| Vose Software

Industry: Aerospace
Product: ModelRisk
Application: Aircraft Lifecycle Cost Analysis Under Uncertainty


A deterministic plan said $745M to fly — the simulation said the 90% range spans $1.2B

A wide-body aircraft leased over 25 years carries roughly $170M in capital cost plus operating, maintenance, and end-of-life spend that a deterministic plan pinned at a total cost of ownership of $745M per tail. The leasing company's investment committee had been pricing the lease at a fixed 0.92% of capital cost per month against that single number. A Monte Carlo lifecycle model told a far wider story: the P10–P90 TCO band ran from $558M to $1,792M — a 90% range of roughly $1.2 billion, with a right-skewed tail driven by fuel-price regimes and heavy-maintenance inflation. The lease pricing was rebuilt around the distribution, not the point.

The chart below is the picture the committee had been missing: a long right tail that the $745M deterministic line sits far down the left side of.

25-year total cost of ownership distribution

Mean TCO came in at $1,140M — well above the deterministic $745M, because the right-skewed cost components (fuel-price tail, heavy maintenance inflation) pull the mean far above the plan. Median TCO was $811M and P95 was $2,559M: a multi-hundred-million-dollar overrun against the deterministic plan, with material probability.

Where the 25-year cost actually lives

The model was assembled over a 300-month horizon with the following stochastic components:

Acquisition — fixed at $192M list price less a negotiated 11.5% launch-customer discount, so $170M. Not stochastic.

Fuel burn — base 14,200 lb/hr cruise, with a LogNormal efficiency-degradation curve adding 0.18% per year (σ 0.05%) reflecting engine wash schedule and aero deterioration. Jet fuel price modeled as a two-regime jump-diffusion (low-vol drift 2%/yr, σ 22%; high-vol drift 5%/yr, σ 48%; switching probability 11%/year). Block hours per year drawn from a Triangular(2,800 / 3,650 / 4,200), reflecting fleet-utilization variability across the 25-year ownership.

Heavy maintenance — D-check every 6 years, cost LogNormal with median $7.8M and σ_log = 0.32. Engine shop visits every 5,400 flight hours at median $4.2M each, also LogNormal. Both inflated at a stochastic inflation rate drawn from an AR(1) process around 3.2%/yr to capture the persistence of aerospace MRO cost inflation.

Crew, navigation, station fees — block-hour-driven, $1,180/hour at year-0, escalating with the inflation process.

Residual value at year 25 — the largest single uncertainty. Modeled as a mixture distribution: 70% probability of "conversion-feasible" (LogNormal, median $38M, σ_log = 0.28); 30% probability of "part-out only" (LogNormal, median $11M, σ_log = 0.35), reflecting whether the freighter conversion market is open or saturated at retirement.

50,000 iterations over the 25-year horizon produced the TCO distribution shown above, with mean $1,140M, P10 $558M, median $811M, P90 $1,792M, and P95 $2,559M.

Three retirement-timing scenarios

The model was rerun against three retirement decisions — keep the airframe to year 25, divest at year 18 into a healthy used market, or divest at year 22 with conversion-line pre-booking — to test the optionality of early exit.

Three retirement-timing strategies: cumulative cost-net-of-residual CDF

The year-18 exit had the tightest distribution (less cumulative fuel and maintenance uncertainty), and the lowest mean cost-net-of-residual at $734M because fewer years of operating cost accrue. The year-22 with-conversion option had a mean of $905M and a P90 of $1,430M — narrower than the full-25-year hold (mean $1,049M, P90 $1,677M), because conversion pre-booking insured against the year-25 residual-mixture tail.

What drives the TCO spread

Tornado: drivers of 25-year TCO

Fuel-price regime persistence drives $47M of P10–P90 spread — the single largest item. Heavy maintenance escalation rate is second at $29M. Residual-value mixture probability — the binary question of whether the year-25 conversion market will be open — drives $26M on its own. Block-hour utilization (whether the asset flies 3,000 hours/yr or 4,000) drives $22M. The point estimate showed none of this.

Why a point estimate misled lease pricing

The leasing company's prior pricing model treated lifecycle cost as a single number and added a 14% margin. The Monte Carlo model showed that at 0.92% of capital cost per month, the lessor recovered TCO + margin in only 56% of simulated paths — there was a 44% probability of negative lifetime return, driven mostly by fuel-price regime and residual-value tail risk.

Repricing to 1.04% per month and inserting a fuel-pass-through clause covering the high-vol regime moved the breakeven-or-better probability to 84%. That clause was the consequence of the simulation — it was not in the prior contract template.

What the model changed

  • Lease rate factor raised from 0.92% to 1.04% of capital cost per month — directly underwritten by the simulation's TCO distribution.
  • Fuel-pass-through clause negotiated into all new long-term leases, triggered when the rolling-36-month average jet fuel price exceeds the high-vol regime threshold.
  • Year-22 conversion-pre-booking option valued at $11M against the year-25 hold — the leasing company purchased conversion slots from two MRO partners on the back of this figure.
  • The investment committee replaced the single-line TCO figure on its underwriting sheet with a P10/P50/P90 triple, plus a stated P(loss) figure.

ModelRisk Functionality Used

  • Two-regime jump-diffusion for jet fuel price across the 25-year horizon — calibrated to 1990–2024 spot data, replacing the prior GBM that under-priced the 2008 and 2022 episodes.
  • Mixture-distribution residual value capturing the binary "conversion market open / closed" outcome at year 25 — a structural feature that a single Triangular cannot represent.
  • AR(1) inflation process on MRO escalation, picking up the documented persistence in aerospace maintenance cost inflation that an independent-year model misses.
  • Lessor cash-flow waterfall computing the probability of negative lifetime return under candidate lease rates — the metric the investment committee priced against.
  • Tornado analysis isolating fuel-price regime and residual-value mixture as the two drivers worth contracting around.

A 25-year cost-of-ownership figure is a distribution more than a billion dollars wide — and lease contracts written against the central estimate quietly transfer the tails to whichever counterparty is too unsophisticated to price them.