| Vose Software

Industry: Real Estate
Product: ModelRisk
Application: Land Development Feasibility Analysis Under Uncertainty


Cost and Schedule Fail Together — and the Joint Tail Is Twice as Likely as the Math Suggests

The feasibility model for turning a 50-acre parcel into 180 finished single-family lots looked safe on paper. The point estimate put the total cost at $39.3M against a $46M funded budget and the program at about 32 months against a 42-month carry-loan deadline — headroom on both. The carry lender funds the deal on the assumption that the developer clears both bars. Rebuilt in ModelRisk, the deal carried a 16.6% chance of going over budget and a 30.6% chance of slipping past the deadline. Either one alone forfeits the deal.

But the number that changed the term sheet was the joint one. The chance of breaching budget and deadline together was 11.4% — more than double the 5.1% a naive "multiply the two probabilities" calculation would give. Cost and schedule are not independent risks the lender can net against each other. They fail together, and the model that treats them as independent under-prices the exact scenario that wipes out the carry reserve.

Why a point estimate fails here

Horizontal land development — raw land to serviced lots — has two outputs that both matter and both bind: total cost and total time. A deterministic feasibility model produces one number for each and stops. It cannot answer the lender's actual question, which is not "what is the expected cost?" but "what is the chance we breach the budget, the deadline, or both at once?" And critically, it cannot represent that the two are correlated. A long entitlement fight burns carry interest (cost) while consuming the clock (time). A regulator-driven servicing redesign raises the cost per lot and pushes the program out. The same frictions drive both axes, so the bad-cost world and the bad-time world are the same world. Independence assumptions hide that overlap precisely where it is most expensive.

The model

The deal is a 50-acre parcel entitled and serviced into roughly 180 lots, funded by a $46M carry loan that matures at month 42 (carry at 10.5%). Five uncertain inputs were entered as distributions:

  • Entitlement durationTriangular (8 / 14 / 30 months). The long-pole activity, heavily right-skewed: approvals rarely come early and occasionally drag for years.
  • Lot yieldNormal around 180 lots, eroded by downzoning and setback requirements.
  • Servicing cost per lotLogNormal, about $0.115M per lot, for roads, sewer, water and grading; bounded at zero and right-tailed.
  • Servicing durationTriangular (6 / 10 / 18 months) for the physical build of the infrastructure.
  • Lot absorption pace — a Poisson draw of finished lots sold per month, which sets how long the carry runs through the sell-down.

The model's signature is a shared regulatory / market-friction factor drawn once per iteration. A hostile environment lengthens entitlement, bids up the cost per lot, cuts the lot yield (down-zoning) and slows absorption — all together. That single factor is what couples cost and time, producing a verified +0.72 cost-to-time correlation. The factor's individual effects check out too: friction-to-entitlement +0.55, friction-to-cost-per-lot +0.40, friction-to-lot-yield -0.87.

Joint density of total cost and program time with the budget cap and deadline

The joint tail the lender funds

The joint-density chart plots every simulated trial as a point — total cost on the horizontal axis, program time on the vertical — with the $46M budget cap and the 42-month deadline drawn as crosshairs. The cloud tilts up and to the right: expensive deals are also slow deals. The upper-right quadrant, where both caps are breached, is the deal-killer. Its probability is 11.4%, against the 5.1% that multiplying the two marginal probabilities would suggest. The correlation more than doubles the chance of the scenario the carry reserve exists to absorb. A lender sizing that reserve off independent probabilities would under-fund it by half.

How much cost is really at risk

The cost axis on its own tells the budget story.

Distribution of total cost to deliver 180 serviced lots

Against the $39.3M point estimate, the simulated mean cost is $41.2M, the P50 $40.5M, the P80 $45.2M and the P90 $48.1M. The probability of exceeding the $46M funded budget is 16.6%. The point estimate was not the expected outcome — it sat below the median, because the right-skewed entitlement and servicing-cost tails pull the mean up. The funded budget covers the deal at roughly the P80, which is a defensible but explicit risk choice the deterministic model never surfaced.

Absorption is the lever on the deadline

Because the sell-down pace is the input the developer can most influence — through pricing, builder relationships and phasing — sweeping it shows how the schedule risk responds.

Probability of breaching the deadline versus lot absorption pace

At the base assumption of 11 lots sold per month, the program has a 31% chance of slipping past the 42-month deadline and a 36% chance of losing the deal (over budget or past deadline). Pushing absorption toward 16 lots per month pulls the deadline-breach probability down sharply, but the lose-the-deal curve flattens out near the budget-breach floor — because once the schedule is safe, the residual risk is cost, which absorption pace cannot fix. The sweep tells the developer exactly where faster sales stop helping and a bigger contingency starts mattering.

What actually drives the program time

Ranking the drivers of program time — the binding constraint in most trials — confirms where to focus.

Tornado chart of the program-time drivers

Against a P50 of 37 months, the entitlement duration is the largest driver at about ±10 months of spread, with the shared regulatory/market friction factor second at ±8 months — bigger than the physical servicing build itself. Lot absorption and lot yield follow. The message for the development team is that the schedule risk lives in the approvals process and the broader regulatory climate, not in the dirt-moving: a pre-application agreement or an entitlement consultant buys down more tail risk than accelerating the contractor.

What the model changed

  • The carry reserve was sized off the joint tail, not the marginals. Funding the 11.4% double-breach scenario rather than the 5.1% independent estimate roughly doubled the reserve the lender required — a number the deterministic model could never have produced.
  • The funded budget was set at the P80 explicitly. The team chose $46M knowing it left a 16.6% exceedance probability, rather than discovering the gap after a cost run.
  • Entitlement de-risking was prioritised over construction speed. Because entitlement and the friction factor topped the time tornado, the budget for pre-application work and a seasoned land-use consultant was approved ahead of contractor incentives.
  • Absorption became a covenant. The sweep showed where faster sales stop reducing total deal risk, so pre-sale targets were set at the point of diminishing returns rather than an arbitrary figure.

ModelRisk Functionality Used

  • Monte Carlo simulation turning a two-output (cost and time) feasibility model into full joint distributions.
  • Triangular, Normal, LogNormal and Poisson distributions for entitlement, lot yield, servicing cost, servicing time and absorption — each chosen for its shape and bounds.
  • A shared regulatory/market-friction factor sampled once per iteration that couples cost and time, verified at a +0.72 cost-to-time correlation.
  • Joint-probability analysis quantifying P(over budget AND past deadline) at 11.4% against a naive-independence 5.1% — the result that resized the carry reserve.
  • Parameter sweeps and sensitivity (tornado) analysis that located the binding risk in entitlement and the regulatory climate rather than the physical build.

In land development the question is never just "how much" or "how long" — it is "what is the chance both go wrong at once?" ModelRisk answers that question directly, and the answer was twice as large as the independence math implied.