Problem 7-5 Bond valuation An investor has two bonds in his portfolio that both
ID: 2777337 • Letter: P
Question
Problem 7-5
Bond valuation
An investor has two bonds in his portfolio that both have a face value of $1,000 and pay a 8% annual coupon. Bond L matures in 11 years, while Bond S matures in 1 year.
Assume that only one more interest payment is to be made on Bond S at its maturity and that 11 more payments are to be made on Bond L.
What will the value of the Bond L be if the going interest rate is 5%? Round your answer to the nearest cent.
$
What will the value of the Bond S be if the going interest rate is 5%? Round your answer to the nearest cent.
$
What will the value of the Bond L be if the going interest rate is 10%? Round your answer to the nearest cent.
$
What will the value of the Bond S be if the going interest rate is 10%? Round your answer to the nearest cent.
$
What will the value of the Bond L be if the going interest rate is 14%? Round your answer to the nearest cent.
$
What will the value of the Bond S be if the going interest rate is 14%? Round your answer to the nearest cent.
$
a) Long-term bonds have lower reinvestment rate risk then do short-term bonds.
b) The change in price due to a change in the required rate of return increases as a bond's maturity decreases.
c) Long-term bonds have greater interest rate risk then do short-term bonds.
d) The change in price due to a change in the required rate of return decreases as a bond's maturity increases.
e) Long-term bonds have lower interest rate risk then do short-term bonds.
Problem 7-5
Bond valuation
An investor has two bonds in his portfolio that both have a face value of $1,000 and pay a 8% annual coupon. Bond L matures in 11 years, while Bond S matures in 1 year.
Assume that only one more interest payment is to be made on Bond S at its maturity and that 11 more payments are to be made on Bond L.
What will the value of the Bond L be if the going interest rate is 5%? Round your answer to the nearest cent.
$
What will the value of the Bond S be if the going interest rate is 5%? Round your answer to the nearest cent.
$
What will the value of the Bond L be if the going interest rate is 10%? Round your answer to the nearest cent.
$
What will the value of the Bond S be if the going interest rate is 10%? Round your answer to the nearest cent.
$
What will the value of the Bond L be if the going interest rate is 14%? Round your answer to the nearest cent.
$
What will the value of the Bond S be if the going interest rate is 14%? Round your answer to the nearest cent.
$
a) Long-term bonds have lower reinvestment rate risk then do short-term bonds.
b) The change in price due to a change in the required rate of return increases as a bond's maturity decreases.
c) Long-term bonds have greater interest rate risk then do short-term bonds.
d) The change in price due to a change in the required rate of return decreases as a bond's maturity increases.
e) Long-term bonds have lower interest rate risk then do short-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 = 80 * [1-(1+5%)^-11]/5% + 1000/(1+5%)^11
= 1249.19
price of bond S = 80 * [1-(1+5%)^-1]/5% + 1000/(1+5%)^1
= 1028.57
b)
price of bond L = 80 * [1-(1+10%)^-11]/10% + 1000/(1+10%)^11
= 870.10
price of bond S = 80 * [1-(1+10%)^-1]/10% + 1000/(1+10%)^1
= 981.82
c)
price of bond L = 80 * [1-(1+14%)^-11]/14% + 1000/(1+14%)^11
= 672.84
price of bond S = 80 * [1-(1+14%)^-1]/14% + 1000/(1+14%)^1
= 947.37
d)
long term bonds have more interets rate risk than short term bond