An investor has two bonds in his portfolio that both have a face value of $1,000

Question

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 17 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 17 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 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.
$  

Why does the longer-term bond’s price vary more than the price of the shorter-term bond when interest rates change?

The change in price due to a change in the required rate of return decreases as a bond's maturity increases.

Long-term bonds have lower interest rate risk then do short-term bonds.

Long-term bonds have lower reinvestment rate risk then do short-term bonds.

The change in price due to a change in the required rate of return increases as a bond's maturity decreases.

Long-term bonds have greater interest rate risk then do short-term bonds.

Explanation / Answer

1)

2)

3)

4)

5)

6)

7) C is the correct answer as with increase in bond maturity the duration increase and duration is a measure of price sensitivity of bond to change in interest rates.

(1+ YTM)^n YTM Period Coupon payment Discounting factor Face value Cash flow for the period Discounted cash flow 4 1 100 1.04 100 96.15384615 2 100 1.0816 100 92.4556213 3 100 1.124864 100 88.89963587 4 100 1.16985856 100 85.4804191 5 100 1.216652902 100 82.19271068 6 100 1.265319018 100 79.03145257 7 100 1.315931779 100 75.99178132 8 100 1.36856905 100 73.0690205 9 100 1.423311812 100 70.25867356 10 100 1.480244285 100 67.55641688 Value of the bond = 811.0896 11 100 1.539454056 100 64.95809316 12 100 1.601032219 100 62.45970496 13 100 1.665073507 100 60.05740861 14 100 1.731676448 100 57.74750828 15 100 1.800943506 100 55.52645027 16 100 1.872981246 100 53.39081757 17 100 1.947900496 1000 1100 564.7105704 Price= sum of discounted cash flows= 1729.940131

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