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55. Box spreads are used to guarantee a fixed cash flow in the future. Thus, they are purely a means of borrowing or lending money, and have no stock price risk Consider a box spread based on two distinct strike prices (K, L) that is used to lend money, so that there is a positive cost to this transaction up front, but a guaranteed positive payoff at expiration. Determine which of the following sets of transactions is equivalent to this type of box spread. (A) A long position in a (K, L) bull spread using calls and a long position in a (K, L) bear spread using puts. (B) A long position in a (K, L) bull spread using calls and a short position in a (K, L) bear spread using puts. (C) A long position in a (K, L) bull spread using calls and a long position in a (K, L) bull spread using puts. (D) A short position in a (K, L) bull spread using calls and a short position in a (K, L) bear spread using puts. (E) A short position in a (K, L) bull spread using calls and a short position in a(K, L) bull spread using puts. IFM-01-18 Page 28 of 105 56. Determine which of the following positions has the same cash flows as a short stock position. (A) Long forward and long zero-coupon bond (B) Long forward and short forward (C) Long forward and short zero-coupon bond (D) Long zero-coupon bond and short forward (E) Short forward and short zero-coupon bond5. You have developed the technology to use gold to produce high capacity fiber optic switches. The technology has cost $ 5 million to develop. You need $50 million of initial capital investment to start production. Sales of the switch sales will be $20 million per year for the next 5 years and then drop to zero. The main cost of production is gold. Each year, you need 20,000 ounces of gold. Gold is currently selling for $250 per ounce. Your supplier thinks that the gold price will appreciated at 5% per year for the next 5 years. The cost of capital is 10% for the fiber- optics business. The tax rate is 35%. The capital investment can be depreciated linearly over the next 5 years. (a) Calculate the after-tax cash flows of the project. (b) Should you take the project? 6. Your company considers a new investment project, which lasts for three years. The project requires a purchase of a new machine, which costs $600,000. This initial investment can be depreciated to zero over the next three years according to a straight line depreciation rule. The machine has no salvage value at the end. Operating revenue is projected to be $400,000 per year. Operating costs for raw materials are $100,000 43 3 2008, Andrew W. La and Jiang Wang 1.8 Capital Budgeting 1 QUESTIONS per year. The above data is summarized in the following table (in thousands of dollars): Capital expenditure | 600 Depreciation 200 200 200 Operating revenue 400 400 400 Operating cost 100 100 100 The corporate tax rate is 30% and the risk-adjusted discount rate is 10%. (a) Compute after-tax cash flows every year. (b) Should we take the project and why? (c) Suppose that you need to purchase an inventory of raw materials now (year 0) instead of year by year in the next three years. This will require an initial expense of $300,000 in inventory, which will then be depleted, by equal amount every year in the next three years. How would your answers to the above questions change? 7. Halliburton is considering for a two-year project. The project requires an initial capital expenditure of $100 million (in year 0), which can be depreciated linearly to zero in the next two years. It generates a revenue of $80 million and a cost of $25 million per year for the next two years (year 1 and 2). The tax rate for Halliburton is 30%. (a) Compute the net after-tax cash flows of the project. (b) The cash flows of this project are risk-free. The market gives the following interest rates: Maturity (years) 1 2 3 . . . Spot interest rate (%) 4.00 6.00 6.50 - - - Should Halliburton take this project? Explain.You, a Belgian importer, have made a large order for Dotty Dolls. You should receive the shipment in six months, just in time for pre-Chtistmas shopping. The sales contract demands immediate payment upon receipt of the shipment. The unit price for your bulk order of 5D,\" dolls is Hl-CD in. The spot exchange rate BEFle-{D is G, and the simple p.s. interest rates for a six month investment in Belgium and Hong Kong are, respectively, Bpercent and 12 percent. {a} How would you hedge your