Question

Bond A is a 6 % coupon bond and makes annual payments with 10 years to maturity. Bond B is a 6% coupon bond and makes annual payments with 20 years to maturity. Both bonds have a market required return of 10% and face value of 1,000.

b) What will happen to the prices of both bonds if the interest rate increases by 2%? Explain

Answer 1

Bond price = Present value (PV) of annual coupon payments + PV of redemption amount (Face value).

Annual coupon for each bond = Face value x Coupon rate = $1,000 x 6% = $60

When interest rate = 10%,

Price, Bond A ($) = 60 x P/A(10%, 10) + 1,000 x P/F(10%, 10) = 60 x 6.1446** + 1,000 x 0.3855**

= 368.68 + 385.5

= 754.18

Price, Bond B ($) = 60 x P/A(10%, 20) + 1,000 x P/F(10%, 20) = 60 x 8.5136** + 1,000 x 0.1486**

= 510.82 + 148.6

= 659.42

When interest rate increases by 2%, new interest rate = 12%,

Price, Bond A ($) = 60 x P/A(12%, 10) + 1,000 x P/F(12%, 10) = 60 x 5.6502** + 1,000 x 0.3220**

= 339.01 + 322

= 661.01

Price, Bond B ($) = 60 x P/A(12%, 20) + 1,000 x P/F(12%, 20) = 60 x 7.4694** + 1,000 x 0.1037**

= 448.16 + 103.7

= 551.86

Therefore, when interest rate increases by 2%, prices of both bonds decrease. The reason is that with increase in interest rate, the discount factors decrease, reducing the present value of coupon payments and present value of face value.