Ali is considering a new business investment. To participate in this business, he must invest 50.000t. There is a 25% chance that the investment will earn back the 50.000t, leaving him just as well off as if he had not made the investment. But there is also a 45% chance that he will lose the 50.000t altogether, although this is counterbalanced by a 30% chance that the investment will return the original 50.000t plus an additional 100.000t. (a) Draw a decision tree model to help Ali decide whether or not he should invest. Clearly lay out your tree, paying attention to decision and chance nodes, the branches out of each node, the payoffs for each branch, and the probabilities for each chance branch. (b) As a young and anxious entrepreneur, Ali displays a risk-averse behavior. Assume that his preferences can be modeled with the logarithmic utility function U(x)=ln(x), where x denotes his total wealth. If Ali's current total wealth adds up to 100.000t (thanks to an inheritance from his grandparent), should he make the investment or avoid it? (c) Repeat part (b), assuming Ali's current total wealth is 1.000.000t. (d) Given the risk model in part (b), what would be Ali's certainty equivalent (CE) of investing in this business? (e) What would be Ali's risk premium (RP) associated with the CE in part (d)? (f) Plot Ali's CE in part (d) as a function of his total wealth, assuming it ranges from 100.000t to 1.000.000t. (Hint: Best/cleanest way to address this question is to prepare an Excel sheet for your calculations.) (g) At what total wealth level, Ali's decision switches between invest and not invest? (Hint: You can, for example, use Excel's GoalSeek feature)