Lesson 5 of 7 11–14% of the exam

By Daniil Tarakanov Updated Oct 22, 20262027 curriculum

Scenario analysis with probability weights

Re-run the whole forecast model under a few coherent scenarios, each giving its own equity value. Weight those values by your subjective probabilities, counting any negative value as zero, and compare the weighted value with market capitalization. Sensitivity analysis instead changes chosen inputs while holding everything else fixed.

5 min cram, 22 min full read. Based on the 2027 CFA® Program Level I curriculum, Equities, Learning Module 8. Sitting in November 2026? The 2026 version of this lesson is still available.

Tailor this to you: take the self-assessment

Before this: Asset and financing models

On the exam

Explain the rationale, construction, and uses of financial statement forecast models in equity valuation
Estimate and interpret the value of an equity security based on the outputs of a financial statement forecast model

Interpret a probability-weighted equity value. Expect: a weighted value from scenario equity values (with a negative scenario set to zero), whether a share looks undervalued, overvalued or fairly valued against market capitalization, what the probabilities are (subjective, not true), and scenario versus sensitivity analysis.

How deeply to learn each part

Know the idea: Understand it in general. It frames other topics, but you will not calculate with it.
Use it: Understand it well enough to solve a question with it. Recognize when it applies.
Memorize: Learn it by heart. The exam will not give it to you.

You know this one. The full lesson is folded away. The takeaways, formulas and checkpoint below are your quick refresher, and the checkpoint is a fair test of whether you still do.

You tested strong here. The full lesson is folded away. The takeaways, formulas and checkpoint below are your quick refresher, and the checkpoint is a fair test of whether you still know it.

Why value more than one future?

A forecast model makes what-if analysis easy: change the story and re-run. In scenario analysis each scenario is a coherent set of assumptions for revenue growth, margins, investment and financing, carried through the statements to its own firm value and equity value. Each one tells its own story, a valuation narrative per scenario . Lesson 7 shows one run in full.

Scenarios can be shown unweighted, as a range (the margin paths in lesson 3), or weighted by probability to give one estimate.

Sensitivity analysis is different. It changes one or more chosen inputs while holding all the others constant, to see how much the value depends on them.

Scenario analysis against sensitivity analysis

Testing a valuation

Scenario analysis Memorize a story, with linked assumptions
- Changes a whole set of linked assumptions, as a story
- Output an equity value per scenario, then a weighted value
Sensitivity analysis Memorize a dial, one input at a time
- Changes chosen inputs, all others held constant
- Output how far value moves per input

Exam tip A scenario is a story; a sensitivity is a dial. A “scenario” that changes one number is a sensitivity.

How do you weight scenario values?

Value each scenario, weight each value by its probability and add them up. That gives the probability-weighted equity value .

Probability-weighted equity value Use it

\text{Equity value} = \sum_{s} p_s \times \max(V_s, 0), \qquad \sum_s p_s = 1

Worked example Tessaly Glass

An analyst values a glass-container maker under four scenarios (CHF million). Market capitalization is 370.

Scenario	Story	Equity value	Probability
Optimistic	faster growth, wider margins, more investment	520	15%
Base	the analyst’s central view: margins recover	410	50%
Stable	costs and assets grow with revenue; margins flat	250	25%
Downside	growth stalls, margins shrink; firm value below debt	−30 → 0	10%

The downside’s computed equity value is negative because firm value falls below debt. Shareholders have limited liability , so equity cannot be worth less than zero (in practice the debt’s market value would fall instead). That gives a negative equity value floored at zero : use 0.
Weighted value: 0.15 × 520 + 0.50 × 410 + 0.25 × 250 + 0.10 × 0 = 78.0 + 205.0 + 62.5 + 0 = 345.5.
The comparison with market capitalization : the base case alone (410, 11% above) says undervalued. The weighted value (6.6% below) says the shares look slightly overvalued, or close to fair. The range changed the conclusion.

Keeping −30 gives 342.5. A plain average of the four (with 0) gives 295.0. Neither is right.

