Chapter 6 Chapter 6

45
The present value of bond principal (20 years duration) is
Rs.215 Present value of interest payments = 1000- 215 = 785
1000/(1.08) 20 i.e.
It interest falls to 6%, the bond value will go up.
The present value of bond principal will be 1000/(1.06) 20 i.e. 312 i.e. the
present value of bond principal will increase by Rs. 97.
The present value of interest payments will be: 80 (11.47) i.e. 918 = i.e. the
present value of interest payments will increase by Rs. 133
The new value of bond will be 312 + 918 = 1230 i.e. the bond value will
increase by Rs.230
% increase in bond value = 23%. There are two components of this %.
(i) % Increase due to present value of principal : ( 97/230) x 100 = 42.17%
(ii) % Increase due to present value of interest: (133/230) x 100 = 57.83%
(b) Present YTM = 7%
Calculation of Bond duration :
Period (X) PV of cash-in-flows (W) XW
1 70 x 0.935 65.45
2 70 x 0.873 122.22
3 70 x 0.816 171.36
4 70 x 0.763 213.64
5 70 x 0.713 249.55
6 1070 x 0.666 4275.72
∑W = 999.62 6 ∑XW = 5097.94
Duration = ∑XW /∑W = 5097.94/1000 = 5.098
(c) Calculation of Bond duration :
Period (X) PV of cash-in-flows (W) XW
1 70 x 0.909 63.63
2 70 x 0.826 115.64
3 70 x 0.751 157.71
4 70 x 0.683 191.24
5 70 x 0.621 217.35
6 1070 x 0.564 3620.88
∑W = 868.78 ∑XW = 4366.45
Duration = ∑XW /∑W = 4366.45/868.78 = 5.026
The duration of the bond decreases as the bond price has reduced while the
receipts have remained unchanged.
6 This value is due rounding off. Otherwise it should be equal to current price of bond i.e. Rs.1000.