Question

The Garraty Company has two bond issues outstanding. Both bonds pay $100 annual interest plus $1,000 at maturity. Bond L has a maturity of 15 years, and Bond S has a maturity of 1 year. What will be the value of each of these bonds when the going rate of interest is: (1) 5%, (2) 8%, and (3) 12%?

Answer 1

Answer:

bond which matures in one year:

At 5 %     $  1,047.62

At 8% $   1,018.52

At 12% $     982.14

bonds which matures in 15-years:

At 5 %     $1,518.9829

At 8% $1,171.1896

At 12% $863.7827

Explanation:

The bonds value will be the discounted value of the coupon payment and the maturity at the given rates:

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

C 100.000

time 1

rate 0.05

$100 \times \frac{1-(1+0.05)^{-1} }{0.05} = PV$

PV $95.2381

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

Maturity   1,000.00

time   1.00

rate  0.05

$\frac{1000}{(1 + 0.05)^{1} } = PV$  

PV   952.38

PV c $95.2381

PV m  $952.3810

Total $1,047.6190

at 8%

$100 \times \frac{1-(1+0.08)^{-1} }{0.08} = PV$

PV $92.5926

$\frac{1000}{(1 + 0.08)^{1} } = PV$  

PV   925.93

Total $1,018.5185

at 12%

$100 \times \frac{1-(1+0.12)^{-1} }{0.12} = PV$

PV $89.2857

$\frac{1000}{(1 + 0.12)^{1} } = PV$  

PV   892.86

Total $982.1429

if the bon matures in 15 years_

at 5%

$100 \times \frac{1-(1+0.05)^{-15} }{0.05} = PV$

PV $1,037.9658

$\frac{1000}{(1 + 0.05)^{15} } = PV$  

PV   481.02

Total $1,518.9829

at 8%

$100 \times \frac{1-(1+0.08)^{-15} }{0.08} = PV$

PV $855.9479

$\frac{1000}{(1 + 0.08)^{15} } = PV$  

PV   315.24

Total $1,171.1896

at 12%

$100 \times \frac{1-(1+0.12)^{-15} }{0.12} = PV$

PV $681.0864

$\frac{1000}{(1 + 0.12)^{15} } = PV$  

PV   182.70

Total $863.7827