1. Arnold Enterprises is evaluating alternative uses for a three-story manufacturing and warehousing building that it has purchased for $850,000. The company can continue to rent the building to the present occupants for $36,000 per year. The present occupants have indicated an interest in staying in the building for at least another 15 years. Alternatively, the company could modify the existing structure to use for its own manufacturing and warehousing needs. Arnold's production engineer feels the building could be adapted to handle one new product line. The cost and revenue data for the product line are as follows:
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Product line
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Initial cash outlay for building modifications
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$65,000
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Initial building outlay for equipment
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$205,000
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Annual pretax revenues (generated for 15 years)
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$165,000
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Annual pretax expenditures (generated for 15 years)
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$75,000
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The building will be used for only 15 years. After 15 years the building will be too small for efficient production. At that time, Arnold plans to rent the building to firms similar to the current occupants. To rent the building again, Arnold will need to restore the building to its present layout. The estimated cash cost of restoring the building is $35,000. The cash cost can be deducted for tax purposes in the year the expenditures occur. Arnold will depreciate the original building shell (purchased for $850,000) over a 30-year life to zero, regardless of which alternative it chooses. The building modifications and equipment purchases are estimated to have a 15-year life. They will be depreciated by the straight-line method. The firm's tax rate is 34 percent, and its required rate of return on such investments is 12 percent. For simplicity, assume all cash flows occur at the end of the year. The initial outlays for modifications and equipment will occur today (year 0), and the restoration outlays will occur at the end of year 15. Which use of the building would you recommend to management?
2. Suppose there are two states of nature in the future. In the asset market, there are the two contingent claims, one for each state. There's a third security with payoffs x=(4,2). Suppose the prices of the contingent claims are both 1/2: p(c(s1))=p(c(s2))=1/2. The price of the third security is 4.
a) What is the payoff matrix X of the asset market? Is the market complete or incomplete? Why? Is there any redundant security?
b) What is the price vector p of the securities market?
c) The law of one price says that the securities with the same payoffs must have the same price. Does the LOOP hold here? Why or why not?
d) Find an arbitrage portfolio. Show that one can possibly receive some positive payoffs without any cost or risk using the arbitrage portfolio.