Question

A 3-year bond carrying 3.1% annual coupon and $8,000-par is putable at par 1 year and 2 years from today. Calculate the value of the underlying straight bond under the forward rate curve below. 1-year spot rate: 1.7%; 1-year spot rate 1 year from now: 2.8%; 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 = (3.1% / 1) * $8000

Coupon per period = $248

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 = $248 / (1 + 1.7%) + $248 / (1 + 1.7%) * (1 + 2.8%) + ($248 + $8000) / (1 + 1.7%) * (1 + 2.8%) * (1 + 4.3%)

Bond price = $8045.0453 or $8045.05