| Vose Software

Industry: Pharmaceutical
Product: ModelRisk
Application: Pricing Optimization (Post-Launch, Ongoing)


Where does EBITDA actually peak? Net-price optimization across a 4-channel payer mix

A specialty therapy three years post-launch sells through a payer mix that looks roughly the same across the industry: about 45% commercial, 28% Medicare Part D, 18% Medicaid, and the remaining 9% through 340B and direct cash. List-price (WAC) decisions cascade through that mix in non-obvious ways. A 5% WAC increase nets less than 5% in commercial because PBMs claw a portion back through rebates; it nets less than zero in Medicaid because the AMP-based best-price clawback can deepen the giveback by 90 basis points for every 100 of list-price increase; and on the cash channel it can lose volume outright if elasticity is high. The deterministic spreadsheet that pricing committees stare at every cycle says "raise WAC, EBITDA goes up." The real distribution says something more interesting.

A specialty pharmaceutical company with a mature asset grossing about $380M at list (WAC) rebuilt its annual price-action analysis in ModelRisk. The decision variable was a single number — the percentage change to WAC list price at the next annual cycle, ranging from −10% to +12%. The objective was the mean and downside-protected (P10) EBITDA under each choice, with the four payer channels modeled separately because their elasticities and gross-to-net mechanics are different.

The whole analysis comes down to one chart — the decision-variable sweep, showing how EBITDA moves as the WAC choice moves, with the uncertainty band drawn around the mean:

How EBITDA responds to the WAC change — sweep vs uncertainty band

The deterministic worksheet — which ignores elasticity and treats GTN realisation as a fixed multiplier — recommended the upper end of the range (+10% to +12% WAC), because to it revenue is monotone in list price. The Monte Carlo simulation shows the opposite: mean EBITDA declines across the whole range as WAC rises, peaking at the bottom of the range (a −10% list action) at roughly $51M, versus about $46M at the status quo and only $36M at +12%. The reason is structural — Medicaid's 0.9 best-price GTN slope and the cash channel's near-unit elasticity take more out of EBITDA on every upward WAC move than the commercial-channel gain puts back in. As WAC rises, mean EBITDA rolls off and the P10 rolls off slightly faster — the upside shrinks and the downside grows at the same time. The optimal action is to hold or trim list price, not raise it.

The four-channel model

Each channel has three uncertain drivers:

  • Own-price elasticity of volume — modeled LogNormal because elasticity is a positive scalar with right skew. Channel-level medians range from 0.08 for Medicaid (largely contracted, almost no observed volume response to WAC moves), through 0.25 for Medicare Part D and 0.45 for Commercial, up to 0.95 for the cash/340B channel where the patient is the marginal payer. Using Normal here, as the prior spreadsheet did, allowed simulated elasticities to go negative — a Giffen-good draw that does not exist in this dataset.
  • Net-price realisation as a Beta distribution centred on the channel-baseline gross-to-net (27% commercial, 45% Medicare D, 74% Medicaid, 32% cash). Beta is bounded on [0, 1] — the right family for a realisation fraction.
  • PBM/AMP rebate response to a list-price change — modeled as a per-channel slope (0.30 cash, 0.42 commercial, 0.55 Medicare D, 0.90 Medicaid). Medicaid's response is the largest because the federal best-price rule mechanically deepens the rebate when WAC moves up.

Volume per channel responds via the constant-elasticity formulation \(q' = q \cdot (1+x)^{-\eta}\), where \(x\) is the WAC change fraction and \(\eta\) is the simulated elasticity. EBITDA aggregates channel revenue, subtracts a $410/course COGS and a $150M fixed SG&A line.

What the deterministic answer would have cost

If the pricing committee had taken the deterministic worksheet's +10% WAC recommendation, expected EBITDA would have landed roughly $13M lower than at the MC optimum (about $38M against $51M), and the downside-protected P10 outcome would have been worse by a similar margin (about $20M against $34M). The committee had been about to approve a modest increase at the prior cycle — directionally the wrong way, on the strength of the deterministic worksheet. The simulation produced a defensible single number with a quantified downside-protection envelope, which is what the CFO had been asking for and not getting.

