In Braavos, Emerald Gate Bridge is painted every two years at a cost of $3 million. Most recently, it has been painted exactly one year ago and the payment was made at that time.

A startup company, Dorne, came up with a new chemical formulation that can be applied as a top coat to any paint. When applied over existing paint, this new product doubles the remaining lifetime of the original paint. It can only be applied over an original paint once. By itself, the overcoat does not replace the paint. It needs to be applied over the paint for it to work.

a) The City of Braavos is using a discount rate of 10% and considering using this product today and each time the bridge is painted in the future (note that, currently the bridge paint has still one year lifetime left). How much should the price of each application be for the city to start using this product today?

b) Assume that the City decided to use the overcoat beginning today but have not paid for it yet. Assume that the overcoat costs $x million per application. Dorne offers the following two payment plans to Braavos:

Option I: You can pay $x million at the time of each application (starting today!) Option II: If you pay the first five applications' cost today, there will be a 50% discount on the price of these first five applications ONLY.

What is the IRR of the discount offered?