19. If the following bonds are identical except for coupon, what is the price of

Question

19. If the following bonds are identical except for coupon, what is the price of bond B? Face value Semiannual Coupon Years to maturity Bond A $1,000 $50 25 $1,150.o0 Bond B $1,000 $40 25 2 Price A) 944.73 $ 975.31 C) $1,037.86 $1,150.00 B) D) E S1,279.47 20. You purchased a 5-year annual interest coupon bond one year ago. Its coupon interest rate was 6% and its par value was $1,000. At the time you purchased the bond, the yield to maturity was 4%. Ifyou sold the bond immediately after receiving the first interest payment and the bond's yield to maturity had changed to 3.5%, your annual total rate of return on holding the bond for that year would have been approximately A) 4.000 B) 5.8% 7.6% 9.0% None of the Above

Explanation / Answer

Solution :

19) First of all we will calculate YTM of Bond A, i.e. r which is the semi annual rate.

We know, n = 25*2 = 50

Interest Payments = $ 50

Maturity Value = $ 1000

Bond Price = Interest payments * PVIFA( r,n) + Maturity Value * PVIF (r,n)

1150 = 50 * PVIFA (r,50) + 1000 * PVIF (r,50)

1150 = 50 * PVIFA (4%,50) + 1000 * PVIF (4%,50)

From present value table and present value annuity tables we will find the values of PVIFA(4%,50) and PVIF(4%,50)

R.H.S. = (50*21.48) + (1000*0.14) = 1214

L.H.S. = 1150

The rate should be increased

1150 = 50 * PVIFA (5%,50) + 1000 * PVIF (5%,50)

From present value table and present value annuity tables we will find the values of PVIFA(5%,50) and PVIF(5%,50)

R.H.S. = (50*18.26) + (1000*0.0872) = 1000

L.H.S. = 1150

This implies that r is between 4% and 5%. Therefore using interpolation,we find r = 4.3%

As bond A & bond B are identical , there semi annual r for bond B = 4.3%

Now, Price of Bond B = Interest payments * PVIFA( r,n) + Maturity Value * PVIF (r,n)

= 40 * PVIFA (4.3%,50) + 1000 * PVIF (4.3%,50)

we will find present value by the formula 1/(1+r)^n

= (40 * 20.42) + (1000 * 0.12)

= approximately equal to $ 944.73

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