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 ​$80 in interest each year​ (at the end of the​ year), but it will never return the principal. The current discount rate for Canadian government bonds is 9.5 ​%. What should this consol bond sell for in the​ market? What if the interest rate should fall to 8.5 ​%? Rise to 10.5 ​%? Why does the price go up when interest rates​ fall? Why does the price go down when interest rates​ rise? If the current discount rate for Canadian government bonds is 9.5 ​%, what should this bond sell for in the​ market? ​$nothing    ​(Round to the nearest​ cent.)

Answer 1

Price of Bond = PV of Cfs from it.

Price of perpectuity Bond = Cash flow / Disc rate

Price of Bond If Int rate is 9.5%:

Price = $ 80 / 9.5%

= $ 842.11

Price of Bond If Int rate is 8.5%:

Price = $ 80 / 8.5%

= $ 941.18

Price of Bond If Int rate is 10.5%:

Price = $ 80 / 10.5%

= $ 761.90

There is inverse relateion between Disc rate & Bond Price.

As the Disc Rate is Increased, PVF will decrease, PV of CFs will decrease. Hence Price of Bond will decrease.

As the Disc Rate is decreased, PVF will increase, PV of CFs will increase. Hence Price of Bond will increase.