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).
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, [email protected]% 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 [email protected]% 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%
A bond with a redemption value of £100 pays coupons of £1.50 semi-annually (i.e. the bond...
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)?
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