Question

Perpetuities.  The Canadian Government has once again decided to issue a consol​ (a bond with a​ never-ending interest payment and no maturity​ date). The bond will pay ​$100 in interest each year​ (at the end of the​ year), but it will never return the principal. The current discount rate for Canadian government bonds is 4.5​%. What should this consol bond sell for in the​ market? What if the interest rate should fall to 3.5​%? Rise to 5.5​%? Why does the price go up when interest rates​ fall? Why does the price go down when interest rates​ rise? If the current discount rate for Canadian government bonds is 4.5​%, what should this bond sell for in the​ market? ​$nothing  ​(Round to the nearest​ cent.)

Answer 1

Value of Bond = PV of Cfs from it.

Value of perpectual Bind = Coupon Amount / Disc rate

IF disc rate is 4.5%:

= $ 100 / 4.5%

= $ 2222.22

IF disc rate is 3.5%:

= $ 100 / 3.5%

= $ 2857.14

IF disc rate is 5.5%:

= $ 100 / 5.5%

= $ 1818.18

There is inverse relation between Disc rate and Price of Bond.

Value of Bond is PV of CFs flow from it,

As dicount rate is increased, PV will decrease and Vice versa. Hence If Disc Rate is Increased, price will decrease and Vice versa.