Ella is a successful entrepreneur that built an empire of baby food products, which she successfully sold. Ella gave most of the sale's proceeds away to charity and had planned to focus on her garden for the foreseeable future. However, being the curious woman that she is, she recently imagined a new potential business project to sell online gardening tools. Ella has estimated that the project will pay next year $25 million with probability p and $15 million with probability 1 - p, and that the required initial investment is $16 million. Ella can pick the probability of success p to be any number she wants between 0.24 and 0.74. However, choosing a higher p requires Ella to stop working on her garden, and this generates a private cost to her equal to k xp, where k > 0. The discount rate is zero. (a) [10 marks] Suppose that Ella finances the project with equity by promising a share a of equity to outside investors in return for the $16 million necessary for the initial investment. Find the expected payoff to Ella expressed as a function of a. For a given a, what probability of success p will Ella choose? (b) [10 marks] Suppose outside investors believe that Ella will choose p = 0.74. Under these beliefs, what is the fraction of ownership that equity investors require for the $16 million? For what values of k will Ella choose p = 0.74? (c) [10 marks] Suppose instead that Ella finances the project using debt by promising a face value FV to creditors in return for $16 million to cover the initial investment. Find the expected payoff to Ella expressed as a function of FV. For a given FV, what probability of success p will Ella choose