Monte Carlo simulation quantifies risk by running a project’s cash-flow model thousands of times, drawing each uncertain input from a probability distribution rather than fixing it at a single estimate. The output is not one present worth but a whole distribution of present worths, which is a far more honest answer than a single number carried to four decimals.
It is the third of the risk-quantification methods this course names, alongside expected value and the decision tree.
Why it exists
A decision tree handles risk beautifully when the uncertainty is discrete: three possible demand levels, two possible regulatory outcomes, each with a probability. Every branch is enumerated and the expected value falls out of the arithmetic.
That breaks down as soon as an input is continuous. Annual revenue is not “high, medium or low” — it is a number that could land anywhere in a range. Enumerating branches for a continuous variable means either discretising it badly or drawing a tree with infinitely many branches. Worse, real projects have several uncertain inputs at once, and a tree over five continuous variables is hopeless.
Sensitivity analysis handles continuous inputs but goes the other way: it varies one parameter at a time and says nothing about probability. It tells you which assumptions matter, not how likely a bad outcome is.
Monte Carlo covers the gap: continuous inputs, several at a time, with probabilities attached.
The procedure
- Build the cash-flow model as usual, with the PW (or IRR, or annual worth) as the output.
- For each uncertain input, replace the point estimate with a distribution.
- Draw one value from each distribution, compute the resulting PW, and record it. That is one trial.
- Repeat for thousands of trials.
- Read the resulting histogram of PW.
A worked case
A five-year project at a 10% MARR. First cost triangular on $90k—$130k with a most-likely $100k; annual savings normal with mean $30k and standard deviation $5k; salvage uniform on $5k—$15k. Each trial computes
Do it once with the most-likely first cost and the mean savings and salvage, the way a deterministic analysis would, and you get PW = \19{,}933$. Comfortably positive; approve it.
Now run 200,000 trials. The distribution comes out with a mean of $13,318 and a standard deviation of $20,801, a median of $13,459, and a 5th-to-95th percentile spread running from -\21{,}179 to \47,357. 26% of the trials lose money.
Two things went wrong with the single number, and the simulation shows both. The point estimate sits $6.6k above the mean because the first-cost distribution is skewed right: its mode is $100k but its mean is $106.7k, and plugging in the most-likely value quietly assumed the best-behaved of the three. And the spread is wide enough that a quarter of the outcomes are losses, which no amount of decimal places on $19,933 would have revealed.
“There is a one-in-four chance this project loses money” is a sentence a decision-maker can act on. “The PW is $19,933” is not.
What it does and doesn’t buy you
The strength is that it propagates uncertainty through a model of any complexity without needing the algebra to come out. Correlations between inputs can be built in — if a downturn depresses both revenue and salvage value, the draws can be correlated so the simulation stops pretending the two are independent.
The weakness is the usual one. The output distribution is only as good as the input distributions, and those are estimates too. A simulation dressed in ten thousand trials and a smooth histogram looks authoritative in a way that its inputs do not deserve, and the precision of the picture is not evidence about the accuracy of the assumptions. Garbage in still applies, now with error bars.
Use it when several inputs are uncertain, continuous, and consequential. For one uncertain input, sensitivity analysis is quicker and clearer. For a handful of discrete outcomes, a decision tree is exact and a simulation is overkill.