Question

A 5 year, $1000 par value bond with an annual coupon rate of 2% was issued for par. At the same time, a 30 year, $1000 par value bond with an annual coupon rate of 2% was issued for par. Which company had the lower credit rating, the one that issued the 5 year bond or the one that issued the 30 year bond? Explain. 5 points   A year later, interest rates had risen by 2% for each bond. What were the new prices for each of the bonds? 10 points   What was the percent change in the price of each of the bonds over the one year period? 10 points Which bond was more affected by the change in the interest rate? Explain

BAII PLUS

Answer 1

1.
5 year bond had lower credit rating because generally short term rates are lower than long term rates so 5 year bond should have had a lower rate than 30 year bond but we see this is not the case. This can then be explaned by higher default risk or lower credit rating of 5 year bond.

2.
New price for 5 year bond=1000*2%/4%*(1-1/1.04^4)+1000/1.04^4=927.40

New price for 30 year bond=1000*2%/4%*(1-1/1.04^29)+1000/1.04^29=660.33

3.
Percentage change for 5 year bond=927.40/1000-1=-7.260%

Percentage change for 30 year bond=660.33/1000-1=-33.967%

4.
30 year bond was more affected as we know long term bonds have higher interest rate risk than short term bonds