Need help with question (I). Could you also please provide formulas on how to ca

Question

Need help with question (I). Could you also please provide formulas on how to calculate E(y1), E(y2), E(1) and E(2)? Ed is an entrepreneur who is deciding between two investment projects. Both projects are risky and require an investment of S150. The following are the details on the two projects: Project 1 consists of founding an economic consulting firm "Excellence with Ed," which is relatively safe: with 75% probability it succeeds and generates $550 of revenues, and with 25% probability it fails and generates only $250 of revenues. Project 2 is to open "Be a slugger with Ed", a baseball clinic for children. Although Ed is an outstanding baseball player, this project is much riskier: with 25% probability, it succeeds and generates $1200 of revenues, and with 75% probability it fails and generates only $160 of revenues. Caitlin is a banker who may offer Ed a loan. Caitlin's opportunity cost of money is 10%. In other words, she would earn a 10% interest rate if she invested the money in a bank instead of lending it to Ed. First, consider that Caitlin offers unlimited liability contracts, i.e. Ed must repay the loan (full principal and interest) whether his project fails or succeeds. Caitlin can specify which project Ed must select and enforce this selection. A credit contract thus specifies two terms: the Project and the interest rate. Let Project Interest Rate> denote the contract. For example, the contract means that Ed must do Project l and the interest rate is 10%. Based on the information provided, answer the following: Now, consider that Caitlin offers a limited liability contract which means that Ed does not have to repay the loan in full if his project fails. However, if Ed's project succeeds he must repay the full loan (principal plus interest). If his project fails, he only has to repay 60% of the total debt obligation (for example, if the interest rate is 30%, he would have to repay 0.6 (1+0.3)*100 if his project fails). (i) Under a limited liability contract as described above, derive expressions for E) and E2), the expected values of Ed's incom es under the two projects; and, E(.) and E(H2), the expected values of Caitlin's profits from loans that finance Projects 1 and 2 respectively, as functions of the interest rate, i.

Explanation / Answer

Expected value of project 1 = (0.75 x 550) + (0.25 x 250) = $475

Expected value of project 2 = (0.75 x 160) + (0.25 x 1200) = $420

Assume that Caitlin invests all the money required for the project

Expected returns of project 1 = (0.75 x (150 x (1 + interest rate))) + (0.25 x (0.6 x 150 x (1 + interest rate)))

Expected returns of project 2 = (0.75 x (0.6 x 150 x (1 + interest rate))) + (0.25 x (150 x (1 + interest rate)))

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