Industry: Energy Product: ModelRisk Application: Energy Contracts (PPAs and Tolling)
A 250 MW combined-cycle gas plant signing a 12-year corporate PPA at $48/MWh fixed looks safe on a deterministic spreadsheet — the contract pays cash if power prices fall and forfeits upside if they rise. The Monte Carlo simulation on the same plant tells a sharper story: the fixed PPA is worth $221M in expected NPV against a merchant baseline of $315M, and — because it strips out the power-price upside while leaving the IPP exposed to floating gas — it actually carries a fatter left tail than merchant, with NPV below $150M in 22% of futures against merchant's 9%. The lesson is that a contract's risk profile is the shape of its NPV distribution, not a single point — and pricing it requires modelling the merchant tail the deterministic comparison never sees.
An IPP and a hyperscale data-centre buyer used ModelRisk to value four contract structures on the same 250 MW asset: fully merchant, fixed-price PPA, floor-only PPA, and a collar with both floor and cap. The objective was to find the structure that maximised the buyer's risk-adjusted procurement cost while leaving the IPP a defensible expected return. The four NPV distributions, plotted as CDFs on a common set of price paths, are the heart of the analysis.
The merchant book carries the highest expected NPV ($315M) but the widest spread; the fixed PPA gives up roughly $94M of expected value for a tighter — though not strictly better — distribution; the collar sits between them. The rest of this study is about reading those shapes correctly.
The plant's gross margin is the spark spread: power price minus the heat rate (7.2 MMBtu/MWh) times gas price minus VOM ($3/MWh). Modelling power and gas independently is the most common mistake in PPA valuation — the two are jointly driven by load and weather, with rank correlation around +0.45 during normal market conditions that rises to +0.75 in stress months. A static Pearson correlation misses this; a copula handles it cleanly.
The price model is:
Aggregated to an annual gross margin on the 250 MW plant, this joint model produces a mean of $41.4M/yr, a P10 of -$18.1M, and a P90 of $88.0M — and a 14.3% probability of a loss-making year, the years that cause merchant operators the most pain.
Each contract is a payoff function applied to the same 50,000 simulated price paths. Letting \(P\) be power and \(G\) gas:
Returning to the CDF above, the chart shows what the deterministic comparison cannot. The fixed PPA gives up the merchant upside entirely but — because the IPP still pays floating gas under the fixed power price — keeps a real downside in winter-stress years. The collar leaves a thin upside while keeping a tighter floor; its NPV distribution sits between merchant and fixed.
Numerically: merchant mean NPV $315M with P10 $162M; fixed PPA mean $221M with P10 $78M; collar mean $291M with P10 $149M. The fixed PPA's lower P10 is the surprise the simulation surfaces: trading away the power upside without hedging the gas leg does not, on its own, buy left-tail protection. The collar — which clips power at both ends while the gas leg floats — is the structure that actually tightens the distribution. Pricing those trade-offs correctly is what the contract negotiation is about.
The biggest driver of the fixed-PPA give-up is forward-curve drift — if the team's view of future power prices is biased upward, the fixed contract looks worse against merchant. Gas-power tail dependence is second: the bigger the joint-stress co-movement, the more valuable the floor and the more the IPP can charge for it. Plant heat rate moves the give-up in dollars per percentage point of efficiency — a 0.3 MMBtu/MWh heat-rate uncertainty is worth roughly $14M across the contract life.
The model output let the IPP propose a structured deal the deterministic talks could not have framed: a collar [$42, $68] with a winter-only floor uplift to $50/MWh during November–March. The added winter floor costs the buyer $9M in expected NPV but cuts the IPP's P10 NPV in stress winters by $34M — a four-to-one risk transfer that both parties signed. The deterministic spreadsheet would have priced a single fixed number; the simulation priced the conditional payoff that actually matters.
A long-dated PPA is an option-laden contract, and an option-laden contract is priced on the shape of the underlying's distribution — not on its mean. Monte Carlo turns that shape into a number both sides can sign.