Question

**Seen a few wrong answers for this question. Please answer if you're 100% sure**

Consider two bonds, each with an interest rate (i) of 5% annum, coupon payments (C) of $20 annum, and face values (F) of $1000. The first bond matures in 20 years and the second bond matures in 10 years.

(a) Find the prices of the two bonds. Next price a console with the same interest rate and coupon payment. Report F × i.
(b) Repeat part (a) when the coupon payment is $100.
(c) Repeat part (a) once again with a coupon payment of $50.

(d) What does this tell you about the price of a console relative to long-run bonds?

Answer 1

a) Price of bond 1 with i=5%, C= $20, F=$1000, n=20 years is:

Price of bond 2 with i=5%, C= $20, F=$1000, n=20 years is:

Price of a console : Coupon payment / interest rate

Price of a console : 20 / 0.05 = $400

b) Price of bond 1 with i=5%, C= $100, F=$1000, n=20 years is:

Price of bond 2 with i=5%, C= $100, F=$1000, n=10 years is:

Price of a console : Coupon payment / interest rate

Price of a console : 100 / 0.05 = $2000

c) Price of bond 1 with i=5%, C= $50, F=$1000, n=20 years is:

Price of bond 2 with i=5%, C= $50, F=$1000, n=10 years is:

Price of a console : Coupon payment / interest rate

Price of a console : 50 / 0.05 = $1000

d) Console bonds do not have a maturity and are life long, where as long term maturity bonds have a fixed maturity and redeemed at the time they are matured. This is why, consoles are priced higher than the long term bonds. Console bonds are also called perpetuity bonds which lasts for an infinite period.