Bond valuation An investor has two bonds in his portfolio that both have a face
ID: 2613085 • Letter: B
Question
Bond valuation
An investor has two bonds in his portfolio that both have a face value of $1,000 and pay a 10% annual coupon. Bond L matures in 13 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 13 more payments are to be made on Bond L.
What will the value of the Bond L be if the going interest rate is 4%? Round your answer to the nearest cent.
$
What will the value of the Bond S be if the going interest rate is 4%? Round your answer to the nearest cent.
$
What will the value of the Bond L be if the going interest rate is 8%? Round your answer to the nearest cent.
$
What will the value of the Bond S be if the going interest rate is 8%? Round your answer to the nearest cent.
$
What will the value of the Bond L be if the going interest rate is 11%? Round your answer to the nearest cent.
$
What will the value of the Bond S be if the going interest rate is 11%? Round your answer to the nearest cent.
$
Why does the longer-term bond’s price vary more than the price of the shorter-term bond when interest rates change?
Explanation / Answer
Answer:Value of a bond = PV of Coupon payments + PV of maturity amount
PV of coupon payments
= Coupon * {(1+market interest rate)no periods *-1}/{(1+market interest rate)no periods * Market Interest rate}
PV of maturity amount = Maturity amount/(1+Interest rate)no of periods
Coupon payment is = $1000*10% = $100
1) Value of bond L @interest rate of 4% = $100 * [{(1+0.04)13 - 1}/(1+0.04)13 *0.04] + $1000/(1+0.04)13
= $998.56+600.57 = $1589.13
2. Value of bond S @interest rate of 4% = PV of (Maturity+Coupon) to be received at end of year 1
= $1,100/(1+.04)1 = $1,057.69
3.
Value of bond L @interest rate of 8% = $100 * [{(1+0.08)13 - 1}/(1+0.08)13 *0.08] + $1000/(1+0.08)13
= $790.38+$367.70 = $1,158.08
4. Value of bond S @interest rate of 8% = PV of (Maturity+Coupon) to be received at end of year 1
= $1,100/(1+.08)1 = $1,018.52
5.
Value of bond L @interest rate of 11% = $100 * [{(1+0.11)13 - 1}/(1+0.11)13 *0.11] + $1000/(1+0.11)13
= $674.99+$257.51 = $932.50
6. Value of bond S @interest rate of 11% = PV of (Maturity+Coupon) to be received at end of year 1
= $1,100/(1+.11)1 = $991
7. It is because the effect of interest rate risk on a bond,i.e. the inverse relationship in bonds price with change in interest rate.
Also the effet is more with long term bond because there is a greater probability that interest rates will rise within a longer time period than within a shorter period. So the greater variation is for this expectation and inverse relationship between the interest rate and value.