Lucas has $ 2,000 that he wishes to invest for one year. He has narrowed his choices down to one of the following two actions:
a1: Buy bonds of X Ltd., a company that has a very high debt– equity ratio. These bonds pay 8% interest, unless X defaults, in which case Lucas will receive no interest but will recover his principal.
a2: Buy Government Savings Bonds, paying 3% interest. Lucas assesses his prior probability of X Ltd. defaulting as 0.45, and of the savings bonds defaulting as zero. His utility for money is given by the square root of the amount of his net payoff. That is, if he buys the savings bonds his net payoff is $ 60, yielding utility of √60 =7.75, etc. Lucas is a rational decision maker.

a. Based on his prior probabilities, which action should Lucas take? Show your calculations.
b. Before making a final decision, Lucas decides he needs more information. He obtains X Ltd’s current financial statements and examines its times- interest- earned ratio. This ratio can be either “HI” or “LO.” Upon calculating the ratio, Lucas observes that it is HI. On the basis of his prior experience in bond investments, Lucas knows the following conditional probabilities:

Which action should Lucas now take? Show your calculations, taken to two decimal places.
c. An accounting standard allows X Ltd. to value its property, plant, and equipment at fair value providing this can be done reliably. The company plans to adopt this option, since it will reduce its debt– equity ratio.
Evaluate (in words only) the likely impact of this adoption on the main diagonal prob-abilities of the information system in partb.

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