Academic journal article Real Estate Economics

Redevelopment of Real Assets

Academic journal article Real Estate Economics

Redevelopment of Real Assets

Article excerpt

Real assets can be redeveloped repeatedly. Commercial or residential real estate can be rehabilitated and modernized or demolished and rebuilt. With redevelopment and rezoning can come increases in density or changes in use. This redevelopment can occur not just once, but many times, at possibly random intervals as properties depreciate or rents rise over time. In other words, the option to redevelop a real asset can be exercised repeatedly, without limitation on the total number of times. This compound option, or option on options, has both an infinite life and an infinite number of compoundings. As such it differs from financial options with their finite lives and finite numbers of compoundings.(1) Because a real option can be exercised repeatedly over its infinite life, it can have a relatively simple solution, as shown in this article.

Sequential redevelopment of real assets is the focus of this model. Here, the value of a representative real asset is determined by two variables: the current price of its rental services and the current quality of the real asset. Redevelopment optimally occurs when the current quality hits a lower bound that depends on the current rent. The asset is then demolished and redeveloped to a higher quality that is determined optimally, conditional on the current rent. Relative to the solution with only one possible redevelopment, the solution with repeated redevelopment has the following properties. Development occurs sooner on average before depreciation has so severely diminished the asset's quality. Also, its quality is improved less during each redevelopment. Not surprisingly, multiple redevelopments raise the present value of the asset or, equivalently, the value of the option to redevelop. Thereby, the ratio of rent to price is reduced. For plausible values of the various parameters, the ratios of rent to price match observed ratios for commercial and residential real estate.

These results can be understood intuitively as follows. Redevelopment has two types of costs: the explicit cost of demolition and reconstruction and, with a restriction on the number of redevelopments, the implicit cost or shadow price of the constraint on subsequent redevelopment. With repeated or unrestricted redevelopment, each redevelopment is then less costly than the single redevelopment when subsequent redevelopment is precluded. If the cost of redevelopment is reduced, then the option to redevelop is exercised more frequently and less extensively each time. This is implemented by initiating redevelopment at a higher quality of the asset and improving the asset less during each redevelopment. Also, without a constraint on redevelopments the option to redevelop repeatedly is more valuable than the option to redevelop only once. Thereby, repeated redevelopment adds value to the asset.

Repeated redevelopment of real assets is also studied in Childs, Riddiough, and Triantis (1996), hereafter called CRT. Written independently, CRT and this article have different assumptions and complementary conclusions. In CRT a site can have a mix of two types of nondepreciating improvements - such as office and retail, or office and industrial. Here, a property can have only one use, but the improvements depreciate over time. In both models the cash inflows are continuous, proportional random walks; in CRT the growth rates can be correlated. In CRT each redevelopment is instantaneous; here it can take time. In both cases the cost of redevelopment is Cobb-Douglas.(2) In CRT the solution is numerical; here it is mostly analytical. The results in CRT are realistic. The mix of two possible uses makes a property more valuable. The additional value is greater if the growth rates of the two cash inflows are less correlated.

All other papers on pricing real assets under uncertainty have precluded repeated redevelopment. In previous stochastic models, either rural land can be developed into urban property that cannot then be redeveloped, or a developed asset can be converted once into a more valuable asset. …

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