Chapter 6 Chapter 6

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be issued at the third year. The bond is redeemable at par on December 31, 2011
at the end of 5 years. Required :
(i) Estimate the current yield and the YTM of the bond.
(ii) Calculate the duration of the NCD.
(iii) Assuming that intermediate coupon payments are, not available for
reinvestment calculate the realised yield on the NCD. (Nov. 2008)
Answer 7
(i) Current yield ( per half year ) = ---------x100 = 7.7778%
90
i.e. 7.7778x2 i.e. 15.5556 % p.a. half-yearly compounded.
Calculation of YTM :
Approximately rate of return = (80/5)/(90)] x 100= 17.78 p.a.
Let YTM is 18% p.a. compounded half-yearly.
Value of bond =
7(annuity for 10 periods at 9%) + 100 ( PVF of period 10 at 9%)
= 7 (6.418) + 100(0.422) = 87.13
NPV at 18% ( compounded half yearly ) : 87.13 – 90 = - 2.87
Let YTM is 17% p.a. compounded half-yearly.
7 7 100
Value of bond = ------- + …………… + -------- + ----------
(1.085) 1 (1.085) 10 (1.085) 10
= 90.16
NPV at 17% ( compounded half yearly ) : 90.16 – 90 = 0.16
0.16
YTM (half-yearly) = 8.50 + -------------- x 0.50 = 8.5264
0.16 – ( -2.87)
YTM = 8.5264 x 2 = 17.05% p.a. half yearly compounded.
(ii) CALCUALTION OF DURATION :
X (Half -year) W XW
1 7 x 0.9214 6.4498
2 7 x 0.8491 11.8874
3 7 x 0.7824 16.4304
4 7 x 0.7209 20.1852
5 7 x 0.6643 23,2505
6 7 x 0.6121 25.7082
7 7 x 0.5640 27.6360
8 7 x 0,5197 29.1032
9 7 x 0.4789 30.1707
10 7 x 0.4413 30.891
10 100 x 0.4413 441.3000
∑ W = 90 ∑XW = 663.0124