Question

Assume a corporate bond with a $1000 face value matures 5 years and 7 months from today and has an annual coupon rate of 8% paid semiannually. There is a 10% chance that the issuer will default at maturity. If the firm defaults, it will pay 80% of what is promised (final coupon + face value) at maturity. Treasuries with the same maturity earn a yield to maturity of 2% and investors in these corporate bonds demand a 3% risk premium over the current rate on Treasuries (thus requiring an expected return of 5%) to compensate for the risk they face (All rates are APRs with semiannual compounding).

Calculate the clean price of the bond.

Answer 1

Expected rate return per annum= 5%

ie. 5%/2= 2.5% per semi-annual compounding period

Semi-annual Coupon amt.=1000*8%/2= 40

r= Expected semi-annual rate of return , found out above-- 2.5% per s/a period

No.of semi-annual coupons still to maturity=(5yrs.*2 s/a periods )+ 1 coupon pmts.(ie. 1 coupon pmt. 1 mth. From now =11 annuity --coupon pmts,

final coupon is combined with amount to be received at maturity ---for ease of calculating probable payments to be received

Amt. to be received on maturity---(10%*80%*(1000+40))+(90%*(1000+40))= (10%*80%*1040)+(90%*1040)=1019.20

This final pmt. Is at end   of s/a period, 12

so, now using the formula to find the clean price of a bond,

Price=(Pmt.*(1-(1+r)^-n)/r)+(Amt. at maturity/(1+r)^n)

ie.(40*(1-1.025^-11)/0.025)+(1019.20/1.025^12)=

1138.40

So, the answer is:

the clean price of the bond= $ 1138.40