Scenario Analysis: Bull, Base, and Bear Cases

Why this matters

Margin of Safety and Valuation Ranges introduced three scenarios for STU Corp and a probability-weighted value. This lesson is about building them well. A single estimate of value hides the most important fact about it, which is how wrong it could be. Scenarios bring that into the open, but only if they're built with care. Three numbers picked a little above and below a base case add nothing.

Scenarios and sensitivities

Two tools look similar and do different jobs.

• A sensitivity changes one input and holds everything else still. Terminal Value and Sensitivity did this with the discount rate and long-run growth. It shows which inputs matter most.
• A scenario changes several inputs together, because in the real world they move together. If a competitor takes STU Corp's customers, its revenue grows more slowly, its margins shrink, and its future becomes less certain, all at once.

Sensitivities tell you where to look. Scenarios tell you what you might find.

Start from the drivers

A growth rate for free cash flow isn't an assumption about the business. It's the result of several. For most companies the drivers are how fast revenue grows, how much of each sales dollar becomes cash, and how much has to be reinvested. Write the story first, then decide what it does to each driver.

	Bear	Base	Bull
The story	Its largest retailer cuts orders and cheaper compatible cartridges arrive	Steady progress in systems and subscriptions	Subscriptions keep growing fast and customers stay loyal
Revenue growth, years 1 to 5	7%	10%	12%
Revenue in year 5, $ millions	561	644	705
Free cash flow as a share of revenue in year 5	10%	11%	12%
Free cash flow in year 5, $ millions	56	71	85
Free cash flow growth that results	5%	10%	14%
Discount rate	10.8%	9.8%	8.8%
Long-run growth	2%	3%	3.5%
Value per share	$28.88	$44.69	$66.94

STU Corp earns $44 million of free cash flow on $400 million of revenue today, which is 11%. In the bear case revenue still grows, but cheaper cartridges force prices down, so less of each dollar becomes cash. In the bull case the mix shifts toward subscriptions, which earn more. The values are the ones from the earlier lesson. What's new is that each growth rate now has a reason.

Notice that each case changes the discount rate and long-run growth as well. A business that has lost its biggest customer is riskier and has weaker prospects. Giving the bear case the same discount rate as the bull case would understate how different those futures are.

Keep each case consistent

A scenario has to be able to happen. Check each one against itself:

• Growth needs investment. A bull case with fast revenue growth and falling capital spending assumes the company can grow without building anything.
• Margins have a ceiling. If the bull case needs margins well above what any company in the industry earns, say why this one would be allowed to keep them.
• The cases shouldn't overlap. If the base case already includes winning the big new contract, the bull case can't count it again.
• The bear case must be bad. It should describe a future in which you'd regret buying, not a slightly slower version of the base case.

Weighting the cases

Multiplying each value by its probability and adding the results gives an expected value. With 25% for the bear case, 50% for the base, and 25% for the bull, STU Corp's is $46.30, as the earlier lesson showed. The probabilities are judgments, so test them.

Weights: bear, base, bull	Expected value per share
25%, 50%, 25%	$46.30
35%, 45%, 20%	$43.61
15%, 50%, 35%	$50.11

Shifting ten points of probability between the bear and bull cases moves the answer by a few dollars either way. Only the most optimistic set of weights reaches STU Corp's $50 share price. If an investment looks attractive only when the bull case is given the most weight, the weights are doing the work the analysis should be doing.

Upside against downside

The expected value is one number. The spread around it matters as much. Compare what could be gained with what could be lost from today's price.

	Buying at $50	Buying at $35
Gain if the bull case happens ($66.94)	+34%	+91%
Loss if the bear case happens ($28.88)	−42%	−17%
Gain or loss in the base case ($44.69)	−11%	+28%

At $50, an investor stands to lose more in the bear case than they'd gain in the bull case, and loses a little even if things go to plan. At $35 the same company, with the same three futures, offers a large gain against a modest loss. Nothing about the business changed. Scenario analysis is often most useful for deciding the price at which an investment becomes worth making.

Signposts

A scenario isn't finished until you know how you'd recognize it. For each case, write down two or three things you could observe in the next year or two that would show it's unfolding. For STU Corp:

• Bear: the largest retailer's share of revenue falls, compatible cartridges appear in stores, or the price per cartridge drops.
• Base: subscriber numbers and revenue per subscriber grow close to plan.
• Bull: subscriptions grow faster than systems for several quarters and fewer subscribers cancel.

Signposts turn a valuation into something that can be checked. When results arrive, you compare them with what each case predicted and shift the weights, as Monitoring Positions and Revisiting a Thesis described. Without them, it's easy to explain any result as consistent with what you already believed.

Key takeaways

• A scenario changes several inputs together in a way that fits one story. A sensitivity changes one.
• Build each case from drivers such as revenue growth, margins, and reinvestment, and check that it could really happen.
• Test the probability weights. If only optimistic weights justify the price, be cautious.
• Compare the gain in the bull case with the loss in the bear case at the price you'd pay.
• Write down the signs that would show which case is coming true, and revisit them.

Check your understanding

An analyst's three cases for a company are $48, $50, and $52 a share. The shares trade at $49. What's the main problem?

1. There should be at least five cases to cover the full range of what might happen.
2. The range is too narrow to be a real bear and bull case, so it hides the risk.
3. The base case is above the price, so the shares must already be undervalued.

A company's scenarios are worth $20, $40, and $70 a share, with probabilities of 30%, 50%, and 20%. The shares trade at $40. What does the analysis say?

1. The expected value is $43, so the shares are a clear bargain at $40.
2. The shares are fairly priced, since the base case equals the price.
3. The expected value is $40, with a 50% loss possible and no margin of safety.

What's next

Scenarios start with assumptions and end with a value. The next lesson runs the calculation the other way. Reverse DCF starts with the price and asks what the market must be assuming.