Question

A 3-year bond carrying 3.4% annual coupon and $10,000-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: 2.2%; 1-year spot rate 1 year from now: 2.8%; 1-year spot rate 2 years from now: 4%. 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 = (3.4% / 1) * $10000

Coupon per period = $340

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 = $340 / (1 + 2.2%) + $340 / (1 + 2.2%) * (1 + 2.8%) + ($340 + $10000) / (1 + 2.2%) * (1 + 2.8%) * (1 + 4%)

Bond price = $10,119.61