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.
Answer:
| 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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