The option value of vacant land and the optimal timing of city extensions

Classic real options theory rests on two debatable assumptions: projects require a fixed investment and generate cash flows that follow a random walk. Relaxing both assumptions leads to radically different conclusions regarding the optimal timing of investment. We model investment using a Stone-Geary production function (Leontief and Cobb-Douglas are special cases) and growth as a mean-reverting Brownian motion. The solution method for this option valuation problem is non-trivial because the state space is two dimensional (level of the cash flow and its growth). For Leontief, the optimal policy is intuitive; the moment of investment involves a trade-off between the level of the cash flow and its growth. For Cobb-Douglas, in contrast, the optimal moment of investment depends only on the growth. More surprisingly, investment should be delayed when growth is high. This conclusion persists in the general Stone-Geary case. Applied to urban real estate, this suggests that up to 20% of cities should delay new construction because of high growth. The option value of vacant land may represent 60% of the value of new construction. High prices of vacant land may thus result from rational investor behavior rather than regulatory inefficiency. Our analysis should be widely applicable, for example to investment in high-growth companies.