Investment hysteresis under stochastic interest rates

Most decision making research in real options focuses on revenue uncertainty assuming discount rates remain constant. For many decisions, however, revenue or cost streams are relatively static and investment is driven by interest rate uncertainty, for example the decision to invest in durable machinery and equipment. Using interest rate models from Cox et al. (1985b), we generalize the work of Ingersoll and Ross (1992) in two ways. Firstly, we include real options on perpetuities (in addition to “zero coupon” cash flows). Secondly, we incorporate abandonment or disinvestment as well as investment options and thus model interest rate hysteresis [parallel to revenue uncertainty, Dixit (1989a)]. Under stochastic interest rates, economic hysteresis is found to be significant, even for small sunk costs.

Introduction
The capital theory of investment has typically ranged from models where investment is costlessly reversible to models where investment is completely irreversible. The traditional case of costlessly reversible investment occurs when there is no difference between the price at which the firm can purchase capital and the price at which it can sell capital. Thus with perfect reversibility the wedge between the investment cost and the disinvestment proceeds is zero and the optimal investment policy of a firm maintains the marginal revenue product of capital equal to the Jorgenson (1963) user cost of capital. The case of costlessly reversible investment is not realistic since it is not expected that a firm can disinvest at no cost. At the other opposite extreme, lies the case of complete irreversible investment when the sale price of capital is zero, i.e., the firm cannot recoup any fraction of the investment cost initially supported. For the sake of simplicity, the extreme assumption that resale of capital goods is impossible, i.e., disinvestment proceeds are zero, is initially introduced by Arrow (1968) and subsequently used by the majority of the literature on optimal investment under uncertainty. This assumption is more realistic since in many economic situations the sale of capital invested cannot be accomplished at the same price. In the limiting case of complete irreversibility, firms are not able to recoup any fraction of the investment cost.

Author: Jose Carlos Dias and Mark Shackleton

Source: Lancaster University Management School

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