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assignment3 solutions

assignment3 solutions - Economics 1745 Professor Borja...

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Economics 1745 Professor Borja Larrain, Fall 2008 Assignment #3 Solutions 1. (a) For a loan of $900,000, the bank will require a repayment of x in the good state such that: 900,000(1.10)=0.55 x + 0.45(0.5 million) x = 1,390,909 The quoted rate is (1,390,909)/(900,000) – 1 = 54.5% (b) For a loan of $1,000,000, the bank will require a repayment of x in the good state such that: 1,000,000(1.10)=0.55 x + 0.45(0.5 million) x = 1,590,909 The promised rate of return is (1,590,909)/(1,000,000) – 1 = 59.09% However, the bank will not make a loan of $1,000,000 because the borrower does not have sufficient funds to repay the loan even in the good state. 2. a) PV(bond) = 0.5(50) + 0.5(20) = 35 (No discounting). PV(equity) = 0.5(50) = 25 b) 50/35 – 1 = 42.8%. c,d) Returns in sunshine: bond = 42.8 %, equity = 100%. Returns in rain: bond = -42.8%, equity = -100%. e) Bond holders get 50 if sunshine and 30 if rain. PV(bond) = 40, PV(equity) = 20. Returns: bond = plus or minus 25%, equity = plus or minus 100%. This reorganization transfers value from equity holders to bond holders. Note that the total value of the firm is still bond + equity = 60. Equity holders have nothing to gain from this, although it would benefit bond holders.
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