# Assume a corporate bond with a

Assume a corporate bond with a \$1000 face value matures 5 yearsand 7 months from today and has an annual coupon rate of 8% paidsemiannually. There is a 10% chance that the issuer will default atmaturity. If the firm defaults, it will pay 80% of what is promised(final coupon + face value) at maturity. Treasuries with the samematurity earn a yield to maturity of 2% and investors in thesecorporate bonds demand a 3% risk premium over the current rate onTreasuries (thus requiring an expected return of 5%) to compensatefor the risk they face (All rates are APRs with semiannualcompounding).

Calculate the clean price of the bond.

 Expected rate return per annum=5% ie. 5%/2= 2.5% per semi-annualcompounding 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 tomaturity=(5yrs.*2 s/a periods )+ 1 coupon pmts.(ie. 1 coupon pmt. 1mth. From now =11 annuity –coupon pmts, final coupon is combined with amountto be received at maturity —for ease of calculating probablepayments to be received Amt. to be received onmaturity—(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 theclean price of a bond, Price=(Pmt.*(1-(1+r)^-n)/r)+(Amt. atmaturity/(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

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