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 6 percent and whose average life is three years, will have to be discounted at 10 percent if they are to be sold in less than two days. If they can be sold in four days, they will have to be discounted at 8 percent.
If they can be sold later than a week, the DI will receive the full market value. Loans are not amortized; that is,the principal is paid at maturity.
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?
B) In a crisis, if depositors all demand payment on the first day, what amount will they receive? What will they receive if they demand to be paid within the week? Assume no demand issurance.