Question: There is a 1 - year zero coupon bond that has a $ 1 0 0 0 face value. We know the 1 - year

There is a 1-year zero coupon bond that has a $1000 face value. We know the 1-year risk-free interest rate is 4%. The 1-year zero-coupon bond with the following risky cash flows:
$1,000 with a probability of 90%
Payoffs =500 with a probability of 10%
The discount rate of the above risky bond is 8%. Answer the following questions.
1. What is the yield to maturity of the bond?
2. Suppose there is a CDS completely hedging away the default risk of the risky bond. What is the price of the CDS?
3. Suppose the bond's default probability is underestimated. What is the consequence to the CDS issuer?

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