Industry: Real Estate Product: ModelRisk Application: Property Valuation Under Uncertainty
A surveyor signs off a stabilised suburban office asset at $70.0M — forward Net Operating Income of $4.20M capitalised at a 6.00% market cap rate. The figure is precise, auditable, and goes straight into the lender's file and the fund's NAV. It is also, almost certainly, wrong by a margin nobody on the deal can see from the number alone.
Re-run the same appraisal as a Monte Carlo simulation in ModelRisk — letting the forward NOI and the cap rate the market will actually pay vary the way they do over a cycle, and cross-checking against the spread in comparable sales — and the $70.0M point turns into a distribution. The mean lands at $70.6M, almost exactly on the surveyor's figure, but the 80% confidence band runs from $59.3M to $82.9M: a $23.7M spread, a third of the headline value. There is only a 29.8% chance the true value sits within +/-5% of the signed appraisal, and an 11.9% chance it is below $60M.
The income approach, V = NOI / cap rate, is a ratio of two numbers that are each genuinely uncertain and — crucially — that move together. In a hot market, rents firm up (NOI rises) and investors accept lower yields (the cap rate compresses), so value rises twice over. When the cycle turns, NOI softens and cap rates widen, so value falls twice over. A point estimate freezes both inputs at their central guess and discards exactly the co-movement that makes the answer wide.
Modelling the two inputs as independent would be just as misleading in the other direction: their errors would partly cancel and the band would collapse — a central-limit artefact, not a real reduction in risk. The model below ties NOI, the cap rate and the comparable-sales evidence to a single shared market-cycle factor, so the appraisal width reflects the way the market actually behaves.
The headline chart plots 200,000 simulated appraisals. The surveyor's $70.0M point sits near the centre, the simulated mean is $70.6M, and the shaded 80% confidence band spans $59.3M to $82.9M. The chance the realised value falls within +/-5% of the point appraisal is just 29.8%; widen the tolerance to +/-10% and it is 55.7%. The left tail carries a real 11.9% probability of a value below $60M — the difference between a comfortable loan-to-value and a covenant breach.
Valuers triangulate. The income approach (NOI / cap rate) is the widest on its own — mean $70.9M, P10 $56.6M, P90 $86.7M — because it compounds two uncertain inputs. The comparable-sales approach ($/sqft on ~150,000 rentable sq ft) is tighter — mean $70.0M, P10 $62.1M, P90 $78.2M — because price-per-foot evidence already blends many transactions. Reconciling them at the surveyor's 65/35 weighting gives the working appraisal: mean $70.6M, P10 $59.3M, P90 $82.9M. Reading any percentile off the curve answers the question the lender actually asks — what is the chance the value is below the figure I am lending against?
Ranking the inputs by their contribution to the spread around the $70.6M mean shows three drivers in a near-tie at the top: the market-cycle factor (+/-$7.9M), which moves rents and cap rates together; the exit/market cap rate (+/-$7.8M); and the forward stabilised NOI (+/-$7.7M). Comparable $/sqft evidence (+/-$7.2M) follows close behind, and property-specific income noise (+/-$3.8M) is roughly half as influential. The message for due diligence: chasing one more decimal of precision on NOI buys little if the cap rate and the cycle are left as guesses.
The final chart plots each simulated draw of NOI against its cap rate. The cloud tilts: high-NOI draws cluster with low cap rates (the hot-market corner, where value compounds upward), and low-NOI draws cluster with high cap rates (the soft-market corner, where value compounds downward). The empirical correlation is -0.44, exactly the negative co-movement the model imposes. One consequence is counter-intuitive but important: the chance of landing in the high-NOI-and-high-cap corner is only 16.9%, against 24.1% if the two were independent — the cycle makes some combinations rarer and the value tails fatter.
The valuation committee stopped treating the surveyor's $70.0M as a fact and started treating it as the centre of a band. With an 11.9% probability of a value below $60M quantified up front, the deal was repapered: the lender sized the loan to the P10 of $59.3M rather than the point figure, and the acquisition team built a price-protection clause keyed to the realised cap rate at close. The appraisal still reads $70.0M on the cover — but every party now knows how much room sits around it.