Sensitivity and scenario analysis

In simple terms

Every valuation depends on assumptions about the future, and none of them is known. Sensitivity analysis and scenario analysis show how much the answer depends on those assumptions. Instead of one number, you get a range, and you learn which assumptions matter most.

Sensitivity tables

A sensitivity table recalculates the value for different combinations of two key inputs, holding everything else constant. In a DCF, the usual pair is the discount rate and the long-run growth rate, because they drive the terminal value.

Sensitivity tables can be built for other pairs too: revenue growth and operating margin, or margin and capital expenditure. Choose the inputs you are least sure about and that matter most.

Scenario analysis

A sensitivity table changes one or two numbers at a time. Real futures change many things together. Scenario analysis builds complete, internally consistent stories:

• Bear case: demand slows, competition cuts prices, margins fall, growth investment is cut, debt becomes more expensive.
• Base case: the most likely path, given what you know.
• Bull case: the company wins share, margins expand with scale, new products succeed.

Within each scenario, assumptions should fit together. A bull case with fast growth needs more investment; a bear case with falling sales probably means lower margins too, because of operating leverage.

The weighted value uses the idea of expected value. The probabilities are judgements, not measurements, so treat the result as a rough guide.

Presenting a valuation as a range

A useful valuation summary states:

1. The range of plausible values, from bear to bull.
2. The base case and the main assumptions behind it.
3. The two or three assumptions that matter most, and why.
4. What would have to be true for the current price to be justified.

This is more honest, and more useful, than a single target price. It also shows how much room for error the current price gives you, which the margin of safety lesson builds on.

When the range is too wide

Sometimes the honest result is that the range is so wide that the valuation does not help: a young company with uncertain products, a business facing a regulatory decision that could go either way, a cyclical company at an unusual point. In such cases, the right conclusion may be that the business is too hard to value, and that is a legitimate reason not to invest.

Why it matters

A single precise number gives a false sense of certainty and invites anchoring on it. Ranges and scenarios show what you really know, what you are assuming, and what could go wrong. They also make it easier to change your mind when facts change, because you have already thought through the alternatives.

Limitations

Sensitivity tables change only a few inputs at a time and can give a misleadingly narrow range if you choose small variations. Scenarios depend on imagination: the real outcome may be outside all of them. Probabilities assigned to scenarios are subjective. These tools organise uncertainty; they do not remove it.

Common mistakes

• Reporting only the base case.
• Choosing ranges that are too narrow to reflect real uncertainty.
• Building scenarios with inconsistent assumptions, such as high growth with low investment.
• Picking the most favourable cell of a sensitivity table and treating it as the answer.

Try it yourself

Take the DCF you built in this module.

1. Build a three-by-three sensitivity table for the discount rate (one point either side of your base) and long-run growth (one point either side).
2. Write a short bear and bull case, with consistent changes to growth, margin and investment, and value each.
3. Assign rough probabilities and calculate a weighted value.
4. Note where the current share price falls within your range.