An entrepreneur wants to raise outside financing to undertake an investment. The investment costs $80m today. Next year, the investment will generate cash flows which depend on whether the entrepreneur exerts effort. If the entrepreneur exerts effort, cash flows will be $120m or $70m with equal probability. When the entrepreneur does not exert effort, cash flows will be equal to $100m or $50m with equal probability, but the entrepreneur receives a private benefit worth $5m. This private benefit cannot be transferred to investors.

a) Assuming that the entrepreneur exerts effort, what proportion of equity, would she have to sell to outside investors to fund the project?