Question

1.We have learned that bond prices move inversely to interest rates as shown in this graphic. Why is this true? Please explain your answer thoroughly.  

2. The Margaret Anne Dance Company issued a $1,000, 30-yr bond 4 years ago with a 4.0% coupon that pays semiannually. The bond is currently priced at $1,040.

What is the Yield to Maturity (YTM) of this bond?

3. If the Yield to Maturity (YTM) changes to 4.75%, what is the new price of the bond?

4. Two bonds have the identical coupon rates of 5.00%. One has a maturity of 2 years and the other has a maturity of 20 years. Which bond’s price is more sensitive to changes in market interest rates?

Answer 1

1.
Rising rates can lead to loss of principal, hurting the value of bonds. Price of a bond is nothing but the present value of cash flows from the bond. So, if rates or yields rise, present value decreases and hence the price decreases because present value is inversely proportional to rates.

Similarly, the case with falling rates.

2.
=RATE(26*2,4%*1000/2,-1040,1000)*2
=3.7576%

3.
=PV(4.75%/2,26*2,-4%*1000/2,-1000)
=888.6943379

4.
Higher maturity bond has higher duration and hence more sensitive because a large portion of the present value comes from cash flows further in time. These cash flows' present value decrease by a larger amount when rates increase. 20 year bond is more sensitive