Question

A $1,000 corporate bond has a maturity date 20 years from now and a coupon rate of 6 percent paid annually. Calculate the value of the bond if the required rate of return is a) 4% b) 6% c) 8%.

Strip the bond into an interest only bond and a face value only bond. That is, create a bond that consists only of the coupon interest payments and one that consists only of the face value. Calculate the value of each of these new bonds with required rates of return of a) 4% b) 6% c) 8%. Which bond has more interest rate risk? Which bond has more default risk? Now say that instead of annual coupon payments, the corporation makes payments every six months. Recalculate the value of your stripped bonds. Explain the results.

Answer 1

Annually Value of Bond Interest payment anually Rate of return@4% Interest=1000*6% Interest=60 Principle payment=1000 Discount Rate =4% Value of bond =60*PVAF(4%,40)+1000*PVIF(4%,40) Value of Bond Interest payment anually Rate of return@8% Interest=1000*6% Interest=60 Principle payment=1000 Discount Rate =8% Value of bond =60*PVAF(8%,40)+1000*PVIF(8%,40) Value of bond =60*13.590+1000*0.456 Value of bond = Value of bond =60*9.818+1000*0.215 Value of bond = 804 1271 Value of Bond Interest payment anually Rate of return@6% Interest=1000*6% Interest=60 Principle payment=1000 Discount Rate =6% Value of bond =60*PVAF(6%,40)+1000*PVIF(6%,40) Value of bond =60*11.470+1000*0.312 Value of bond = 1000

STRIPS- Interest Payment anually Rate of return@4% Value of bond =Present value of Interest+Principle value of Principle Value of bond =60*PVAF(6%,40) +1000*PVIF(6%,40) Present value of Interest= 60*13.590 = 815.4 Principle value of Principle= 1000*0.456 = 456 Rate of return@6% Value of bond =Present value of Interest+Principle value of Principle Value of bond =60*11.470+1000*0.312 Present value of Interest= 60*11.470 = 688 Principle value of Principle= 1000*0.312 = 312 Rate of return@8% Value of bond =Present value of Interest+Principle value of Principle Value of bond =60*9.818+1000*0.215 Present value of Interest= 60*9.818 = 589 Principle value of Principle= 1000*0.215 = 215

Semi anually Value of Bond Interest payment semi anually Rate of return@4% Interest=1000*6%*6/12 Interest=30 Principle payment=1000 Discount Rate For 6 Months=4%*6/12=2% Value of bond =30*PVAF(2%,40)+1000*PVIF(2%,40) Value of Bond Interest payment semi anually Rate of return@8% Interest=1000*6%*6/12 Interest=30 Principle payment=1000 Discount Rate For 6 Months=8%*6/12=4% Value of bond =30*PVAF(4%,40)+1000*PVIF(4%,40) Value of bond =30*27.355+1000*0.453 Value of bond = 1274 Value of bond =30*19.793+1000*0.208 Value of bond = 802 Value of Bond Interest payment semi anually Rate of return@6% Interest=1000*6%*6/12 Interest=30 Principle payment=1000 Discount Rate For 6 Months=6%*6/12=3% Value of bond =30*PVAF(3%,40) +1000*PVIF(3%,40) Value of bond =30*23.115+1000*0.307 Value of bond = 1000

STRIPS - Interest Payment Semi anually Rate of return@4% Value of bond =Present value of Interest+Principle value of Principle Value of bond =30*27.355+1000*0.453 Present value of Interest= 30*27.355 = 821 Principle value of Principle= 1000*0.453 = 453 Rate of return@6% Value of bond =Present value of Interest+Principle value of Principle Value of bond =30*23.115+1000*0.307 Present value of Interest= 30*19.793 = 693 Principle value of Principle= 1000*0.307 = 307 Rate of return@8% Value of bond =Present value of Interest+Principle value of Principle Value of bond =30*19.793+1000*0.208 Present value of Interest= 30*19.793 = 594 Principle value of Principle= 1000*0.208 = 208