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Valuation Under Uncertainty

How to make investment decisions when every estimate of value is a wide range: how to see the range, how to combine methods, and how to turn uncertainty into rules about price and position size.

Lesson 10 of 10 · 7 min read · Advanced · Members · Last reviewed October 2026

The short version

Every valuation is a range presented as a number. The honest approach is to find out how wide the range is, by varying the assumptions together and by using more than one method, and then to decide what to do with it. A narrow range around a price says the investment is fairly valued. A price well below the whole range is an opportunity. A range so wide that it includes almost any price means the company is too hard to value, and passing is a legitimate answer. Uncertainty should also set the size of the margin of safety you demand and the size of the position you take. The goal isn't precision. It's to avoid being confidently wrong.

By the end of this lesson, you'll be able to

  • Distinguish the different sources of uncertainty in a valuation
  • Show a valuation as a range, using combinations of assumptions and more than one method
  • Set a margin of safety and a position size that reflect how uncertain the estimate is

Why this matters

The core DCF lesson valued STU Corp at $44.69 a share. That figure has four digits and no claim to them. It came from assumptions about growth, risk, and the distant future, each of which could reasonably be different. The lessons in this module have added more methods and more numbers. This one is about what to do with all of them, because an investor who forgets that the estimate is uncertain will act as though they know more than they do.

Three kinds of uncertainty

  • The inputs. You don't know what growth, margins, or the discount rate should be. This is the uncertainty that scenarios and sensitivities address.
  • The method. A DCF, a set of comparable companies, and a sum of the parts can give different answers for the same company, and none is the true one.
  • The outcome. Even a perfectly judged probability is only a probability. A company with a 70% chance of succeeding fails three times in ten, and you only get to see one of the ten.

The first two can be reduced by work. The third can't. It can only be managed, through diversification and position size.

Seeing the range

A sensitivity changes one input at a time. For STU Corp, moving each assumption a little gives a narrow band.

STU Corp's value per share when one assumption moves
AssumptionLowerBaseHigher
Growth for five years: 9%, 10%, 11%$42.89$44.69$46.55
Discount rate: 10.3%, 9.8%, 9.3%$41.53$44.69$48.35
Long-run growth: 2.5%, 3%, 3.5%$42.23$44.69$47.53

Each row looks reassuring: a few dollars either way. But assumptions don't move one at a time, and they can be wrong by more than this.

Now let all three vary together, across the ranges used for the bear, base, and bull cases in Scenario Analysis: Bull, Base, and Bear Cases: growth of 5%, 10%, or 14%, a discount rate of 8.8%, 9.8%, or 10.8%, and long-run growth of 2%, 3%, or 3.5%. That's 27 combinations.

STU Corp's value per share across 27 combinations of assumptions
Value per share
Lowest$28.88
A quarter of the results are below$37.53
Middle result$44.69
A quarter of the results are above$52.53
Highest$66.94
Combinations above the $50 share price7 of 27
Combinations below $409 of 27

The middle result is the same $44.69, but it now sits in a range from under $29 to almost $67. Half of the combinations fall between about $38 and $53. Only 7 of the 27 put the value above today's price. That's a more useful statement than "$44.69", and it leads to a clearer conclusion: at $50, more of the reasonable outcomes are below the price than above it.

Professionals sometimes take this further with simulation, drawing thousands of combinations at random. The idea is the same, and so is the limit. The spread that comes out depends entirely on the ranges that go in. A simulation can't tell you whether 5% to 14% growth is the right range. It only shows what follows if it is.

The rest of this lesson is for members

Still to come in this lesson: Using more than one method, Three situations, Turning uncertainty into rules, the key takeaways, and 2 quiz questions with explanations.

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