Beyond Normal and Triangular: Beta Distributions for Monte Carlo DCF Valuation

Purpose — Monte Carlo simulation has been available to property valuers for over fifty years but remains largely unadopted. This paper examines whether the probability distributions used in existing implementations have contributed to that resistance. The normal and triangular distributions used as defaults in academic literature do not match how valuers assess market variables. Beta distributions offer a better fit for these variables. They are confined to the valuer’s specified range, shaped by market judgement, and available through native Excel functions.

Design/methodology/approach — The paper traces distributional assumptions across the Monte Carlo valuation literature, from Pyhrr (1973) through to post-2005 applications that shifted predominantly toward development appraisal, identifies the theoretical limitations of normal, triangular, and log-normal distributions, and develops the case for beta distributions through the intermediate step of the PERT distribution. A comparative illustration replicates the four-variable DCF model of French and Gabrielli (2005a) under four distributional assumptions (normal, triangular, PERT, and general beta) using 10,000 iterations with correlated inputs implemented through Cholesky decomposition.

Findings — Distributional choice affects all output statistics relevant to uncertainty reporting. The triangular distribution produces a 90% certainty range that is 55% wider than the beta distribution with valuer-specified parameters. The beta distribution allows the valuer to express directional market views that shift the output mean by approximately 7% of capital value, a capability unavailable with the triangular or PERT distributions.

Practical implications — The beta distribution requires no software beyond Excel’s built-in BETA.INV function. It takes four inputs (minimum, maximum, α, β), where the minimum and maximum are the same bounds valuers already specify for triangular distributions. The PERT distribution serves as a transitional step, deriving α and β automatically from the familiar three-point estimate. The Monte Carlo model used in this paper, including correlated inputs, four-distribution comparison, convergence testing, and sensitivity analysis, was adapted from an existing workbook in a single working session using a generative AI add-in for Excel.

Originality/value — The beta distribution has appeared in the property Monte Carlo literature since Pyhrr (1973) but has never been examined in detail. Gimpelevich (2011) noted its potential superiority without developing the point. This paper addresses that gap and shows that distributional choice has material consequences for every output statistic a valuer reports to a client.