We re-examine the basic investment problem of deciding when to incur a sunk cost to obtain a stochastically¯uctuating bene®t. The optimal investment rule satis®es a trade-off between a larger versus a later net bene®t; we show that this trade-off is closely analogous to the standard trade-off for the pricing decision of a ®rm that faces a downward sloping demand curve. We reinterpret the optimal investment rule as a markup formula involving an elasticity that has exactly the same form as the formula for a ®rm's optimal markup of price over marginal cost. This is illustrated with several examples.
This paper derives a real options model of flexibility and applies it to shipping, valuing the option to switch between the dry bulk market and wet bulk market for a combination carrier, a ship type that is capable of operating in both markets but that has fallen out of favor due to high price tags. The model is a mean-reverting (Ornstein-Uhlenbeck) version of a standard entry-exit model with stochastic prices. A closed form solution for the value of flexibility is derived, expressed in terms of Kummer functions. The estimated value of flexibility is related to historical price differentials between combination carriers and oil tankers of comparable size. Based on numerical experiments it is concluded that new combination carriers may enter the market in the near future.
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