HI, I have a finance homework question. I tried to answer. And there's few answers that I'm not sure.if you can please solve and let me know if my answers are correct and if not tell me the right answer(with formulas or calculations).thank you

XYZ company is facing financial difficulties and needs to raise capital quickly in order to remain solvent. The company has decided to try to raise the money in the bond market but has two bond issue options to consider. Option A) Issue a balloon bond with just one payment of $1000000 and a covenant restricting the D/E ratio to be less than 2 or Option B) Issue a coupon bond that pays $26016 every 6 months and pays $867187 at maturity. Both bond choices would have 10 years to maturity. The first option has a 10% chance of defaulting at maturity whereas the second option has a 22% chance of defaulting on the first coupon payment (immediately). Assume if the XYZ defaults investors will always receive $0. If interest rates are 2% per year, answer the following:

a) What is the default-free present value of each bond?
answer that I got is : OPTION A:820348.2919 OptionB:1181102.581

b) What is the risk-neutral valuation of each bond if the chance of default is considered?
OPtion A: 82034.8299 Option B: 20092.551

c) If the option A bond's chance of default would be 25% without the covenant, what is the risk-neutral value of the covenant on that bond?

Answer: 205087.075


thank you

For (a) I have slightly different values than yours for both bonds. I priced 'em both using semiannual compounding (i.e. 1% per semiann period). I can see that you used annual compounding for Bond A, and you're a price is correct under an annual compounding assumption. Check your text for the requested compounding frequency. Also, show how you arrived at your price for B.

For (b) the problem gives you a very simple outcome space for risk-neutral pricing: The bond holders have a 90% probability of receiving ALL the promised cash flows of A, and a 10% chance of receiving nothing. For B, they have 78% odds of getting everything as scheduled, and 22% odds of getting zilch. In other words, it's "all or nothing" for both securities.

This immediately simplifies to

[Price considering default possibility] = [Price without considering default possibility] x [Probability of NOT defaulting]

For (c), redetermine A's risk-neutral price assuming a 25% default probability. Compare it to A's RN price you figured in part (b). The excess of A's RN price in part (b) over its RN price with a 25% default probability, is the value provided by the covenant.

An equivalent approach to (c) is to notice that the covenant gets the bond holders an extra 15 percentage points of probability of receiving the maturity payoff for A. So the covenant generates value equal to 15% of A's no-default present value.