Question

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. By using interpolation method, compute the redemption yield (annual effective).

Answer 1

Period	Cash Flow	Discountig Factor [1/(1.03^period)]	PV of cash flows (cash flow*discounting factor)	Discountig Factor [1/(1.02^period)]	PV of cash flows (cash flow*discounting factor)	Discountig Factor [1/(1.018^period)]	PV of cash flows (cash flow*discounting factor)	Discountig Factor [1/(1.017^period)]	PV of cash flows (cash flow*discounting factor)
0	-95.25	1	-95.25	1	-95.25	1	-95.25	1	-95.25
1	1.5	0.9708738	1.45631068	0.9803922	1.470588235	0.9823183	1.473477407	0.9832842	1.4749263
2	1.5	0.9425959	1.41389386	0.9611688	1.441753172	0.9649492	1.447423779	0.9668478	1.4502716
3	1.5	0.9151417	1.37271249	0.9423223	1.413483502	0.9478872	1.421830824	0.9506861	1.4260291
4	1.5	0.888487	1.33273057	0.9238454	1.385768139	0.9311269	1.396690397	0.9347946	1.4021919
5	1.5	0.8626088	1.29391318	0.9057308	1.358596215	0.914663	1.371994496	0.9191687	1.3787531
6	1.5	0.8374843	1.25622639	0.8879714	1.331957073	0.8984902	1.347735261	0.903804	1.3557061
7	1.5	0.8130915	1.21963727	0.8705602	1.305840268	0.8826033	1.323904972	0.8886962	1.3330443
8	1.5	0.7894092	1.18411385	0.8534904	1.280235557	0.8669974	1.300496043	0.8738409	1.3107614
9	1.5	0.7664167	1.1496251	0.8367553	1.255132899	0.8516673	1.277501024	0.8592339	1.2888509
10	1.5	0.7440939	1.11614087	0.8203483	1.23052245	0.8366084	1.254912598	0.8448711	1.2673067
11	1.5	0.7224213	1.08363191	0.804263	1.206394559	0.8218157	1.232723573	0.8307484	1.2461226
12	1.5	0.7013799	1.05206982	0.7884932	1.182739763	0.8072846	1.210926889	0.8168618	1.2252926
13	1.5	0.6809513	1.02142701	0.7730325	1.159548788	0.7930104	1.189515608	0.8032072	1.2048109
14	1.5	0.6611178	0.99167671	0.757875	1.136812537	0.7789886	1.168482916	0.789781	1.1846714
15	1.5	0.6418619	0.96279292	0.7430147	1.114522095	0.7652147	1.147822118	0.7765791	1.1648687
16	1.5	0.6231669	0.93475041	0.7284458	1.092668721	0.7516844	1.127526638	0.7635979	1.1453969
17	1.5	0.6050164	0.90752467	0.7141626	1.071243844	0.7383933	1.107590018	0.7508338	1.1262507
18	1.5	0.5873946	0.88109191	0.7001594	1.050239062	0.7253373	1.088005912	0.738283	1.1074244
19	1.5	0.570286	0.85542904	0.6864308	1.02964614	0.7125121	1.068768086	0.725942	1.0889129
20	1.5	0.5536758	0.83051363	0.6729713	1.009457	0.6999136	1.049870418	0.7138072	1.0707108
20	100	0.5536758	55.3675754	0.6729713	67.29713331	0.6999136	69.99136123	0.7138072	71.380723
		PV =	-17.5662123	PV =	-3.42571667	PV =	-0.2514398	PV =	1.3830262

IRR is the rate of return at which NPV=0

Here, NPV@1.7% is positive and @1.8% is negative.

Therefore, IRR is between 1.7% and 1.8%

IRR = Rate at which positive NPV + [Positive NPV/(Positive NPV-Negative NPV)]

= 1.7% + [1.383/(1.383-(-0.2514)]

= 1.7% + [1.383/1.6344]

= 1.7% + 0.08462% = 1.78462%

(Explanation & Logic of the method: NPV @1.7% is 1.383 and NPV@1.8% is -0.2514. i.e. 1% increase in required rate of return reduces NPV by 1.383+0.2514=1.6344. We want NPV=0. Therefore, Proportionate increase in required rate of return to reduce NPV by 1.383 is calculated)

Annual Effective Redemption Yield = (1+Semi-Annual Yield)^2 -1 = [(1+0.017846)^2] -1 = 0.03601 = 3.601%