Step 2 on your calculator

0.15×520=STO1 78
0.5×410=STO2 205
0.25×250+RCL1+RCL2= 345.5 (the downside adds 0.10 × 0)

STO store · RCL recall a stored number

0.15ENTER520×0.5ENTER410×+0.25ENTER250×+ 345.5 (the downside adds 0.10 × 0)

ENTER enter (on the HP, puts the number on the stack)

InteractiveTessaly Glass: one equity value from four scenarios

Try this 0 of 3

Shift the probabilities until the weighted value also says 'undervalued'
Turn off the floor and see the weighted value fall
On the sensitivity tab, find the input that moves value most

Scenario equity values (CHF m)

Optimistic520

Base410

Stable250

Downside−30

Probabilities (always sum to 100%)

Optimistic15%

Base50%

Stable25%

Downside10%

CompareFloor negative values at zerolimited liability

Market capitalization (CHF m)370

Hover over or tap a box to follow its path.

Weighted value, base case and market capitalization (CHF m)

Probability-weighted equity value345.5

Verdict on the weighted valueovervalued (−6.6%)

Base case alone saysundervalued (+10.8%)

Trap: plain average295.0

Trap: weighted, no floor342.5

Show working

Optimistic: 0.15 × 520.0 = 78.0

Base: 0.5 × 410.0 = 205.0

Stable: 0.25 × 250.0 = 62.5

Downside: 0.1 × 0.0 (computed −30.0, floored to 0) = 0.0

Weighted equity value = 345.5. Against market capitalization of 370: −6.6%, so the shares look overvalued.

Shareholders have limited liability, so a negative equity value counts as zero. Keeping it gives 342.5.

A plain average of the four (520.0, 410.0, 250.0, 0.0) is 295.0: it ignores the probabilities.

Probability-weighted equity value on your calculator

(0.15×520)+(0.5×410)+(0.25×250)+(0.1×0)=345.5

0.15ENTER520×0.5ENTER410×+0.25ENTER250×+0.1ENTER0×+345.5

ENTER enter (on the HP, puts the number on the stack)

Display: 345.5

A value is a range with weights, and the weights are yours.

Exam tip Probability-weight the equity values, not the inputs. Then floor any negative equity value at zero.

What do the probabilities mean?

They are the analyst’s subjective probabilities , a matter of judgment. They are unlikely to equal the true probabilities, which nobody can know.
Only one scenario will happen. The weighted value summarizes a range of outcomes; it is not a forecast of any one of them.
Scenarios let the analyst build narratives into the value. They do not make the estimate more accurate.
The model is revised as quarterly or semiannual reports and other news arrive, and the scenarios and weights with it. That is updating the model .
A second weighting tool: for a company that might fail, weight a going-concern value and a distress value by the probability of distress (lesson 6).

Go deeper Why the base case is not the answer

The base case can carry the largest weight and still mislead, because the other scenarios are not symmetric around it. In the Tessaly example the downside and stable cases pull the weighted value 64.5 below the base case.

How does sensitivity analysis look?

Worked example One input at a time

A simple valuation has next-year free cash flow to the firm of 30, a weighted average cost of capital (WACC) of 8%, growth of 2% and debt of 150. Firm value is 30 ÷ (0.08 − 0.02) = 500, so equity is 350. Hold everything else and move one input:

Input changed	Low	High
Growth 1% / 3%	equity 278.6	equity 450.0
WACC 9% / 7%	equity 278.6	equity 450.0
Free cash flow 27 / 33	equity 300.0	equity 400.0

Growth and WACC move equity value more than a 10% change in cash flow.

Growth of 3% on your calculator

0.08−0.03=1/x×30−150= 450

1/x reciprocal

30ENTER0.08ENTER0.03−÷150− 450

ENTER enter (on the HP, puts the number on the stack)

Memorize this

MemorizeWeighted scenario value

Step	Rule
Value each scenario	re-run the model to a firm and equity value
Floor	negative equity value → 0 (limited liability)
Weight	Σ p × value, probabilities sum to 1
Compare	weighted value vs market capitalization

Memory hook Run, floor, weight, compare.

Know it cold Probabilities are subjective, not true; scenarios add narrative, not accuracy; update as news arrives.

MemorizeScenario or sensitivity?

Memory hook A scenario is a story; a sensitivity is a dial.

