On the debt capacity of growth and decay options

This paper focuses on the impact of debt on the optimal policy for investment and hiring, in the light of the theory of real options. We consider a stochastic demand for the product sold by the company. We examine in particular the investment and hiring choices when, in case of enhancement levels of investment and employment, the additional cost is funded in whole or through the issuance of a new bond. We deal with this management problem in the Merton (1974)’s framework. We detail and analyze the optimal strategies. We show in particular that, in the presence of growth option, the value of the …rm is the sum of two barrier options, one of "up-and-in call" type, the other of "up-and-out call" type. The barrier corresponds to a threshold of the demand for the product sold by the …rm. The novelty of our approach is based on the combination of the optimization of the …rm management for a given production function with the valuation of its equity and debt as in Merton (1974). Recall that, in such a case, the equity value is a call option with value of the …rm as underlying asset and the amount of the debt to be repaid at maturity as the strike. Our results di¤er quite signi…cantly from those of the standard framework introduced by Tserlukevich (2008).