Question

Suppose you are thinking of investing on a Corporate bond that has a potential to go into default. It promises to pay $80.00 at the end of every year for 4 years as well as pay the face value of $1,000 at the end of the 4h year. Today is the 1 day of year 1 a) (s points): What is the coupon rate of this bond? b) (15 points): What is the price of such a bond if the promised yield is l 1.76% currently at the market? c) (50 points): You obtained the following information after your research: The probability of default within one year of the issue of the bond is 30% in which case only 50% (this is called a "hair cut") of the agreed amount of coupon and face value payments will be made at the originally agreed times Alternatively, you can invest on a 4-year US bond with 4% coupon and $1,000 face value that sell for $964.54 today. At most how much would you pay for this bond today? The yield offered by the US Bond is d) (5 points): Assume that the market also expects the haircut to be 50% in case of a default. Is market's average expectation of the default probability same as yours? (10 points) Why or why not? Explain with a sentence how can you deduce the answer without making any further calculations. 35 points) What is the market's expectation of default probability?

I only need part (c) and if possible the questions after it

Answer 1

Answer:

We would be ready to pay the amount which would amount to same yield as of $ - year US bond

Calculation of YMT of 4 - Year US bond

YTM = [Annual interest + (par value - bond price)/years till maturity]/(par value + bond price)/2

=[40+(1000 - 964.54)/4]/1000 + 964.54)/2

=4.97%

Calculation of price of corporate bond

Expected interest = Probability*amount + probability *amount = 80*0.70 + 40*0.30 = $68

Expected face value at year 4 = probability*amount+probability*amount = 1000*0.70+500*0.30 = $850

Price of bond at YTM 4.97%

= Interest 1/(1+YTM)+interest2/(1+YTM)^2+Interest3/(1+YTM^3+(FV+Interest4)/(1+YTM)^4

= 68/1.0497+68/(1.0497)^2+68/(1.0497)^3+(850+68)/(1.0497^4

= 64.78+61.71+58.79+756.10

Price of bond =$941.38