Know it cold Scenario: a coherent set of assumptions changes together. Sensitivity: chosen inputs change, all others held constant.

Scenario analysis against sensitivity analysis

Testing a valuation

Scenario analysis Memorize a story, with linked assumptions
- Changes a whole set of linked assumptions, as a story
- Output an equity value per scenario, then a weighted value
Sensitivity analysis Memorize a dial, one input at a time
- Changes chosen inputs, all others held constant
- Output how far value moves per input

Probability-weighted equity value

\text{Equity value} = \sum_{s} p_s \times \max(V_s, 0), \qquad \sum_s p_s = 1

Quick example

Three scenarios: 90 (probability 35%), 60 (40%) and −20 (25%). The negative value counts as zero, so the weighted value is 0.35 × 90 + 0.40 × 60 + 0.25 × 0 = 55.5.

On your calculator

0.35×90=STO1 31.5
0.4×60+RCL1= 55.5

STO store · RCL recall a stored number

0.35ENTER90×0.4ENTER60×+ 55.5

ENTER enter (on the HP, puts the number on the stack)

How it is asked

Weighted value with a negative scenario

Values 160 (30%), 100 (40%), 60 (25%), −50 (5%).

48 + 40 + 15 + 0 = 103. Keeping −50 (100.5) is the trap.
Fairly valued?

Base case 3.9bn, weighted 3.2bn, market cap 3.5bn.

Judge by the weighted value: about 9% below market cap, so the shares look overvalued. The base case is the trap.
What are the probabilities?

Are scenario probabilities objective?

No: subjective; unlikely to equal the true, unknowable probabilities.
Scenario versus sensitivity

Only terminal growth changes; everything else is held.

Sensitivity analysis.

Exam traps

Comparing the base case, not the weighted value, with market capitalization.
Keeping a negative scenario equity value instead of setting it to zero.
Weighting the inputs (growth, margins) instead of the scenario values.
Treating the probabilities as objective, or the weighted value as more accurate than a single case.
Calling a change in one input, with everything else held, a scenario: that is sensitivity analysis.

Checkpoint

3 exam-style questions. About 90 seconds each.

1Compared with sensitivity analysis, scenario analysis most likely:
2An analyst values a company's equity under four scenarios: upside CHF 180 million (probability 20%), base CHF 120 million (50%), stable CHF 70 million (20%) and downside −CHF 40 million (10%), where firm value is below the face value of debt. The probability-weighted equity value is closest to:
3An analyst's base case values a company's equity at USD 2.6 billion. Weighting four scenarios by the analyst's probabilities gives USD 2.1 billion. The company's market capitalization is USD 2.3 billion. The most appropriate conclusion is that the shares appear:

Key takeaways

Each scenario re-runs the whole model to its own equity value.
Weighted value = Σ probability × equity value, with negative values set to zero.
Compare the weighted value, not the base case, with market capitalization.
Probabilities are subjective; scenarios add narrative, not accuracy. Sensitivity analysis moves chosen inputs and holds the rest.

Probability-weighted equity value

\text{Equity value} = \sum_{s} p_s \times \max(V_s, 0), \qquad \sum_s p_s = 1

Quick example

Three scenarios: 90 (probability 35%), 60 (40%) and −20 (25%). The negative value counts as zero, so the weighted value is 0.35 × 90 + 0.40 × 60 + 0.25 × 0 = 55.5.

On your calculator

0.35×90=STO1 31.5
0.4×60+RCL1= 55.5

STO store · RCL recall a stored number

0.35ENTER90×0.4ENTER60×+ 55.5

ENTER enter (on the HP, puts the number on the stack)

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Practice exam-style questions on Financial Statement Forecasting

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Questions candidates ask

How do you calculate a probability-weighted equity value?

Value equity under each scenario, set any negative value to zero, multiply each by its probability and add them up. Compare the result with market capitalization.

Why is a negative scenario equity value set to zero?

Shareholders have limited liability. If firm value falls below debt, the debt's market value falls instead, and equity is worth about zero, not less.

What is the difference between scenario and sensitivity analysis?

A scenario changes a whole set of linked assumptions as one story. Sensitivity analysis changes chosen inputs while holding all others constant.

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