| Vose Software

Industry: Manufacturing
Product: ModelRisk
Application: Optimizing Factory Automation Investment Decisions Under Uncertainty


A $28M Robotics Capex with a 41% Chance of Negative NPV

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.

NPV distribution — $28M automation investment, 7-year horizon

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.

Where the uncertainty actually lives

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.

What the simulation revealed

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.

What actually drives NPV

Tornado: drivers of NPV at the $28M capex

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).

Phased commitment: half now, half on milestone

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%.

Full deployment vs phased commitment — NPV CDF

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.

What the model changed

  • The $28M one-shot capex became a $14M + $14M phased commitment, with the second tranche gated on a measured 11% efficiency uplift in the first three months of operation.
  • A performance-guarantee clause was negotiated into the contract, refunding capex proportionally to under-delivered uplift.
  • An obsolescence buy-back clause committed the vendor to upgrade hardware at marginal cost if a successor platform launched within 5 years — repricing the discrete obsolescence distribution.
  • The board's 25%-probability-of-loss policy still required a documented mitigation: the phased option cut loss probability from 41 % to 38 % and roughly halved the downside (P10 from −$14.6M to −$9.0M), and the performance-guarantee clause closed the remaining gap to the 25 % threshold.
  • The deterministic NPV memo template was retired for capex decisions above $5M; all such proposals now ship with the NPV distribution and tail probability.

ModelRisk Functionality Used

  • Triangular and Beta distributions on operational uplift parameters, replacing under-bounded Normal/LogNormal specifications that allowed physically impossible draws.
  • Geometric Brownian motion for the unit-demand path, with annual drift 3% and volatility 14% calibrated to the company's six-year demand series — appropriate for trending consumer-electronics volumes.
  • Discrete obsolescence-life distribution integrated into the terminal-value calculation, so early-obsolescence draws correctly truncated the cash-flow horizon.
  • NPV at 8% WACC computed per trial across 100,000 trials, producing the full distribution that supplied P(NPV < 0), P10, and the tail expectation in the loss region.
  • Comparative scenario simulation of full vs phased deployment, with the same input draws applied to both structures so the comparison isolated structural risk transfer from input-distribution noise.
  • Tornado on NPV that reranked the team's diligence priorities away from demand research toward contract-clause negotiation.

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.