Question

A 3-year bond carrying 2.2% annual coupon and $100-par is putable at par 1 year and 2 years from today. Calculate the value of the putable bond under the forward rate curve below.

1-year spot rate: 2.1%;

1-year spot rate 1 year from now: 3.3%;

1-year spot rate 2 years from now: 4.2%.

Assume annual compounding. Round your answer to 2 decimal places (nearest cent).

Answer 1

No of periods = 3 years

Coupon per period = (Coupon rate / No of coupon payments per year) * Par value

Coupon per period = (2.2% / 1) * $100

Coupon per period = $2.2

Bond price = Coupon / (1 + 1 year spot rate) + Coupon / (1 + 1 year spot rate) * (1 + 1 year spot rate 1 year form now) +  (Coupon + Face value) / (1 + 1 year spot rate) * (1 + 1 year spot rate 1 year form now) * (1 + 1 year spot rate 2 year form now)

Bond price = $2.2 / (1 + 2.1%) + $2.2 / (1 + 2.1%) * (1 + 3.3%) + ($2.2 + $100) / (1 + 2.1%) * (1 + 3.3%) * (1 + 4.2%)

Bond price = $97.2351 or $97.24