Per-channel net price at the optimum

At the optimal −10% WAC change, each channel's realised net price has its own distribution shape. The four panels make the cross-channel asymmetry visible:

Per-channel net price at the MC-optimal WAC strategy

Because the optimum trims list price, three of the four channels see net price ease down from the status quo — Commercial from about $4,234 to $4,029, the cash channel from $3,944 to $3,704, Medicare D barely changing at around $3,159. Medicaid is the asymmetric one: its net price actually rises, from about $1,508 to $1,824, because the 0.9 best-price slope works in reverse — cutting WAC unwinds part of the AMP-based giveback. The dashed black line on each panel shows the status-quo realised net price; the asymmetry of the four shifts, and Medicaid moving against the others, is exactly what the deterministic single-cell calculation cannot show.

What swings the optimum

A tornado around the MC-optimal strategy isolates the largest sources of remaining EBITDA uncertainty.

Tornado: what swings EBITDA at the MC-optimal WAC strategy

The commercial-channel gross-to-net base is the largest mover — unsurprising, since commercial is 45% of volume and its rebate level sets the floor on realised price — which directs the next year's pricing-research investment toward tightening the commercial GTN estimate via PBM-data triangulation. Commercial elasticity is the second mover, sharpened by a small RWE study. Medicaid's GTN slope is third and is largely outside the company's control; it is a regime parameter the model surfaces but cannot reduce. The swings are modest in absolute terms — single-digit to low-tens of millions — which is itself the finding: once the four channels are modeled honestly, the EBITDA answer is fairly robust to the remaining parameter uncertainty.

Three strategies, three EBITDA CDFs

The strategy choice is best summarised by the full EBITDA distribution under each:

Three pricing strategies — annual EBITDA CDF

The MC-optimal curve sits to the right of both the status quo and the naïve-max curves at every percentile — first-order stochastically dominant over the alternatives in this model. That is a strong claim and one the pricing committee was understandably careful with; the simulation's defensible per-channel elasticities and Beta GTN distributions were what allowed the dominance result to survive committee scrutiny.

What the model changed

  • Annual price action set at the MC-optimal −10% list move rather than the deterministic upper bound — preserving an estimated $13M of mean EBITDA ($51M vs $38M) and a comparable amount of P10 downside protection relative to the deterministic +10% recommendation.
  • Pricing committee adopted decision-variable sweeps with P10/P50/P90 bands as the standard format for the annual cycle, replacing the single-point spreadsheet.
  • Channel-level GTN slope tracking added to the quarterly finance review, with Medicaid's slope flagged as the binding constraint on upward WAC moves.
  • Commercial GTN and elasticity research commissioned — the tornado-implied highest-marginal-value pieces of pricing intelligence, sharpening the two parameters that move the EBITDA answer most.

ModelRisk Functionality Used

  • LogNormal elasticities per channel with channel-specific medians (0.08 Medicaid through 0.95 cash) — replacing the Normal elasticities that allowed negative draws.
  • Beta gross-to-net realisations per channel — bounded on [0, 1] as required by the underlying ratio.
  • Constant-elasticity volume response \(q' = q(1+x)^{-\eta}\) evaluated per trial per channel, then aggregated to portfolio EBITDA in-cell in Excel.
  • Decision-variable sweep across 23 WAC-change values with full distribution per value, plotted as a P10–P90 envelope around the mean.
  • One-at-a-time tornado on five parameters (three elasticities and two GTN inputs) at the MC-optimal strategy, used to direct the next year's pricing-research spend.
  • CDF dominance comparison of three strategies, which gave the committee a defensible first-order argument rather than a single-point comparison.

Post-launch pricing is not a question of "how much can we raise list?" — it is a question of which direction the EBITDA surface actually slopes once gross-to-net mechanics, channel elasticities, and rebate slopes are all priced in stochastically. Monte Carlo simulation in ModelRisk makes that surface visible, and here it reverses the seductive deterministic answer entirely: the value-maximising move is to hold or trim list price, not to chase the revenue line upward into a giveback that more than erases the gain.