Question

The Government of Canada 2-year coupon bond has a face value of $1,000 and pays annual coupons of $30. The next coupon is due in one year. Currently, the one and two-year spot rates on Government of Canada zero coupon bonds are 5% and 5.5%. Use this information to answer part a) and b).

a) What is the correct price for the coupon bond at time zero (immediately)?

A) $925.46

B) $952.41

C) *$953.98

D) $971.68

E) $1009.54

b) What is the expected price for the coupon bond at year one (after the first coupon is paid)?

A) $953.98

B) *$971.69

C) $976.30

D) $980.95

E) $1009.54

Looking for the process work to understand why the solution for part a) is $953.98 and for b) is $971.69.

Answer 1

a)

The price of bond at time zero can be calculated with the help of below expression:

Here,

y₁ is 1-year spot rate,

y₂ is 2-year spot rate.

Substitute 30 for coupon payment, 1,000 for face value, 0.05 for y₁ and 0.055 for y₂,

Thus, the correct option is 'c', that is, $953.98.

b)

To calculate the price of bond after 1 year, the face value and last coupon payment should be discounted back for 1 year.

These cash flows can be discounted back with the help of interest rate applicable on year 2.

Interest rate which work on only year 2 is calculated below:

Here,

f(1,1) is the forward applicable after year 1 for next year, that is, applicable from year 2.

The price of bond after 1 year is calculated below:

Thus, the correct option is 'b', that is $971.69.