payment for the dolls? {h} Suppose that three months after hedging the purchase, there is a fire in the doll factory. The dolls will not he delivered, but you still have an outstanding forward purchase contract for HKD 5133,\". If the spot rate is now 15.], and the simple pa. interest rates for a three-month investment are 8 percent and 13 percem, in Belgium and Hong Kong, respectively, what is the value of your forward contract? Have you made a gain or loss? Q1. For each pair shown below, which of the two describes a forward contract? Which describes a futures contract? (a) standardized/made to order (f) for hedgers/speculators (b) interest rate risko interest rate risk (g) more expensive/less expensive (c) ruin risko ruin risk (h) no credit risk/credit risk (d) short maturities/even shorter maturities (i) organized marketo organized market (e) no secondary market/liquid secondary market26. For this problem assume that it is possible to borrow and lend risklessly at a rate of 4%. Also assume that the expected return on the tangency (i.e., the optimal) portfolio composed only of risky assets is 13% with a standard deviation of 18%. Below we list 6 pairs of expected return and standard deviation combinations. For each pair determine whether or not the pair is feasible. If it is feasible, then there is at least one investment that can be made using risky assets and riskless borrowing or lending that produces this level of expected return and standard deviation. Then, if the pair is feasible, determine whether it is efficient or not. It is efficient if the expected return is the highest level that can be obtained for the associated level of standard deviation. Pair Standard Deviation Expected Return a 20.00% 24.75% 12.00% 18.00% 30.00% 19.00% 60.00% 50.00% 10.00% 4.00% 45.00% 56.50% 27. Parmacheenee Belle's entire common stock portfolio ($500,000) is al- lotted to an index fund tracking the Standard & Poors 500 index. The expected rate of return on the index is 9.5% and the standard deviation is 18% per year. The one year risk-free rate is 2.0%. Now Ms. Belle receives a strongly favorable security analyst's report on Mycronics Corp. The analyst projects a return of 25%. Myroncis has a high volatility (40% annual standard deviation) but its correlation coefficient with the S&P 500 is only .3. Assume the return in the analyst's report is an unbiased forecast. Should Ms. Belle sell part of her index fund holdings and invest in Myronics? If so, how much? Note: Ms. Belle can also lend or borrow at the 2.0% risk-free rate. 28. Samantha Darling's entire common stock portfolio ($100,000) is allot- ted to an index fund tracking the Standard & Poors 500 index. The 27 3 200, Andrew W. In and Jiang Wang 1.6 Risk & Portfolio Choice 1 QUESTIONS expected rate of return on the index is 12% and the standard deviation is 16% per year. The one-year risk-free rate is 5.5%. Now Samantha receives a strongly favorable security analyst's report on e. Coli Corp. The analyst projects a return for e. Coli of 25%. e. Coli has a high volatility (50% annual standard deviation) but its correlation coefficient with the S&P 500 is only .4. Assume the analyst's report is accurate. Should Samantha sell part of her index fund holdings and invest in e.Coli? If so, now much? Note: Samantha can also lend or borrow at the 5.5% risk-free rate. 29. You are a salesman/ investment advisor working for a major investment bank. Whenever clients contact you with money to invest, your job is to help them find an appropriate mutual fund to invest in given their financial position. The available investments are: Fund | E[R] .(R) A 10% 15% B 20% 45% C 20% 55% Assume throughout this problem that you only recommend one of the three funds to your clients (possibly a different recommendation for different clients though). a) Would you recommend investment C to someone who comes to you with all his investment funds? Explain. b) Which investment would you recommend to Keith Richards, the really, really old rock star from the Rolling Stones? Assume he invests all his wealth in your particular recommendation. c) Might your answer to b) change if Keith invests only half his wealth in your particular recommendation? If so, under what circumstances? 30. Sarah runs an investment consulting business offering advice to clients on portfolio choices, using what she has learned in 15.401. Her analysis shows that the efficient frontier of risky assets can be obtained by mix