Spring 2015: Midterm B for 1:00 Class. Problems (75 points each)

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1 Spring 2015: Midterm B for 1:00 Class Name Notes: 1) Annuity and perpetuity may have growing or constant cash flows. 2) While you are welcome to solve any problem to a final answer, you will only earn points on most problems for setting them up. Setting up means writing down the appropriate equations and plugging in the appropriate numbers. For multistep problems, you can plug unsolved variables into later steps. Note however, that to solve some problems you will have to do some calculations. Problems (75 points each) 1. Set up the calculations needed to determine the net present value of a project which will cost $5 million today and which will generate its first semiannual cash flow of $500,000 four months from today. Subsequent semiannual cash flows will shrink by 2% each and will continue through nine years and 10 months from today. The beta of the project is 0.8, the risk-free interest rate is 3%, and the expected return on the market equals 9%.

2 2. Blasting Rock Inc. is considering whether to spend $6 million refurbishing an abandoned facility that it acquired for $1 million ten years ago. The facility could be sold as is for $3 million after taxes today. The cost of refurbishing the facility could be depreciated according to the 10-year MACRS class. Variable costs associated with the facility would equal 60% of revenues and fixed costs associated with the new facility would $5 million per year. The firm s marginal tax rate equals 35%. Using this information and the information in the table below (all millions) set up the calculations needed to determine the free cash flow associated with the factory for today and five years from today. Year Rev Cash Accts. Rec. Inv. Acct. Pay

3 3. Assume you have calculated the returns on Wal-Mart (WMT) and the S&P500 (S&P) for the past four years as follows: Year WMT S&P % 24% % 13% % 5% % 23% Set up the calculations needed to determine the beta of a portfolio in which you short-sell $200,000 of stock in Microsoft (MSFT) which has a beta of 1.6 and buy $1,000,000 of Wal-Mart stock.

4 4. Assume GlaxoSmithKline (GSK) has an expected return of 8% and a standard deviation of returns of 15%, Honda Motor Corp (HMC) has an expected return of 11% and a standard deviation of returns of 25%, and Sears Holdings (SHLD) has an expected return of 16% and a standard deviation of returns of 40%. Assume also that the correlation between the three stocks vary between +0.2 and Note: Answer all of the following on the same graph. a. Sketch a reasonable set of portfolios you could build in which you take long and short positions in these three stocks. Identify the best portfolio if you want to achieve a standard deviation of returns equal to 20%. b. Assume risk-free bonds earn 6%. Show whether you are better or worse off in part b. than in part a. c. Show whether you are better or worse off (compared to part b) if the standard deviation of returns of all three stocks fall by 5%.

5 5. Given the following information, set up a table that shows the highest arbitrage profit that it is possible to earn today. Show also that the conditions of arbitrage are met. Assume that one-year Treasuries earn a return of 1% and that two-year Treasuries earn a return of 2%. On a per-share basis, the ETF owns one share of Eli Lilly and two shares of Sysco. It also owns one-year Treasuries that mature for $100 and has shorted two-year treasuries that mature for $300. The ETF will distribute all cash flows from the securities it owns. Payments in one Payments in two Bid Ask year if economy is years if economy is Security Price Number Price Number Weak Strong Weak Strong Eli Lilly $ $ $150 $200 $300 $500 Sysco $ $ $100 $150 $200 $400 ETF $ $