Question

Show all your work (use of formula, etc.) in solving the problems. You still need to show your work even if you use the financial calculator to get the answers. Please do not use excel. Thank you!

4. Bond Q is a 4 percent coupon bond. Bond R is an 6 percent coupon bond. Both bonds have 15 years to maturity, make annual coupon payments, and have a YTM of 6 percent. If interest rate (YTM) changes from 6 percent to 8 percent, what is the percentage price change of these bonds? What if the YTM suddenly falls from 6 percent to 4 percent instead? What does this problem tell you about the interest rate risk of lower-coupon bonds?

Answer 1

Here is the data for both the bonds:

	Bond Q	Bond R
YTM	6%	6%
Coupon	4%	6%
Par value	100	100
Coupon frequency	Annual	Annual
Annual interest	4	6

Now, the formula for calculating price. price is nothing but the present value of all the future cash flows of the bond

Price = Coupon payment * (1- (1+YTM)^-n)/YTM + Par value * (1+YTM)^-n

So for Bond Q:

P(Q) = 4* (1-(1+6%)^-15)/6% + 100*(1+6%)^-15 = 80.6

P(R) = 6* (1-(1+6%)^-15)/6% + 100*(1+6%)^-15 = 100. Note that when coupon = YTM, than bond is trading at par.

a) if interest rate changes to 8% from 6% = the price should decline as price and yields are inversely related.

P(Q) = 4* (1-(1+8%)^-15)/8% + 100*(1+8%)^-15 = 66

P(R) = 6* (1-(1+8%)^-15)/8% + 100*(1+8%)^-15 =83

b) if interest rate changes to 4% from 6% = the price should increase as price and yields are inversely related

P(Q) = 4* (1-(1+4%)^-15)/4% + 100*(1+4%)^-15 = 100. At par value as coupon is same as YTM

P(R) = 6* (1-(1+4%)^-15)/4% + 100*(1+4%)^-15 =122

Bonds offering lower coupon rates generally will have higher interest rate risk than similar bonds that offer higher coupon rates, as can be seen above