13. Calculate the fair present value of the following bonds, all of which have a

Question

13. Calculate the fair present value of the following bonds, all of which have a 10 percent coupon rate (paid semiannually), face value of $1,000, and a required rate of return of 8 per- cent. (LG 3-5) a. The bond has 10 years remaining to maturity. b. The bond has 15 years remaining to maturity. c. The bond has 20 years remaining to maturity. d. What do your answers to parts (a) through (c) say about the relation between time to maturity and present values? 14. Repeat parts (a) through (c) of Problem 13 using a required rate of return on the bond of 11 percent. What do your cal- culations imply about the relation between time to maturity and bond price volatility? (LG 3-5) 15. A $1,000 par value bond with five years left to maturity pays an interest payment semiannually with a 6 percent cou- pon rate and is priced to have a 5 percent yield to maturity. If interest rates surprisingly increase by 0.5 percent, by how much will the bond's price change? (LG 3-4)

Explanation / Answer

Solution:

13

Solution:

13

(a) Facts Given: Annual Coupon Rate (I): 10.00% Semiannually Coupon Rate (I/2): 5.00% Par Value of Bonds $1,000 Period of Maturity(Yrs) 10 Years Semiannually (Yrs*2) 20 Required Rate of Return 8% Discount Rate (Return/2) 4% Calculate the fair present value of bond Interest on bond 5%*1000= $50.00 Face Value of Bond $1,000 Fair Present Value of bond= 50PVIFA(4%,20)+ 1000PVIF(4%,20) Fair Present Value of bond= 50*13.5903+1000*0.4564 Fair Present Value of bond= $1135.915 b) if Years to maturity 15 years, semiannually Yrs*2= 30 Fair Present Value of bond= 50PVIFA(4%,30)+ 1000PVIF(4%,30) Fair Present Value of bond= 50*17.2920+1000*0.3083 Fair Present Value of bond= $1172.90 c) if Years to maturity 20 years, semiannually Yrs*2= 40 Fair Present Value of bond= 50PVIFA(4%,40)+ 1000PVIF(4%,40) Fair Present Value of bond= 50*19.7928+1000*0.2083 Fair Present Value of bond= $1197.94 d) There is a positive relation between present values and time to maturity as time to maturity increases present value also increases 14 a) Facts Given: Annual Coupon Rate (I): 10.00% Semiannually Coupon Rate (I/2): 5.00% Par Value of Bonds $1,000 Period of Maturity(Yrs) 10 Years Semiannually (Yrs*2) 20 Required Rate of Return 11% Discount Rate (Return/2) 5.5% Fair Present Value of bond= 50PVIFA(5.5%,20)+ 1000PVIF(5.5%,20) Fair Present Value of bond= 50*11.9504+1000*0.3427 Fair Present Value of bond= $940.22 b) if Years to maturity 15 years, semiannually Yrs*2= 30 Fair Present Value of bond= 50PVIFA(5.5%,30)+ 1000PVIF(5.5%,30) Fair Present Value of bond= 50*14.5337+1000*0.2006 Fair Present Value of bond= $927.29 c) if Years to maturity 20 years, semiannually Yrs*2= 40 Fair Present Value of bond= 50PVIFA(5.5%,40)+ 1000PVIF(5.5%,40) Fair Present Value of bond= 50*16.0461+1000*0.1175 Fair Present Value of bond= $919.805 Conclusion: As the required rate of return increases from 8% to 11%, there is inverse relation between bond price and time to maturity As the time to maturity increases bond price decreases 15 Facts Given: Annual Coupon Rate (I): 6.00% Semiannually Coupon Rate (I/2): 3.00% Par Value of Bonds $1,000 Period of Maturity(Yrs) 5 Semiannually (Yrs*2) 10 Required Rate of Return 5% Discount Rate (Return/2) 2.5% Fair Present Value of bond= 30PVIFA(2.5%,10)+ 1000PVIF(2.5%,10) Fair Present Value of bond= 30*8.7521+1000*0.7812 Fair Present Value of bond= $1043.763 If interest rate increase by 0.5%, Coupo rate = 6.5%, Semiannually: 3.25% Fair Present Value of bond= 32.50PVIFA(2.5%,10)+ 1000PVIF(2.5%,10) Fair Present Value of bond= 32.50*8.7521+1000*0.7812 Fair Present Value of bond= $1065.6432 Increase in Bond Price on increase in interest rate by 0.5%= $1065.6432 - $1043.763= $21.8802

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