Question

he Faulk Corp. has a bond with a coupon rate of 4 percent outstanding. The Yoo Company has a bond with a coupon rate of 10 percent outstanding. Both bonds have 17 years to maturity, make semiannual payments, and have a YTM of 7 percent. If interest rates suddenly rise by 2 percent, what is the percentage change in the price of these bonds

Answer 1

Answer:

Faulk: -0,1925629 = -19.25%

Yoo: 0,1615398 = 16.15%

Explanation:

We need to solve forthe present value of the coupon and maturity on each bond considering the yield to maturity of 7% and 9% and compare the price variations:

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 20.000

time 34

rate 0.035

$20 \times \frac{1-(1+0.035)^{-34} }{0.035} = PV$

PV $394.0137

$\frac{Maturity}{(1 + rate)^{time} } = PV$  

Maturity   1,000.00

time   34.00

rate  0.035

$\frac{1000}{(1 + 0.035)^{34} } = PV$  

PV   310.48

PV c $394.0137

PV m  $310.4761

Total $704.4897

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 20.000

time 34

rate 0.045

$20 \times \frac{1-(1+0.045)^{-34} }{0.045} = PV$

PV $344.9352

$\frac{Maturity}{(1 + rate)^{time} } = PV$  

Maturity   1,000.00

time   34.00

rate  0.045

$\frac{1000}{(1 + 0.045)^{34} } = PV$  

PV   223.90

PV c $344.9352

PV m  $223.8959

Total $568.8311

Price variation on Faulk

($568.8311  - $704.4897) / $704.4897  = -0,1925629

Yoo Company:

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 50.000

time 34

rate 0.035

$50 \times \frac{1-(1+0.035)^{-34} }{0.035} = PV$

PV $985.0342

$\frac{Maturity}{(1 + rate)^{time} } = PV$  

Maturity   1,000.00

time   34.00

rate  0.035

$\frac{1000}{(1 + 0.035)^{34} } = PV$  

PV   310.48

PV c $985.0342

PV m  $310.4761

Total $1,295.5103

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 50.000

time 34

rate 0.045

$50 \times \frac{1-(1+0.045)^{-34} }{0.045} = PV$

PV $862.3379

$\frac{Maturity}{(1 + rate)^{time} } = PV$  

Maturity   1,000.00

time   34.00

rate  0.045

$\frac{1000}{(1 + 0.045)^{34} } = PV$  

PV   223.90

PV c $862.3379

PV m  $223.8959

Total $1,086.2338

($1,295.5103  - $1,086.2338 ) / $1,295.5103 = 0,1615398