a time base = {'sales': 10000, 'price': 100, 'unit_cost': 60} base_profit = profit(**base) variables = ['sales', 'price', 'unit_cost'] changes = np.arange(-0.3, 0.31, 0.1) # -30% to +30% sensitivity = {} for var in variables: profits = [] for chg in changes: params = base.copy() params[var] = base[var] * (1 + chg) profits.append(profit(**params)) sensitivity[var] = profits # Tornado chart ranges = {} for var, profits in sensitivity.items(): worst_idx = profits.index(min(profits)) best_idx = profits.index(max(profits)) ranges[var] = (min(profits) - base_profit, max(profits) - base_profit) ranges_df = pd.DataFrame(ranges, index=['downside','upside']).T ranges_df['total_range'] = ranges_df['upside'] - ranges_df['downside'] ranges_df = ranges_df.sort_values('total_range', ascending=True) fig, ax = plt.subplots(figsize=(10, 5)) ax.barh(ranges_df.index, ranges_df['downside'], color='#c0392b', alpha=0.75, label='Downside') ax.barh(ranges_df.index, ranges_df['upside'], color='#2e7d5a', alpha=0.75, label='Upside') ax.axvline(0, color='black', linewidth=0.8) ax.set_title('Tornado Chart — Sensitivity of Profit') ax.legend() plt.show()
🔵 Full PowerMonte Carlo Simulation
# Monte Carlo simulation using triangular distributions from scipy import stats as st N = 10_000 # number of iterations np.random.seed(42) # Triangular distributions (min, mode, max) sales_sim = st.triang(# c = (mode-min)/(max-min) c=(260-180)/(340-180), loc=180, scale=340-180).rvs(N) spend_sim = st.triang(c=(31-22)/(42-22), loc=22, scale=42-22).rvs(N) fixed_cost_sim = st.triang(c=(650-580)/(790-580), loc=580, scale=790-580).rvs(N) # Calculate annual profit for each of 10,000 iterations revenue_sim = sales_sim * 365 * spend_sim profit_sim = revenue_sim - fixed_cost_sim * 1000 # costs in $ profit_K = profit_sim / 1000 # in $000s # Summary statistics print(f"Mean: ${profit_K.mean():.0f}K") print(f"P10 (10th pct): ${np.percentile(profit_K, 10):.0f}K") print(f"P90 (90th pct): ${np.percentile(profit_K, 90):.0f}K") print(f"P(loss): {(profit_K < 0).mean()*100:.1f}%") print(f"P(profit > $500K): {(profit_K > 500).mean()*100:.1f}%") # Plot distribution fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 5)) ax1.hist(profit_K, bins=80, color='#c8922a', alpha=0.75, edgecolor='white') ax1.axvline(0, color='red', linestyle='--', label='Break-even') ax1.set_title('Monte Carlo: Profit Distribution') ax1.set_xlabel('Profit ($000s)') ax1.legend() # Cumulative distribution (S-curve) sorted_p = np.sort(profit_K) cdf = np.arange(1, N+1) / N ax2.plot(sorted_p, cdf*100, color='#2c5f8a', linewidth=2) ax2.axhline(50, color='#c8922a', linestyle='--', label='P50 (median)') ax2.set_title('Cumulative Distribution (S-Curve)') ax2.set_xlabel('Profit ($000s)') ax2.set_ylabel('Probability (%)') ax2.legend() plt.show()
@RISK and Crystal Ball — Excel add-ins for Monte Carlo

For analysts who prefer Excel over Python, @RISK (Palisade) and Crystal Ball (Oracle) are industry-standard Excel add-ins that integrate Monte Carlo simulation directly into spreadsheet models. You define distributions by right-clicking cells and selecting distribution types — no formulas or code. They produce output histograms, S-curves, and sensitivity (tornado) charts automatically. Widely used in finance, engineering, and consulting.

Interactive Practice

Three Simulators

Build intuition for scenario analysis, sensitivity analysis, and Monte Carlo through live interaction.

Simulator 1 · Scenario Builder

A telecom company faces declining profitability. Build three scenarios by adjusting the five key variables. Watch how profit changes under each scenario.

Adjust sliders for each scenario, then compare all three.

Simulator 2 · What-If Calculator

Starting from a base business model, apply specific what-if changes and see the immediate profit impact.

Base Model: Revenue = $1,000,000 · Costs = $700,000 · Profit = $300,000
Click a what-if scenario to calculate the impact instantly.

Simulator 3 · Monte Carlo Explorer

Run a live Monte Carlo simulation for a product launch. Adjust the uncertainty on key inputs and watch how the profit distribution changes.

Adjust uncertainty sliders to see how wider or narrower input distributions affect the profit outcome.
Best Practice & Assessment

Common Mistakes & Knowledge Check

Six mistakes that undermine risk analysis — followed by five assessment questions.

Mistake 01

Presenting a single-point forecast without scenarios

"Revenue will be $4.2M next year." Without a range or confidence interval, this implies false precision. Any business plan based on a single number is a plan without risk awareness. Always accompany forecasts with a spread of scenarios.

Mistake 02

Building scenarios that are not internally consistent

A "Worst Case" where demand falls 30% but prices stay flat is not a coherent scenario — in a real downturn, pricing pressure typically increases too. Scenarios must reflect how variables actually co-move in the real world.

Mistake 03

Confusing sensitivity analysis with scenario analysis

Sensitivity analysis changes one variable at a time. Scenario analysis changes multiple variables simultaneously. Mixing them produces results that cannot be cleanly interpreted. Maintain discipline: one variable at a time for sensitivity; coherent multi-variable stories for scenarios.

