Preferred Equity Investment Model

This project is a combination of math and corporate finance. Here is the situation. I am investing $25mm convertible preferred equity at 10% coupon on 9/1/2017 and another $25mm convertible preferred equity at 10% coupon on 12/1/2017. I will receive 1% closing fee for each investment. Interest is paid quarterly. Assume the company goes public 6/30/2018 for $100mm. Assume the IPO price per share is $10 and that the company will pay a 10% dividend yield on the common (it is a mortgage REIT). My question is this: I want to structure the investment to earn a 20% IRR and I don't know how to do this. For example, would I convert my preferred into common at the IPO at a discounted price such that the # of shares would result in 20% IRR? Would I require warrant coverage with the preferred equity? If so, what is the calculation for the correct coverage?