Please help me to solve this problem set of Fixed income subject

Fixed Income Case 05: Radu Gabudean Professor Anh Le Radu Gabudean, an associate in a fixed income trading group of a prominent investment bank, is assigned to price a straight bond issued by General Motors Corporation (GM). Having obtained his PhD in Finance from the Stern School of Business, New York University, Radu thinks that this pricing exercise should be straightforward. In addition, this new bond issued by GM has a pretty simple structure: It is a zero coupon bond with one year till maturity and face value of $1,000,000. Checking with his assistants, he obtains the following information about GM as of today: Market capitalization: 5.51 billions Total Debt: $43.21 billions Asset volatility: 45% Expected recovery given default 55% GM: Returns on equity F: Returns on equity 0.15 0.15 0.1 0.1 0.05 0.05 0 0 0.05 0.05 0.1 0.1 In addition, his assistant also collects some information on Ford (F) who is in a very similar line of business with GM. Market capitalization: 10.67 billions Total Debt: $166.03 billions Asset volatility over the last year: 18% per annum Expected recovery given default 45% The current 5year continuously compounding riskfree rate is 4% p.a. Interestingly, F has just issued a very similar bond: one year to maturity, zero coupon, face value $1,000,000 for a price of $807,414.48 which implies a semiannual compounding yield of 22.58% p.a. In discussing with his assistants, Steve and Paul: Paul thinks that Ford is heavily leveraged: their total debt is about 16 times their total equity. To this extent, GM looks much better: GM's equity is only about one eighth of its debt. Therefore, Fixed Income Case 05: Radu Gabudean Professor Anh Le Paul thinks that GM's bond should be discounted at a yield lower than 22.58% to reflect their safer leverage position. Steve agrees with Paul but points out the difference in asset volatility. Although in the same line of business, for some reason, GM's asset values seem to fluctuate more widely with a volatility of 40% compared to 18% for F. This is also obvious by looking at the equity returns graph: there are more wide swings in GM's equity returns than with F's. Therefore, Steve argues that GM is fundamentally more risky than F. Since GM's asset volatility is more than double F's asset volatility, this makes GM look even worse even after taking into account their differences in leverage. As a result, Steve thinks that they should discount GM's bond at a yield higher than the 22.58% yield that markets use to price F's bond. Radu sees the points raised by Paul and Steve but mentions that the expected recovery on F's bond is relatively unattractive at 45%. This means if F defaults on their bond, bond holders are expected to recover only 45 cents out of $1 face value. On the other hand, the recovery for GM bonds is 55 cents out of a dollar. This makes GM's bond relatively more attractive. After the discussions, Radu is so confused that he decides to seek help. Your job: is to help Radu to price GM's bond