Question

The Canadian government decided to issue a consol (a bond with a never-ending interest payment and no maturity date). The bond will pay $50 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 6.5%.
1. What should this consol bond sell for in the market?
2. What if the interest rate should fall to 4.5%? Rise to 8.5%?
3. Why does the price go up when interest rates fall?
4. Why does the price go down when interest rates rise?

Answer 1

Answer:

present value of perpetuity  = $1111.11

present value of perpetuity  = $588.23

if interest rate fall price go up and interest rate rise price go down

Explanation:

given data

bond pay = $50

solution

first we find present value of perpetuity for 6.5 % that is

present value of perpetuity = $\frac{cash flow}{discount}$     ..............1

present value of perpetuity =  $\frac{50}{0.065}$

present value of perpetuity  = $769.23

now  present value of perpetuity for 4.5%

so from equation 1 we get

present value of perpetuity =  $\frac{50}{0.045}$

present value of perpetuity  = $1111.11

and

now  present value of perpetuity for 8.5%

so from equation 1 we get

present value of perpetuity =  $\frac{50}{0.085}$

present value of perpetuity  = $588.23

so

here we know that current price of perpetuity & discount rate is inversely proportional

so current present value is find by divide cash flow by discount rate

here discount rate higher value of perpetuity

so if interest rate fall price go up and interest rate rise price go down