The year $2019$ brought along a massive increase in the sales of electric vehicles EVs. EV sales exceeded $2\mathrm{.}1$ million units globally $($Source: IEA Global EV Outlook $2020)$ and shows a continued growth pattern into the year $2020.$ A typical EV battery weighs about $400$ kg and has about $10$ kg of lithium in it$.$ Lithium currently sells for $$9/$kg on the global commodity market.

At present, basically all the lithium used to make new batteries comes from lithium mines with Australia and Chile having the largest production volumes. But, in the future, there exists another important source for lithium and that is recycling. Redwood Materials is a start$-$up created by Tesla$$s cofounder and former chief technology officer, JB Straubel. While Tesla is known for making batteries, the focus of Redwood Materials is to recycle these batteries.

Since the expected lifetime for an EV $($and its batteries$)$ is about $10$ to $15$ years, Straubel and his team estimate that within two decades, many millions of tons of lithium ion battery materials will reach the end of their useful lives. His vision is to reuse these battery cells $($or at least the materials of the cells, such as the lithium$)$ to reduce the need to extract and refine new materials. Separating the materials in a battery is remarkably difficult. Presently, Redwood Materials mostly recycles batteries from phones, power tools, and laptop computers because there are very few EVs reaching the end of their useful life.

Independent of the batteries coming from an iPhone or a Tesla, the process at Redwood Materials uses old batteries as an input. The first step is to dismantle the product. Subsequent steps then decompose the batteries and recover valuable materials such as lithium, nickel, copper, or cobalt. Ideally, this process recovers all the materials. But, this is currently not technically feasible. At present the recovery rates for lithium is around $80$ percent, which really can be thought of as a production yield $(80$ percent of the lithium flowing into the process as part of old batteries comes out at the other end as recycled lithium that can be sold again$).$

QUESTION

Introduction

Assuming Redwood Materials would recycle $10$ percent of the batteries in the global EV market, the recovery rate remains at $80$ percent, the EV market grows at $50$ percent per year, the lifespan of a battery is $15$ years, and lithium prices remain at $$9/$kg$,$ how much revenue would the company make each year in the period from $2035$ to $2050$ from selling recycled lithium?

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