Question

2. * A bond with a redemption value of £100 pays coupons of £1.50 semi-annually (i.e. the bond holder receives £1.50 twice per year), with the first coupon due in half a year. The bond will mature in ten years' time. It is currently selling for £95.25. (a) Without making any calculations can you determine what is greater between the redemption yield and the interest yield? Why? (b) Compute the redemption yield (annual effective)?

Answer 1

Solution (a)
1.Redemption yield is greater than Interest yield
1.The redemtion yield and Price of the bond are inversely related, and in this case the current price of the bond (95.25) is less that redemption value (100) due to which the redemption yield paid to the investor will be high
Solution (b)
Redemption value	100
Coupon payment	1.5
Frequency of coupon payment	2
Maturity in years	10
Current price	95.25
Redemtion yield - Computation
Type of payment	Period	Amount	Yield @ 1.7%	Yield @ 1.8%
Coupon	1	1.5	1.4749	1.4735
Coupon	2	1.5	1.4503	1.4474
Coupon	3	1.5	1.4260	1.4218
Coupon	4	1.5	1.4022	1.3967
Coupon	5	1.5	1.3788	1.3720
Coupon	6	1.5	1.3557	1.3477
Coupon	7	1.5	1.3330	1.3239
Coupon	8	1.5	1.3108	1.3005
Coupon	9	1.5	1.2889	1.2775
Coupon	10	1.5	1.2673	1.2549
Coupon	11	1.5	1.2461	1.2327
Coupon	12	1.5	1.2253	1.2109
Coupon	13	1.5	1.2048	1.1895
Coupon	14	1.5	1.1847	1.1685
Coupon	15	1.5	1.1649	1.1478
Coupon	16	1.5	1.1454	1.1275
Coupon	17	1.5	1.1263	1.1076
Coupon	18	1.5	1.1074	1.0880
Coupon	19	1.5	1.0889	1.0688
Coupon	20	1.5	1.0707	1.0499
Principal	20	100	71.3807	69.9914
		Total	96.6330	94.9986
By interoploation method we get
Redemption yield		1.7845%	Semi anually
Stated annual rate		3.5690%	(=1.7845%*2)
Converting to Effective annual rate
Formula		{(1+r%/n)^n}-1
Since the payments are made semi annually here n=2
Effective annual rate =		3.6008%	{(1+3.5690%/2)^2}-1