Question

A 3-year bond carrying 3.5% 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: 2.6%;

1-year spot rate 2 years from now: 4.3%.

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 = (3.5% / 1) * $100

Coupon per period = $3.5

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 = $3.5 / (1 + 2.1%) + $3.5 / (1 + 2.1%) * (1 + 2.6%) + ($3.5 + $100) / (1 + 2.1%) * (1 + 2.6%) * (1 + 4.3%)

Bond price = $101.4982 or $101.50