Mistake 04

Treating the Expected Value as the "most likely" outcome

Expected Value is the probability-weighted average outcome — not the most probable one. In the market entry example, EV = $340K but the most likely individual outcome may be either $800K or −$300K. Communicate this distinction clearly to stakeholders.

Mistake 05

Assigning distributions in Monte Carlo without justification

Picking "Normal" for every variable because it is familiar is not analysis — it is assumption. Each input distribution should reflect the actual uncertainty characteristics of that variable. Costs are often lognormal; subjective estimates are often triangular. Document the choice.

Mistake 06

Never updating the analysis as new information arrives

A scenario built in January with January's assumptions becomes stale as the year progresses. Risk analysis must be a living tool — re-run when key assumptions change significantly. A static risk register reviewed once a year is a compliance exercise, not a management tool.

Set 08 · Key Takeaway
The goal is not to predict the future. It is to understand which assumptions matter most — and to make decisions that hold up even when those assumptions are wrong.

Knowledge Check

Q1 — A business analyst builds a scenario analysis for a new product launch. The Worst Case shows: Sales = 7,000 units, Price = $95, Cost = $70, Profit = $175,000. Which question should the analyst ask next?
A
Is the worst case scenario probable?
B
Which scenario worries management most — and which assumptions drive the largest differences between scenarios?
C
Should we add a fourth "catastrophic" scenario?
D
Can we re-run the model with better data?
Scenario analysis is most valuable not for its numbers but for the conversations it enables. The two questions that matter most: (1) "Which scenario worries management most?" — focuses attention on risk appetite. (2) "Which assumptions drive the largest differences?" — identifies the variables most worth monitoring and managing. $175K worst case vs $825K best case is a 4.7× spread — the analysis has revealed significant exposure, now it must drive action.
Q2 — A sensitivity analysis shows that a 10% change in unit cost produces a 6% change in NPV, while a 10% change in sales volume produces a 40% change in NPV. What should management conclude?
A
Unit cost is more important than sales volume because cost management is within our control
B
Sales volume is the critical variable — NPV is 6.7× more sensitive to volume changes than to cost changes. Monitoring and protecting sales volume should be the primary risk management focus.
C
Both are equally important — manage all variables equally
D
Neither variable matters — the NPV is positive in the base case
Sensitivity analysis reveals that volume is 40/6 ≈ 6.7× more sensitive than cost. The tornado chart would show volume as the widest bar. Management effort, monitoring frequency, and contingency planning should be proportional to sensitivity. This does not mean ignoring cost — but it does mean that the biggest risk is demand shortfall, not cost overrun. Build volume tracking into the monthly review first.
Q3 — A Monte Carlo simulation on a capital investment produces: Mean profit = $520K, P10 = −$80K, P90 = $980K, P(loss) = 12%. The board's risk appetite is "no more than 5% probability of a loss." What is the correct conclusion?
A
Proceed — the mean outcome is strongly positive at $520K
B
Do not proceed without modification — the 12% probability of loss exceeds the board's 5% threshold. Identify which inputs drive the downside and explore risk mitigation options.
C
The simulation is unreliable — P10 to P90 is too wide a range
D
Proceed — the P90 outcome of $980K is excellent
The board's risk appetite is the binding constraint, not the mean. 12% probability of loss against a 5% threshold means this investment fails the governance test despite its positive expected value. Next steps: run a sensitivity analysis on the Monte Carlo inputs to identify which variables most drive the downside. Then explore: can contract structures, insurance, staged investment, or operational changes reduce P(loss) below 5%? If yes, resubmit. If not, the investment does not meet the board's risk criteria.
Q4 — An analyst uses Goal Seek in Excel to answer: "At what sales volume do we break even?" The formula is Profit = Sales × (Price − Cost) − Fixed Costs. Goal Seek should be configured as:
A
Set cell: Profit formula cell · To value: 0 · By changing cell: Sales volume cell
B
Set cell: Sales volume cell · To value: 0 · By changing cell: Profit formula cell
C
Set cell: Fixed costs cell · To value: 0 · By changing cell: Profit formula cell
D
Set cell: Profit formula cell · To value: Sales × (Price − Cost) · By changing cell: Fixed costs
Goal Seek works backwards from a target: "Set [output formula] To [target value] By Changing [input cell]." For break-even: Set cell = Profit cell (the formula output), To value = 0 (break-even), By changing cell = Sales volume (the input to adjust). Excel iterates until Profit equals 0, reporting the sales volume that achieves it. The "Set cell" must always be a formula — not a raw input value.
Q5 — A market entry decision tree shows EV(Enter) = $340K and EV(Don't Enter) = $0. However, "Enter" has a 20% probability of a $300K loss. The company's annual profit is $200K and a $300K loss would threaten solvency. Should they enter?
A
Yes — EV maximisation always gives the right answer
C
Yes — EV of $340K far exceeds the $0 from not entering
B
Not necessarily — EV maximisation assumes the firm can absorb all losses. A 20% probability of a $300K loss when annual profit is $200K represents an existential risk. Risk aversion is rational here — the worst case threatens the firm itself.
D
No — negative outcomes should always prevent entry regardless of EV
Expected Value maximisation is the rational choice for an organisation that faces many similar decisions and can absorb individual losses. But when a single loss could threaten solvency, risk aversion is economically rational — not irrational. A $300K loss on $200K annual profit means the firm could go insolvent. The correct analysis: acknowledge the positive EV, but explore risk mitigation (joint venture to share downside, phased entry to limit initial exposure, insurance) before committing to the full investment.