We consider firms facing uncertain demand, and study their problem of investing in an electricity line between two neighbouring countries, under capacity constraints, and incentive schemes. We consider three ownership structures: a state-owned transmission company, a merchant transmission investor, and a regulated firm. The firm's problem is to choose the optimal time and size of the interconnector. The government is concerned with the incentive design. We investigate how price caps, capacity targets and merchant investments affect the critical investment thresholds and characterize the government's optimal incentive. We find that price caps speed-up projects' development, while capacity targets reduce under-investments in capacity markets. Finally, we study the effect of investment decisions on the social welfare value.