This paper aims to analyze the sensitivity of the supply of a perennial crop, i.e, miscanthus for which high interest arises when it is dedicated to second generation biofuels production. We develop a methodology based on the "Faustmann's rule" usually used in forest management fields. We first determine the yield growth function over time and the discounted present value of this crop in a deterministic case. Then, a stochastic process based on a beta distribution is introduced to manage the variability of miscanthus yield. A short-term agricultural model (AROPAj) is used to highlight the large scale impact of annual yield randomization. This analysis details the impact assessment regarding optimal length cycle, land use, N input demand and nitrate losses. Ideally, miscanthus would be grown on marginal land. However, miscanthus profitability causes farmers to cultivate it on the most productive land generally devoted to food crops. An increase in yield potential leads to significant direct and indirect land re-allocation, favoring therefore the competition between food and biofuel production.This change in land use leads to a substantial decrease in N-input application and, consequently, in nitrate losses. Results significantly changes when yields are affected by annual randomized variability. Throughout a sensitivity analysis, we notice that yields, renewal cycle costs and the discount rate may interact with yield randomization and significantly affect the future profitability of miscanthus.