Question: Collateralized Debt Obligations
Nopay Bank is going to issue collateralized debt obligations (CDOs) against the entire issue of the 10-year risky debt of Fortune Limited as presented here:
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Fortune Limited
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Market Value of Assets
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Market Value of Debt and Equity
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Assets
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$100
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10-yr Debt (Face = $66.8)
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??
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Equity
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??
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The risky debt is a zero-coupon bond that pays no interest. At maturity, the bond will pay the investors just the face value.
The underlying assets of Fortune Limited are valued at $100 today. The volatility of asset value in terms of annualized standard deviation is estimated to be 25%. The risk free rate of interest is 5% per year compounded continuously.
The entire issue of the 10-year risky debt with face value equal to $66.8 is to be placed into a debt pool. Against the debt pool, Nopay Bank will issue 10-year CDO with face value equal to $50 that pays no interest. The rest of the 10-year risky debt will be held in the debt pool as over-collateralization (equity).
(a) Determine the market value of the 10-year risky debt.
(b) Determine the market value of Fortune's equity.
(c) Determine the market value of the 10-year CDO that pays no interest.
(d) Determine the market value of the over-collateralization.
(e) Determine the cost of insurance to protect the CDO investors against Fortune's default.
(f) Determine the market value of Fortune's equity and the market value of the over-collateralization (equity of the debt pool) when the volatility of the asset value increases from 25% to 50%. Explain your findings with the results of part (b) and part (d) above.