Chief Executive Elon Musk said the compact SUV would first debut in a long-range version with a range of 300 miles priced at about $47,000.
A standard version, to be available sometime in 2021, would cost about $39,000, Musk said.
The vehicle will be the fifth model for the electric carmaker, which has spent the past three years struggling to fulfill its March 2016 promise to produce a mass-market electric sedan for $35,000.
Tesla finally began selling versions of that sedan, the Model 3, for $35,000 on 28 February, though the milestone came amid typical Tesla chaos: the company said it would help achieve the price cut by closing all its stores and moving to online-only sales, only to backtrack less than two weeks later.
Other turmoil has stemmed from Tesla’s mercurial chief executive, who continues to generate controversy and headlines for all the wrong reasons.
In late February, the US Securities and Exchange Commission asked a judge to hold Musk in contempt of court for allegedly violating a settlement requiring him not to publish “inaccurate and material information” about the publicly traded company on his Twitter feed.
Last week, it was revealed that Musk’s security clearance, which he needs for his company SpaceX, is also under review by the Pentagon, after the billionaire smoked marijuana on a live-streamed podcast in September.
Tesla has also been dogged by complaints about customer service and repairs. On 21 February, Consumer Reports withdrew its recommendation for the Model 3 over concerns with reliability.
The company is banking on the electric crossover vehicle to revive excitement about the brand, even as traditional carmakers expand their electric vehicle offerings. Musk told investors on a conference call in January that he expects demand for the Model Y to be anywhere from 50% higher to double that of the Model 3.
But Tesla’s targeted volume production date of late 2020 for the new model would put it behind electric SUV offerings from Volkswagen AG’s Audi, Daimler AG’s Mercedes-Benz and BMW.
Tesla’s previous SUV, the Model X, is a luxury model that has not proved particularly popular. The Model Y will be built on the same platform as the Model 3 and use many of the same parts, which will potentially streamline some of the company’s notorious production problems.
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