Check My WorkCheck My Work Problem 5-9 Bond Valuation and Interest Rate Risk The
ID: 2776985 • Letter: C
Question
Check My WorkCheck My Work
Problem 5-9
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.
Why does the longer-term (15-year) bond fluctuate more when interest rates change than does the shorter-term bond (1 year)?
-Select-IIIIIIItem 7
I. Longer-term bonds have more reinvestment rate risk than shorter-term bonds.
II. Shorter-term bonds have more interest rate risk than longer-term bonds.
III. Longer-term bonds have more interest rate risk than shorter-term bonds.
Problem 5-9
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.
What will be the value of each of these bonds when the going rate of interest is 5%? 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 $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 $
What will be the value of each of these bonds when the going rate of interest is 11%? 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 $
Why does the longer-term (15-year) bond fluctuate more when interest rates change than does the shorter-term bond (1 year)?
-Select-IIIIIIItem 7
I. Longer-term bonds have more reinvestment rate risk than shorter-term bonds.
II. Shorter-term bonds have more interest rate risk than longer-term bonds.
III. Longer-term bonds have more interest rate risk than shorter-term bonds.
Explanation / Answer
price = C * [1-(1+i)^-n]/i + 1000/(1+i)^n
where
C = coupon amount per period
i= interest rate per period
n=number of periods
a)
price of bond L = 100 * [1-(1+5%)^-15]/5% + 1000/(1+5%)^15
= 1518.98
price of bond S = 100 * [1-(1+5%)^-1]/5% + 1000/(1+5%)^1
= 1047.62
b)
price of bond L = 100 * [1-(1+7%)^-15]/7% + 1000/(1+7%)^15
= 1273.24
price of bond S = 100 * [1-(1+7%)^-1]/7% + 1000/(1+7%)^1
= 1028.04
c)
price of bond L = 100 * [1-(1+11%)^-15]/11% + 1000/(1+1%)^15
= 928.09
price of bond S = 100 * [1-(1+11%)^-1]/11% + 1000/(1+11%)^1
= 990.99
d)
long term bonds have more interets rate risk than short term bonds