Bond Valuation and Interest Rate Risk: The Garraty Company has two bond issues o
ID: 2734932 • Letter: B
Question
Bond Valuation and Interest Rate Risk:
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.
1.) What will be the value of each of these bonds when the going rate of interest is 4%? Assume that there is only one more interest payment to be made on Bond S. Round your answers to the nearest cent.
Bond L $
Bond S $
2.) What will be the value of each of these bonds when the going rate of interest is 7%? Assume that there is only one more interest payment to be made on Bond S. Round your answers to the nearest cent.
Bond L $
Bond S $
3.) What will be the value of each of these bonds when the going rate of interest is 15%? Assume that there is only one more interest payment to be made on Bond S. Round your answers to the nearest cent.
Bond L $
Bond S $
Explanation / Answer
Bond Price = C x [1-{1/(1+r)n}]/r +M/(1+r)n
Coupon Amount =$100
M= Face Value =$1,000
1)
Bond L:
No of years= 15 years
r=rate of interest = 4% or 0.04
Bond L= 100 x [1-{1/(1+0.04)15}]/0.04+ 1,000/(1+0.04)15
= 100 x [1-{1/(1.04)15}]/0.04 + 1,000/(1.04)15
= 100 x [1-{1/1.800944 }/0.04 + 1,000/1.800944
= 100 x [1-{0.555265}/0.04 + 555.2645
= 100 x 0.444735/0.04 + 555.2645
= 100 x 11.11839 + 555.2645
= 1111.839+555.2645
=$1,667.10
Bond S:
No of years= 1 years
r=rate of interest = 4% or 0.04
Bond L= 100 x [1-{1/(1+0.04)1}]/0.04+ 1,000/(1+0.04)1
= 100 x [ 1-{1/1.04}/0.04 + 1,000/1.04
= 100 x1(-0.961538462)/0.04 + 961.5385
= 100 x 0.038461538/0.04 + 961.5385
= 100 x 0.961538462 + 961.5385
= 96.1538462 + 961.5385
=$ 1057.69
2)
Bond L:
No of years= 15 years
r=rate of interest = 7% or 0.07
Bond L = 100 x [1-{1/(1+0.07)15}]/0.07+ 1,000/(1+0.07)15
= 100 x [1-{1/(1.07)15}/0.07 + 1,000/(1.07)15
= 100 x [ 1-{1/(2.759031541)}/0.07 + 1,000/2.759031541
= 100 x (1-0.36244602)/0.07 + 362.4460196
= 100 x 0.63755398/0.07 + 362.4460196
= 100 x 9.107914005 + 362.4460196
= 910.7914005+ 362.4460196
=$1,273.23
Bond S:
No of years= 1 years
r=rate of interest = 7% or 0.07
Bond L= 100 x [1-{1/(1+0.07)1}]/0.07+ 1,000/(1+0.07)1
= 100 x [1-{1/1.07}]/0.07 + 1,000/1.07
= 100 x (1-0.934579439)/0.07 + 934.5794
= 100 x 0.065420561/0.07 + 934.5794
= 100 x 0.934579439 + 934.5494
= 93.4579439 + 934.5494
= $ 1028.03
3)
Bond L:
No of years= 15 years
r=rate of interest = 15% or 0.15
Bond L= 100 x [1-{1/(1+0.15)15}]/0.15+ 1,000/(1+0.15)15
= 100 x [1-{ 1/(1.15)15}] /0.15 + 1,000/(1.05)15
= 100 x [1-{1/8.137062}]/0.15 + 1,000 /8.137062
= 100 x [(1-0.122894)/0.15] + 122.8944852
= 100 x (0.877106)/0.15 + 122.8944852
= 100 x 5.84737 + 122.8944852
= 584.737 + 122.8944852
= $ 707.63
Bond S:
No of years= 1 years
r=rate of interest = 15% or 0.15
Bond L= 100 x [1-{1/(1+0.15)1}]/0.15+ 1,000/(1+0.15)1
= 100 x [1-{1/(1.15)}]/0.15 + 1,000/1.15
= 100 x [1-0.869565] /0.15 + 869.5652174
= 100 x 0.130435/0.15 + 869.5652174
= 100 x 0.869565 + 869.5652174
= 86.9565 + 869.5652174
= $ 956.52