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4. You are a U.S.-based company that just imported some raw materials for (200,000 from France. You owe (200,000 to the French supplier in one year. You are concerned about the amount in dollars you will have to pay for this purchase in one year. Suppose: Current Spot exchange rate is $1.50/E One-year Forward exchange rate is $1.25/( U.S. interest rate is 3.00% per year Interest rate in Europe is 4.00% per year Call option with strike price of $1.30/6 is available with premium of $0.1/E Put option with strike price of $1.30/C is available with premium of $0.2/E You forecast that the spot exchange rate in one year could be $1.20/6, $1.30/E, $1.40/6, or $1.50/6 with equal probability. a. Suppose you decide to do nothing. In one year, what will be the dollar cost in the four possible scenarios? (2 points) b. Explain in detail how you can lock in the exact dollar cost of this purchase by using forward contract. Specifically, do you take a long or short position in a E forward contract and for how much amount? What dollar cost can you lock in with this strategy? (4 points) c. Explain in detail how you can lock hedge your position using money market hedge. Write down the detailed steps one needs to take to implement the money market hedge and calculate the dollar cost in each of the four scenarios. (6 points) d. Explain in detail how you can hedge using option. Should you take a long or short position in put or call options on euros? Write down whether you will exercise the option (i.e., is it in the money, at the money, or out of the money?) and calculate the dollar cost (including option premium you paid) in each of the four possible scenarios. (6 points) Hint: at the end, provide a table that summarizes the dollar cost in each scenario like the following: State Future spot rate Cost in Euro Unhedged Forward Money Market |Option 1 1.2 200,000.00 2 1.3 200,000.00 3 1.4 200,000.00 4 1.5 200,000.004. You are a U.S.-based company that just imported some raw materials for 6200,000 from France. You owe (200,000 to the French supplier in one year. You are concerned about the amount in dollars you will have to pay for this purchase in one year. Suppose: Current Spot exchange rate is $1.50/E One-year Forward exchange rate is $1.25/( U.S. interest rate is 3.00% per year Interest rate in Europe is 4.00% per year Call option with strike price of $1.30/6 is available with premium of $0.1/6 Put option with strike price of $1.30/6 is available with premium of $0.2/6 You forecast that the spot exchange rate in one year could be $1.20/6, $1.30/6, $1.40/6, or $1.50/6 with equal probability. a. Suppose you decide to do nothing. In one year, what will be the dollar cost in the four possible scenarios? (2 points) b. Explain in detail how you can lock in the exact dollar cost of this purchase by using forward contract. Specifically, do you take a long or short position in a 6 forward contract and for how much amount? What dollar cost can you lock in with this strategy? (4 points) c. Explain in detail how you can lock hedge your position using money market hedge. Write down the detailed steps one needs to take to implement the money market hedge and calculate the dollar cost in each of the four scenarios. (6 points) d. Explain in detail how you can hedge using option. Should you take a long or short position in put or call options on euros? Write down whether you will exercise the option (i.e., is it in the money, at the money, or out of the money?) and calculate the dollar cost (including option premium you paid) in each of the four possible scenarios. (6 points) Hint: at the end, provide a table that summarizes the dollar cost in each scenario like the following: State Future spot rate Cost in Euro Unhedged Forward Money Market |Option 1 1.2 200,000.00 2 1.3 200,000.00 3 1.4 200,000.00 4 1.5 200,000.00Risk Premium 0.0026 E[R] (note R = r-ri) 0.0026 Hints: The alpha and beta come directly from the regression coefficient estimates. The weekly variance of returns can be calculated as the Total Sum of Squares (SS) divided by the total degrees of freedom (df). . The residual standard deviation can be calculated from the Standard Error of the regression (in the regression statistics box). Calculate the variance of the residuals as the square of residual standard deviation. . Finally, calculate the risk premium using the expected return equation: E[R.] = Bix(Market Risk Premium). b) Step 2: Calculate the covariance matrix of the excess returns. Complete the matrix below. Remember, the index model makes a simplifying assumption about the covariances, so we can use the formula: COV(n, r,) = BB,OM] S&P500 AIG CITI S&P500 AIG CITI c) Now we have all the information we need to calculate the initial position in each security. Note: We will ignore systematic risk at first, to make things easier, and we'll account for it later in the process. Compute the initial position in each security, and scale them so that these weights sum to one. What are the weights? (Hint: Steps 1 and 2) d) Using the weights you calculated in step (c), calculate the weighted average alpha, the weighted average beta, and the weighted average residual variance. (Hints: Steps 3, 4, and 6) e) Now that you know the weights for the individual assets, calculate how much money you should put in the active portfolio. [Hint: see step 5 from Bodie, Kane, and Marcus, page 266]Question 4 Assume a Modigliani-Miller (MM) world. Gemini Ltd. is an all-equity firm with 10 million shares outstanding. Its only asset is $100 million of cash invested in the risk-free asset, which pays 10% per year. Gemini can invest $50 million of its cash today into one of two mutually exclusive projects, A or B. Project A is expected to generate a perpetual stream of free cash flows, starting with $13.5 million in exactly one year, thereafter growing at an expected rate of 3% per year. Project B, also perpetual, is expected to produce a free cash flow of $10 million in exactly one year's time, growing at an expected rate of 5% per year thereafter. The risk of both projects is diversifiable. State any additional assumptions you may need to make when answering the question. Show all working and calculations. Required: a) Calculate the NPV and IRR of each project. If the NPV and IRR rankings disagree, explain the source of the conflict. (5 marks) b) Which project should Gemini choose? Why? (4 marks) c) Assume Gemini invests in project B. What is the firm's new share price after Investment? (2 marks) After taking project B, Gemini considers acquiring Leo Corp., an all-equity firm with 20 million shares outstanding, currently trading at $2 per share. The difficulties of integrating disparate organizations means the synergies from the acquisition are uncertain. With probability 60%, integration will be successful, in which case the value of Leo's assets will improve by 30% under the new management. However, if the merger is implemented poorly (probability 40%), the acquisition will destroy 20% of Leo's asset value. Remember that information in an MM world is symmetric - insiders at firms and in the market are equally informed about the synergy outcome, which will only be revealed after the acquisition is completed. Assume managers always act in the interest of existing shareholders and that all participants are risk-neutral. Also assume that in any takeover, 100% of target shares are acquired by the bidder. d) Assume Gemini does not have to pay a premium to acquire Leo. Advise Gemini on the merits of the acquisition. If it financed the takeover using shares in the combined entity, how many shares will Gemini need to offer for each Leo share? Would Gemini's shareholders be better off (in expectation) if the acquisition was financed using cash from the company accounts instead? Explain
