Question

6.1.3 A 10% bond with face amount 100 matures in 3 years. (a) Find the value of the bond based on each of the following term structures for zero coupon bond spot rates, where r, denotes the nominal annual spot rate convertible semiannually for a t-year term zero coupon bond. (1) rs =.075 n =.0775 11.5 =.08 m2 =.08 12.5 =.0825 rz =.085 (ii) rs = .14 r = 1375 rs =.135 =.1325 P2.5 =.13 rz =.1275 (iii) rs = 12 15.12 11.5 =.12 = 12 12.5 =.12 Þz =.12 (b) For each of the bond prices found in (a), find the corresponding yield to maturity. (C) Repeat part (a) for an 8% bond and for a 12% bond.

Answer 1

Here Interest half yearly so Interest = 10/2 =>5
(a)	Part (i)			Part (ii)			Part (iii)
	Working	Amount		Working	Amount		Working	Amount
	=5/(1+0.075*0.5)^1	4.819		=5/(1+0.14*0.5)^1	4.673		=5/(1+0.12*0.5)^1	4.717
	=5/(1+0.0775*0.5)^2	4.634		=5/(1+0.1375*0.5)^2	4.377		=5/(1+0.12*0.5)^2	4.450
	=5/(1+0.08*0.5)^3	4.445		=5/(1+0.135*0.5)^3	4.110		=5/(1+0.12*0.5)^3	4.198
	=5/(1+0.08*0.5)^4	4.274		=5/(1+0.1325*0.5)^4	3.868		=5/(1+0.12*0.5)^4	3.960
	=5/(1+0.0825*0.5)^5	4.085		=5/(1+0.13*0.5)^5	3.649		=5/(1+0.12*0.5)^5	3.736
	=5/(1+0.085*0.5)^6	3.895		=5/(1+0.1275*0.5)^6	3.451		=5/(1+0.12*0.5)^6	3.525
	=100/(1+0.085*0.5)^6	77.901		=100/(1+0.1275*0.5)^6	69.018		=100/(1+0.12*0.5)^6	70.496
	Value of Bond	104.053		Value of Bond	93.147			95.083
(b)	yield to maturity
	={(100-104.053)+5}*2	=1.82%		={(100-93.147)+5}*2	=25.45%		={(100-95.083)+5}*2	=10.34%
	104.053			93.147			=95.083
c} (a)	Part (i)			Part (ii)			Part (iii)
when 8% bond	Working	Amount		Working	Amount		Working	Amount
	=4/(1+0.075*0.5)^1	3.855		=4/(1+0.14*0.5)^1	4.673		=4/(1+0.12*0.5)^1	3.774
	=4/(1+0.0775*0.5)^2	3.707		=4/(1+0.1375*0.5)^2	4.377		=4/(1+0.12*0.5)^2	3.560
	=4/(1+0.08*0.5)^3	3.556		=4/(1+0.135*0.5)^3	3.288		=4/(1+0.12*0.5)^3	3.358
	=4/(1+0.08*0.5)^4	3.419		=4/(1+0.1325*0.5)^4	3.095		=4/(1+0.12*0.5)^4	3.168
	=4/(1+0.0825*0.5)^5	3.268		=4/(1+0.13*0.5)^5	2.920		=4/(1+0.12*0.5)^5	2.989
	=4/(1+0.085*0.5)^6	3.116		=4/(1+0.1275*0.5)^6	2.761		=4/(1+0.12*0.5)^6	2.820
	=100/(1+0.085*0.5)^6	77.901		=100/(1+0.1275*0.5)^6	69.018		=100/(1+0.12*0.5)^6	70.496
	Value of Bond	98.823		Value of Bond	90.132			90.165
d]a)	Part (i)			Part (ii)			Part (iii)
when 12% bond	Working	Amount		Working	Amount		Working	Amount
	=6/(1+0.075*0.5)^1	5.783		=4/(1+0.14*0.5)^1	4.673		=4/(1+0.12*0.5)^1	3.774
	=6/(1+0.0775*0.5)^2	5.561		=4/(1+0.1375*0.5)^2	5.253		=4/(1+0.12*0.5)^2	3.560
	=6/(1+0.08*0.5)^3	5.334		=4/(1+0.135*0.5)^3	4.932		=4/(1+0.12*0.5)^3	3.358
	=6/(1+0.08*0.5)^4	5.129		=4/(1+0.1325*0.5)^4	4.642		=4/(1+0.12*0.5)^4	3.168
	=6/(1+0.0825*0.5)^5	4.902		=4/(1+0.13*0.5)^5	4.379		=4/(1+0.12*0.5)^5	2.989
	=6/(1+0.085*0.5)^6	4.674		=4/(1+0.1275*0.5)^6	4.141		=4/(1+0.12*0.5)^6	2.820
	=100/(1+0.085*0.5)^6	77.901		=100/(1+0.1275*0.5)^6	69.018		=100/(1+0.12*0.5)^6	70.496
	Value of Bond	109.284		Value of Bond	97.039			90.165