REAL OPTIONS VALUATION OF ABANDONED FARMLAND

 

Michi Nishihara

 

Abstract

 

Recently, there has been increasing concern about whether food production can keep pace with population growth in the future (Gilland (2002)). Promoting the effective use of agricultural land is critical in resolving the issue. However, abandoned farmland that will not be cultivated for several years has become more prevalent in Japan. In fact, Japan’s total area of abandoned farmland has almost tripled in the last two decades. The purpose of this paper is to investigate the problem of abandoned farmland and offer suggestions for promoting its effective use. I investigate the decision-making process of an owner of abandoned land using the real options framework. The real options approach, in which option pricing theory is applied to real investment problems, is useful in evaluating land development in the face of uncertainty about cash flows from the development (Capozza and Helsley (1990), Capozza and Li (1994), Geltner et al (1996)). For instance, Capozza and Helsley (1990) and Capozza and Li (1994) apply real options models to land conversion decisions, whereas [5] investigates land development timing with an alternative land use choice in terms of a max-option. Several papers, including Plantinga et al (2002) and Plantinga and Miller (2002), provide empirical evidence for real options valuations. Although the previous studies assume that the owner optimizes the development (or conversion) timing, this is not the case with Japan’s abandoned farmland. In most cases, abandoned farmland is currently restricted to agricultural use but will be available for nonagricultural use with environmental and regulatory changes at some point in the future. This paper models the decision-making process of an owner of abandoned farmland as follows. An opportunity that enables development for nonagricultural use comes as an exponential distribution. Before the arrival of the conversion opportunity, the owner has the option to cultivate the land with sunk costs at an arbitrary time. As soon as the land conversion opportunity arrives, the owner will immediately sell the land to a developer for residential or commercial use. This assumption is consistent with the fact that the price of land for nonagricultural use is much higher than that of land for agricultural use. To maintain brevity, I assume that cash flows from agricultural and nonagricultural land use follow bi-dimensional geometric Brownian motions. Although the problem is expressed as a complex bi-dimensional optimal stopping problem like Nishihara (2010, 2011), I reduce it to a standard one-dimensional problem and derive a closed-form solution under plausible assumptions. The value of abandoned land is derived as a sum of the values of the cultivation option and prospective land conversion. Further, I calibrate the model with Japan’s land price data from 2005. Results show that a slight probability of conversion greatly increases the value of abandoned land and discourages the owner from cultivating the land. I argue that, in order to promote agricultural use of land, the government needs a zoning ordinance that completely removes owners’ anticipation of land conversion. It seems that owners’ abandonment of farmland is primarily caused by the insufficient restriction. In addition, I explore why an owner of abandoned farmland neither sell nor lease the land to a more efficient farmer. With the same anticipation of land conversion, an inefficient owner would sell or lease the land to a more experienced farmer who is eager to cultivate it. However, in Japan’s current system, less productive farmers are more likely to receive permission for land conversion. As a result, the anticipation of land conversion differs between inefficient and efficient farmers. I demonstrate that only a small gap in the anticipation prevents the owner of abandoned land from selling or leasing the land to a more productive farmer. As a policy implication, I argue that the government needs a unified guideline for all farmers, even if it does not completely remove the anticipation of land conversion due to the prospective Trans-Pacific Partnership which might force the government to deregulate the conversion of agricultural land.

 

Lecture Notes in Management Science (2011) Vol. 3: 73-74

3rd International Conference on Applied Operational Research, Proceedings

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ISSN 2008-0050 (Print)

ISSN 1927-0097 (Online)

 

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