Industry: Manufacturing Product: ModelRisk Application: Optimizing Factory Automation Investment Decisions Under Uncertainty
A consumer-electronics manufacturer was weeks away from signing a $28 million automation contract for its Vietnam assembly line — six-axis robots, an AI-driven optical inspection cell, AGVs for inter-station transport, and the SCADA/MES integration to make it all observable. The deterministic NPV from the vendor's business case was +$12.4 million over a seven-year horizon, with an IRR of 17 %. The board's investment committee asked the question the deterministic model could not answer: what is the probability we lose money on this?
The corporate finance team built a Monte Carlo NPV model in ModelRisk that ran 100,000 trials over the seven-year horizon with stochastic inputs on efficiency gains, labour-cost trajectory, defect-rate reduction, demand path and technology-obsolescence timing. The deterministic +$12.4M case turned out to sit out in the upper-middle of the distribution, not at its centre: the simulated mean NPV was $6.9M, the median only $4.1M, and — the number that stopped the deal — P(NPV < 0) = 41%, with P(NPV < −$5M) = 29%. The chart below is the whole argument: a long right tail that earns the vendor's headline figure in the good cases, against a left tail that loses real money two times in five.
The deterministic $12.4M is reachable — it sits at roughly the 67th percentile — but it is a hopeful outcome, not an expectation. The right-skew is what pulls the mean ($6.9M) above the median ($4.1M): the upside scenarios (high efficiency uplift compounding against fast-rising Vietnamese wages) are genuinely large, but they do not happen often enough to make the central case look like the vendor's slide. Those numbers turned a "go" memo into a stage-gated investment.
The vendor's deterministic case stacked single-point estimates on five drivers. Each was repriced as a defensible distribution.
Efficiency gain. Vendor pilot at a sister facility delivered an 18% throughput uplift, but two earlier deployments had returned 7% and 11%. Triangular(min = 5%, mode = 14%, max = 25%) captured the integration risk that has historically eroded vendor promises.
Defect-rate reduction. The legacy model used a LogNormal "mean 30%, sd 10%" — sloppy parameterisation that allowed >70% reductions in roughly 2% of draws (implausible). Replaced with Beta(α = 4, β = 6) scaled to (0, 60%), mean 24%, with the upper bound at 60% reflecting the physical limit (residual defects from non-automated stages remain).
Labour-cost inflation. The Vietnam Statistics Office series shows 7–11% annual wage growth, not Normal-with-4%-mean. Modelled as Triangular(4%, 7.5%, 11%) per year, compounded — a 7-year horizon turns a 7.5% annual rate into a labour bill that grows about 66%, and the 11% high end more than doubles it, which is what makes the automation case work or fail.
Demand path. Annual unit demand modelled as geometric Brownian motion with drift 3% and volatility 14% — appropriate for trending consumer-electronics volumes where year-on-year shocks compound. The realised demand path scales the labour and rework savings each year, so a weak-demand decade quietly erodes the automation case even when the technology performs.
Obsolescence horizon. The vendor warrants the cell for 10 years; competing technology disclosures suggest a meaningful chance of disruption sooner. Discrete distribution: P(useful life = 5 yr) = 15%, P(7 yr) = 30%, P(10 yr) = 40%, P(15 yr) = 15%. The terminal-value calculation uses the realised life, not a deterministic 10.
The distribution is wide and right-skewed: P10 = −$14.6M, P50 = $4.1M, P90 = $31.8M. The 41% probability of negative NPV is concentrated in scenarios that combine two adverse draws: low efficiency gain + early obsolescence, or low efficiency gain + flat labour costs. Neither tail event is exotic, and their joint occurrence drives the loss tail — the 29% of trials that come in below −$5M.
The board's risk appetite — "no investment with more than 25% probability of negative NPV without a documented mitigation plan" — was breached. The deterministic memo would have walked straight into that policy without anyone noticing.
Efficiency gain dominates the tornado — by a wide margin — followed by labour-cost trajectory, then obsolescence horizon, then defect-rate reduction. Demand volatility, the variable the operations team had spent the most time debating, ranks fifth. That reordering itself was a contribution: the next month's pre-contract work was redirected from demand market research to two activities that actually move the answer — a performance-guarantee clause on the efficiency gain (vendor pays back capex proportionally if uplift < 10%) and a buy-back clause on obsolescence (vendor obligated to upgrade at marginal cost if successor technology is released within 5 years).
The simulation then evaluated a phased alternative: deploy three of the six robotic cells for $14M now, observe one quarter of operating data, then commit the second tranche only if measured efficiency uplift ≥ 11%.
The phased option behaves like a real option to abandon: gating the second tranche on observed performance means the bad scenarios never see the full $28M committed. It raises mean NPV from $6.9M to $8.9M, lowers P(NPV < 0) from 41% to 38%, and — most importantly — lifts the P10 from −$14.6M to −$9.0M, a +$5.6M improvement at the downside that comes almost entirely from cutting losses short rather than from any extra upside. The capital committee read the curve and approved the phased structure unanimously. The vendor agreed to the performance-guarantee clause to keep the deal alive, which compressed the loss tail further at P10.
A deterministic NPV of +$12.4M and a 41% probability of losing money are statements about the same investment, and the second one is the one that gets the contract restructured.