3. Bond valuation An investor has two bonds in his portfolio that both have a fa
ID: 2741344 • Letter: 3
Question
3.
Bond valuation
An investor has two bonds in his portfolio that both have a face value of $1,000 and pay a 7% annual coupon. Bond L matures in 20 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 20 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 9%? Round your answer to the nearest cent.
$
What will the value of the Bond S be if the going interest rate is 9%? Round your answer to the nearest cent.
$
What will the value of the Bond L be if the going interest rate is 12%? Round your answer to the nearest cent.
$
What will the value of the Bond S be if the going interest rate is 12%? Round your answer to the nearest cent.
$
Explanation / Answer
Value of the bond= Present value of its future coupon payments at the going interest rate+ PV of its face value to be received at its maturity ie. Using the PV of annuity formula & PV of single sum to be received at a future date, Value of the bond=( Coupon payment*((1-(1+r)^-n)/r)+(FV/(1+r)^n) Where, Coupon payment = the annual coupon $ amount= 1000*7%=70 r= Going interest rate n= No.of periods remaining to maturity FV= Face Value= 1000 Using the above, we find the values at different situations as follows: Value of the Bond L be if the going interest rate is 5% Coupon payment = the annual coupon $ amount= 1000*7%=70 r= Going interest rate=5% n= No.of periods remaining to maturity=20 FV= Face Value= 1000 Substituting in the above formula, we get Value of the bond=(70*((1-(1+0.05)^-20)/0.05)+(1000/(1+0.05)^20) 1249.24 Value of the Bond S be if the going interest rate is 5% Coupon payment = the annual coupon $ amount= 1000*7%=70 r= Going interest rate=5% n= No.of periods remaining to maturity=1 FV= Face Value= 1000 Substituting in the above formula, we get Value of the bond=(70*((1-(1+0.05)^-1)/0.05)+(1000/(1+0.05)^1) 1019.05 Value of the Bond L be if the going interest rate is 9% Coupon payment = the annual coupon $ amount= 1000*7%=70 r= Going interest rate=9% n= No.of periods remaining to maturity=20 FV= Face Value= 1000 Substituting in the above formula, we get Value of the bond=(70*(1-(1+0.09)^-20)/0.09)+(1000/(1+0.09)^20) 817.43 Value of the Bond S be if the going interest rate is 9% Coupon payment = the annual coupon $ amount= 1000*7%=70 r= Going interest rate=9% n= No.of periods remaining to maturity=1 FV= Face Value= 1000 Substituting in the above formula, we get Value of the bond=(70*(1-(1+0.09)^-1)/0.09)+(1000/(1+0.09)^1) 981.65 Value of the Bond L be if the going interest rate is 12 % Coupon payment = the annual coupon $ amount= 1000*7%=70 r= Going interest rate=12 % n= No.of periods remaining to maturity=20 FV= Face Value= 1000 Substituting in the above formula, we get Value of the bond=(70*(1-(1+0.12)^-20)/0.12)+(1000/(1+0.12)^20) 626.53 Value of the Bond S be if the going interest rate is 12 % Coupon payment = the annual coupon $ amount= 1000*7%=70 r= Going interest rate=12 % n= No.of periods remaining to maturity=1 FV= Face Value= 1000 Substituting in the above formula, we get Value of the bond=(70*(1-(1+0.12)^-1)/0.12)+(1000/(1+0.12)^1) 955.36
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