Scenario analysis

A sensitivity grid moves one or two dials and freezes everything else. That's useful, but economically naive, because in the real world drivers move together. A housing slump doesn't politely lower Home Depot's growth and leave its margins alone. It cuts traffic, shifts the sales mix away from big-ticket items, deleverages fixed costs and compresses margins, all at once. There are two upgrades, and the second needs more machinery than the first.

Scenario analysis: coherent stories, with drivers that move together. Write two or three internally consistent worlds. Each one is a one-sentence story, and every driver in it is that story told in numbers. This is Damodaran's narrative-to-numbers idea. When the story changes, all the numbers change with it. Here's the Home Depot-style retailer in three worlds:

What makes a good scenario?

These rules keep scenarios from turning into wishful thinking. (1) Coherence. You may not borrow the bull's margins for the bear's growth, and each column must survive the question "tell me the world in which all of these hold at once." (2) Probabilities are confessions. Weight the scenarios (say 25/55/20 here, giving an expected value ≈ $280), but report the spread alongside. A $183 to $378 range around a $354 price is the real information. It tells you the price is above even a probability-weighted value, and roughly at the bull case. (3) Three scenarios, not nine. Beyond bear/base/bull you're pretending to a resolution you don't have. (4) The bear is a different world, and "base minus 10%" doesn't describe one. Writing it is where you discover what actually kills the thesis, which feeds question 4 of the spine and the pre-mortem habit of Phase 8.

How does Monte Carlo simulation work in a DCF?

Monte Carlo: the grid, generalized. Instead of three hand-picked worlds, let a spreadsheet draw thousands. Assign distributions to the 2 or 3 drivers that dominate your grid, draw them jointly, recompute value on each draw and look at the distribution of outputs. Here's the HD-style machine with growth ~ Normal(5%, 1.5%) truncated at [0%, 10%], margin ~ Normal(14.1%, 0.8%) and terminal g ~ Uniform(2.2%, 3.2%), over 10,000 draws. (A sheet with 100 rows of NORM.INV(RAND(),…) teaches the same lesson.)

P10 ≈ $247    P25 ≈ $266    Median ≈ $289    P75 ≈ $313    P90 ≈ $334
P(value > $354 price) ≈ 4%

That last line is the payoff. Under your own stated uncertainty, only ~4% of coherent worlds justify today's price. No point estimate gives you a sentence that sharp. Five habits keep Monte Carlo from turning into random-number theater.

(1) Put distributions only on drivers you can reason about: base rates, history, the grid's dominant dials. That means 2 or 3 drivers, never 15. (2) Respect correlation. If growth and margin move together in reality, draw them jointly, or admit that your spread is understated, because independent draws narrow the output in a misleading way. (3) Never report the mean as "the value". The distribution is the answer, so use percentile bands and probability-of-X statements. (4) The output inherits every bias of your inputs. Monte Carlo formalizes your uncertainty, and it doesn't discover the truth. Garbage distributions in, confident-looking garbage out. (5) The constraints still bind inside every draw, with g capped and reinvestment tied. Build them into the recalculation, as the app's sandbox does.

Which tool should you use when?

So where does each tool belong? Run the grid always, since it costs nothing. Build scenarios on every serious valuation, because they force bear-case thinking. Save Monte Carlo for when the decision hangs on tail probabilities, or when a driver really is distributional, like commodity prices or approval odds. You'll meet those again in the cyclicals and Dark-Side cases. All three exist to enforce one guardrail: valuation is a range, and anyone quoting you a point is either new or selling something.