Problem III: Project Art

The controller of Project Art, a large multi$-$divisional design company, is evaluating a capital project proposed by one of its divisions. If undertaken, the capital project will have a certain payout of $$120$m at the end of one year. The actual cost, which will be paid up front, is uncertain, but the controller believes that it will be:

$$90$m with probability of $25\%$

$$70$m with probability of $50\%$

$$50$m with probability of $25\%$

Project Art faces a cost of capital of $20\%$ per year, and cannot observe $($now or later$)$ the actual cost of the project. The controller can announce a policy of accepting only projects with an internal rate of return greater than a given hurdle rate. A hurdle rate here is a minimum return on investment $($e$.$g$.,$ at the $$90$m cost$,$ the project has a rate of return of $($$$120-$$$90)/$$$90=33\mathrm{.}3\%).$

What policy $($i$.$e$.,$ what hurdle rate$)$ will maximize Project Art$$s net present value, and why? Be sure to explain the economics of your answer, not just the mathematics. Note: There is actually a range of correct answers to this question.