1. Consider a 3-yr corporate bond paying a coupon of 7% per year payable semi-annually and has a yield of 5% (expressed with semi-annual compounding). Assume the yield for all maturities on risk-free bonds is 4% per annum. Assume that default can take place every 6 months immediately before a coupon payment. Also assume that the recovery rate is 45%. Estimate the default probabilities assuming that the unconditional default probabilities are the same on each possible default date..
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The following is the balance sheet of a DI (millions)
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ASSETS
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Liabilities & Equity
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CASH
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$2
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Demand deposits
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$50
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LOANS
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50
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Equity
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5
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Primeses and Equipment
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3
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TOTAL
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55
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Total
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55
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The asset-liability management committee has estimated that the loans, whose average interest rate is
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6 percent and whose average life is three years, will have to be discounted at 10 percent if they are to
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be sold in less than two days. If they can be sold in four days, they will have to be discounted at 8 percent.
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If they can be sold later than a week, the DI will receive the full market value. Loans are not amortized; that is,
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the principal is paid at maturity.
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A) What will be the price received by the DI for the loans if they have to be sold in two days? In four days?
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B) In a crisis, if depositors all demand payment on the first day, what amount will they receive? What will
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they receive if they demand to be paid within the week? Assume no demand issurance
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