s in 3 years. A 10% bond with face amount 100 mature owing tem (e) Find the valu
ID: 2786935 • Letter: S
Question
s in 3 years. A 10% bond with face amount 100 mature owing tem (e) Find the value of the bond based on each of the following tm structures for zero coupon bond spot rates, where o) denote the nominal annual spot rate convertible semiannually for a 6.1.3 year term zero coupon bond (i) so(.5) = .075 So(1) = .0775 So(1.5)-.08 so(2) =.08 So(2.5) = .0825 so(3) = .085 (ii) so(·5)-.14s(I)-.1375 so(1.5)-.135 s0(2) =.1325 so(2.5) =.13 so(3) = .1275 (iii) so(5)-.12 s0(1) = . 12 so(3) = .12 so(1.5) = .12 so(2)-.1 so(2.5)-.12 (b) For each of the bond prices foun corresponding yield to maturity. in (a), find the (c) Repeat part (a) for an 8% bond and for a 12%Explanation / Answer
Coupon=10%*100/2=5
a
1
Price=5/(1+7.5%/2)+5/(1+7.75%/2)^2+5/(1+8%/2)^3+5/(1+8%/2)^4+5/(1+8.25%/2)^5+105/(1+8.5%/2)^6
=104.0534
2
Price=5/(1+14%/2)+5/(1+13.75%/2)^2+5/(1+13.5%/2)^3+5/(1+13.25%/2)^4+5/(1+13%/2)^5+105/(1+12.75%/2)^6
=93.1473
3
Price=5/(1+12%/2)+5/(1+12%/2)^2+5/(1+12%/2)^3+5/(1+12%/2)^4+5/(1+12%/2)^5+105/(1+12%/2)^6
=95.08268
b
Let ytm be y
1
104.0534=5/(1+y/2)+5/(1+y/2)^2+5/(1+y/2)^3+5/(1+y/2)^4+5/(1+y/2)^5+105/(1+y/2)^6
Hence, y=0.084424=8.4424%
2
93.1473=5/(1+y/2)+5/(1+y/2)^2+5/(1+y/2)^3+5/(1+y/2)^4+5/(1+y/2)^5+105/(1+y/2)^6
Hence, y=0.128233=12.8233%
3
95.08268=5/(1+y/2)+5/(1+y/2)^2+5/(1+y/2)^3+5/(1+y/2)^4+5/(1+y/2)^5+105/(1+y/2)^6
hence, y=0.12=12%
c
For 8% bond: Coupons=8%*100/2=4
1
Price=4/(1+7.5%/2)+4/(1+7.75%/2)^2+4/(1+8%/2)^3+4/(1+8%/2)^4+4/(1+8.25%/2)^5+104/(1+8.5%/2)^6
=98.82293
2
Price=4/(1+14%/2)+4/(1+13.75%/2)^2+4/(1+13.5%/2)^3+4/(1+13.25%/2)^4+4/(1+13%/2)^5+104/(1+12.75%/2)^6
=88.32145
3
Price=4/(1+12%/2)+4/(1+12%/2)^2+4/(1+12%/2)^3+4/(1+12%/2)^4+4/(1+12%/2)^5+104/(1+12%/2)^6
=90.16535
For 12% bond: Coupons=12%*100/2=6
1
Price=6/(1+7.5%/2)+6/(1+7.75%/2)^2+6/(1+8%/2)^3+6/(1+8%/2)^4+6/(1+8.25%/2)^5+106/(1+8.5%/2)^6
=109.2838
2
Price=6/(1+14%/2)+6/(1+13.75%/2)^2+6/(1+13.5%/2)^3+6/(1+13.25%/2)^4+6/(1+13%/2)^5+106/(1+12.75%/2)^6
=97.97316
3
Price=6/(1+12%/2)+6/(1+12%/2)^2+6/(1+12%/2)^3+6/(1+12%/2)^4+6/(1+12%/2)^5+106/(1+12%/2)^6
=100
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