Question

There are two companies named AA and BB. Company AA has a 5-year, 4% annual coupon bond with a $100 par value. BB has a 20-year, 3% annual coupon bond with a $100 par value. Both bonds currently have a yield to maturity of 2.5%.

Answer the following questions:

a. By how much do you think the price of each bond will change if interest rates suddenly fall by 2 percentage point (e.g from 3% to 1%)?

b. By how much do you think the price of each bond will change if interest rates suddenly increase by 3 percentage points?

c. Considering the price sensitivity of the five-year bond relative to the 20-year bond, what can you conclude?

Answer 1

(a) AA:

Price of bond is present value cashflow to be received from the bond i.e. coupon payment and par value.

n= 5 years, c=4%, FV=$100, i=2.5%, coupon payment (PMT) = 4 (100x4%)

Price of Bond, PV = $106.97

Now, if interest rate suddenly fall by 2%

n= 5 years, c=4%, FV=$100, i=0.5%, coupon payment (PMT) = 4 (100x4%)

Price of Bond, PV = $117.24

The change in bond price is $10.27 i.e. 9.6%

BB

n= 20 years, c=3%, FV=$100, i=2.5%, coupon payment (PMT) = 3 (100x3%)

PV = $107.79

Now, if interest rate suddenly fall by 2%

n= 20 years, c=3%, FV=$100, i=0.5%, coupon payment (PMT) = 3 (100x3%)

Price of Bond, PV = $147.47

The change in bond price is $39.68 i.e. 36.81%

(b) Now, if interest rate suddenly increases by 3%

AA

n= 5 years, c=4%, FV=$100, i=5.5%, coupon payment (PMT) = 4 (100x4%)

Price of Bond, PV = $93.59

The change in bond price is $-13.38 i.e. -12.5%

BB

n= 20 years, c=3%, FV=$100, i=5.5%, coupon payment (PMT) = 3 (100x3%)

Price of Bond, PV = $70.12

The change in bond price is $-37.67 i.e. 34.94%

(c) When the yield to maturity decreases by 2%, the change in the price of 5-year and 20-year bond is 9.6% and 36.81% respectively. When the yield to maturity increases by 3%, the change in the price of 5-year and 20-year bond is 12.5% and 34.94% respectively. The price of 20-year bond is more sensetive to changes in yield than the price of 5-year bond due to the impact of present value calculation. So it can be concluded that, the price of a bond with longer maturity is more sensetive to a change in yield than is the price of a bond with shorter maturity.