Industry: Real Estate
Product: ModelRisk
Application: Land Acquisition Decision-Making Under Uncertainty

$26M of Appraisals, a 14-Parcel Assembly, and a 22% Chance the Site Costs More Than the $32M Budget

The development site does not exist yet — it has to be assembled from 14 separately-owned parcels into one contiguous block. Independent appraisals sum to $26.0M, the number that went into the first board deck. The probabilistic rebuild in ModelRisk priced the assembly as what it actually is: a sequence of 14 negotiations, each with an uncertain asking price, a chance the owner holds out for a premium once they see the developer is committed, and — for the three parcels the project cannot be built without — a chance the deal never closes. The result: a mean assembly cost of $29.0M, a P90 of $34.6M, a 22% probability of breaching the $32M budget, and a 13% probability that a critical parcel fails to close at all. The $26M appraisal sum sits at roughly the 5th percentile of what the assembly actually costs.

Why a point estimate fails here

Summing 14 appraisals is not a forecast of the assembly cost — it is the cost in the single world where every owner sells at appraisal, on the first offer, in order. That world has almost no probability. Two structural features make the real distribution sit well to the right of the sum:

• Holdout dynamics. Land assembly is sequential and visible. The more parcels a developer has already closed, the more leverage each remaining owner holds — the project is now hostage to the parcels still outstanding. A point estimate cannot represent "the last owner asks for 90% over appraisal because they know they are the last."
• Correlated asks. Every owner is pricing into the same local land market. A hot market lifts all 14 asks together. Treating them as 14 independent draws collapses the spread of the sum toward its mean (a central-limit artefact) and badly understates the budget-overrun probability.

The four uncertainty channels

Per-owner asking price. Each parcel's ask is LogNormal around its appraised value, with idiosyncratic spread of 16–30% depending on how clean the title and comparables are. The smaller, scrappier parcels (alley parcel, rear access strip, old garage site) carry the widest spreads.

Shared land-market factor. A single LogNormal(0, 0.12) market multiplier scales every owner's ask together — a hot market lifts all asks about 12% at one sigma. This is the common factor that gives the assembled total its real width.

Holdout premium. Owners are negotiated in order of size (anchor parcels first). The holdout probability rises from 8% for the first parcel to 45% for the last as leverage shifts to the remaining owners. When a holdout fires, the premium is Triangular(15%, 35%, 90%) on top of the ask.

Critical-parcel failure. Three parcels are critical — the site is unbuildable without them. A holdout on a critical parcel has a 22% chance of never closing, forcing a forced-assemblage over-pay modelled at Triangular(1.6x, 2.2x, 3.5x) of the ask.

What the assembly actually costs

The distribution is right-skewed and lands far above the $26.0M appraisal sum. The mean is $29.0M and the median $28.6M — the assembly costs about $3M more than the appraisals on a typical outcome, purely from holdout premiums and a normal market. The P90 is $34.6M, and the expected cost in the worst 10% of assemblies (the tail beyond P90) is $37.4M — driven by the cases where a critical-parcel holdout forces a forced-assemblage over-pay. Against the $32M budget the probability of overrun is 22% — better than one assembly in five blows the budget the appraisal sum made look comfortable.

How much budget buys what confidence

Treating the budget as a dial and reading the probability the assembly closes within it turns the distribution into a procurement decision:

At the $26M appraisal sum the probability of completing the assembly is near zero — that figure was never a budget, it was a floor. At $30M the confidence is 63%; at $32M it is 78%; at $34M it is 88%; at $36M it is 94%. The 80% confidence level needs roughly a $32M budget — about $6M, or 23%, above the appraisal sum. The curve tells the board exactly what a given confidence costs, and makes the holdout-and-failure risk a budgeted line rather than a surprise.

Which parcels drive the spread

The two anchor parcels — the corner lot (±$2.58M) and the anchor frontage (±$2.52M) — dominate the spread, because they are both the most expensive parcels and critical (a holdout there can trigger a forced-assemblage over-pay). The mid-sized south and north infill lots follow at ±$2.0–2.2M each. The implication for the deal team is direct: secure the two critical anchors first and quietly — before the market knows an assembly is underway — because they carry the most cost risk, and the holdout premium on them only grows as the rest of the block closes.

Holdout leverage rises as the assembly proceeds

This is the dynamic the appraisal sum cannot see. The holdout probability climbs from 8% on the first parcel negotiated to 45% on the last. The mean premium paid over appraisal rises in step — from about 6% on the first-position parcel to 22% on the last. The final parcel, appraised at $0.70M, is paid an average of $0.85M once its holdout leverage is priced in. The escalation is not a fee schedule; it is the emergent cost of being a committed buyer with no walk-away option once 13 of 14 parcels are under contract.

What the model changed

• Budget reset from $26M to $32M. The board re-authorised the assembly at the 80%-confidence figure, not the appraisal sum, removing the near-certain mid-assembly funding gap.
• Critical parcels secured first. The two anchors and the access strip were optioned quietly and early — before any public assembly signal — cutting their holdout premium and the 13% critical-failure probability.
• A forced-assemblage contingency of ~$5M was carried explicitly for the critical-parcel-failure tail, rather than discovered when an owner refused to close.
• Walk-away triggers were set per parcel at the simulated P90 ask, so the deal team had a quantified ceiling rather than negotiating against an open-ended commitment.

ModelRisk Functionality Used

• Sequential assembly simulation with a position-dependent holdout probability — capturing the leverage shift that makes the last parcel cost the most relative to appraisal.
• Shared land-market common factor across all 14 LogNormal asks — imposing the correlation that gives the assembled total its real width and prevents the central-limit collapse that an independent-sum model produces.
• Conditional critical-parcel failure branch that converts a holdout on a must-have parcel into a forced-assemblage over-pay, surfacing the 13% probability that a deal-killing parcel never closes.
• Budget-confidence sweep that prices the trade between authorised budget and probability of completing the assembly.
• Rank-correlation tornado that ranked the 14 parcels by their contribution to cost risk and pointed the deal team at the two anchors.

Land assembly is a sequence of dependent negotiations, not a sum of independent appraisals. Monte Carlo simulation in ModelRisk is what makes the holdout dynamics and correlated asks visible — and once they are, the budget, the negotiation order, and the walk-away ceilings all become numerical decisions rather than hopes.