Question

Question:

An investor is planning to invest in the bond market and has the following choices:

Bond A:

This is a coupon bond from ABM Ltd. The bond has a face value of $1,000 and a coupon rate of 5% paid semi-annually. The bond matures in 8 years.

Bond B:

This is a zero-coupon bond from ABM Ltd. The bond has a face value of $1,000. Interest on this bond compounds semi-annually. The bond matures in 8 years.

The market rate of interest for both bonds is 4%.

Considering the above information, please answer the following:

1. Determine the value of both bonds.                                                       [2 bonds x 1.5 marks = 3 marks]
2. For both bonds, state if they sell at par or premium or discount.                                                [2 marks]
3. Suppose the investor buys a zero-coupon bond of ABM Ltd.for the price (i.e., value) determined in (a)and then sells the bond for $710 after 4 years. Determine the realised yield for the investor.
                                                                                                                                                                   [2.5 marks]

Answer 1

a.

Market interest rate= 4% ; Semi annual rate =2%

Coupon rate =5% ; Semi annual=2.5% ; Coupon amount=1000*2.5%=25$

No of terms= period of 8 year semi annually= 16 terms

Coupon Bond
Terms	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16
Coupon	25	25	25	25	25	25	25	25	25	25	25	25	25	25	25	1025
Present value	24.50980392	24.02921953	23.55805836	23.09613565	22.64327025	22.19928455	21.76400447	21.33725928	20.91888165	20.5087075	20.10657598	19.71232939	19.32581313	18.94687561	18.57536825	746.6569591
Coupon Bond Price	1067.888547
Zero Coupon Bond
Terms	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16
Payments	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1000
Present value	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	728.4458137
Zero coupon Bond Price	728.4458137

b.

From the bond price we can see that Coupon bond is selling at a premium(higher than face value) ; whereas Zero coupon bond selling at a discount( lesser than face value)

c.

Buying Price= 728.446$ ; Selling price after 4 years=710$

From Yield equation ; 728.446(1+Yield)^4 = 710 ;

Hence realised yield= (710/728.446)(1/4)-1 = -.64% [-ve yield observed]