Answer:
Laurel: price will decrease by 4.73% if the rates increases by 2%
and it will increase by 5.66% if the rates decreases by 2%
Hardy:
+22.28% if rate fall by 2%
-16.05% if rate decrease by 2%
Explanation:
To solve for percentage we use $1 as face value
We solve calculating the preent value of the coupon payment using the present value of an ordinary annuity formula
and add it with the present value of maturity which is calculate with the present value of lump sum
Laurel Inc:
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C 0.0350
time 6.0000
rate 0.0450
[tex]0.035 \times \frac{1-(1+0.045)^{-6} }{0.045} = PV\\[/tex]
PV 0.1805
[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]
Maturity 1.00
time 3.00
rate 0.09
[tex]\frac{1}{(1 + 0.09)^{3} } = PV[/tex]
PV 0.77
PV c $0.1805
PV m $0.7722
Total $0.9527
0.9527 - 1 = - 0.0473
a decrease of 4.73 if rate increase by 2%
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C 0.0350
time 6.0000
rate 0.0250
[tex]0.035 \times \frac{1-(1+0.025)^{-6} }{0.025} = PV\\[/tex]
PV 0.1928
[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]
Maturity 1.00
time 3.00
rate 0.05
[tex]\frac{1}{(1 + 0.05)^{3} } = PV[/tex]
PV 0.86
PV c $0.1928
PV m $0.8638
Total $1.0566
5.66% increase if rates fall 2%
For Hardy Corp we do the same procedure
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C 0.0350
time 32.0000
rate 0.0250
[tex]0.035 \times \frac{1-(1+0.025)^{-32} }{0.025} = PV\\[/tex]
PV 0.7647
[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]
Maturity 1.00
time 16.00
rate 0.05
[tex]\frac{1}{(1 + 0.05)^{16} } = PV[/tex]
PV 0.46
PV c $0.7647
PV m $0.4581
Total $1.2228
22.28% if rate fall by 2%
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C 0.0350
time 32.0000
rate 0.0450
[tex]0.035 \times \frac{1-(1+0.045)^{-32} }{0.045} = PV\\[/tex]
PV 0.5876
[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]
Maturity 1.00
time 16.00
rate 0.09
[tex]\frac{1}{(1 + 0.09)^{16} } = PV[/tex]
PV 0.25
PV c $0.5876
PV m $0.2519
Total $0.8395
0.8395 - 1 = 0.1605
