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: 1.6%;

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

Annual Coupon on Bond = Coupon Rate * Par Value = 3.5% * 100 = $3.5

Put Price = Par Value = $100

Present Value at end of Year 2 = Par Value + Coupon in 3 rd Year / (1+Spot Rate 2 years from now)

Present Value at end of Year 2 = (100 + 3.5) / (1+4.3%)

Present Value at end of Year 2 = 103.5/ 1.043

Present Value at end of Year 2 = 99.233

Since the present value at Year 2 is less than put price of 100, the bond is put and sold back at 100 hence present value at Year 2 = 100

Present Value at end of Year 1 = Value at end of year 2 + Coupon in 2 nd Year / (1+Spot Rate 1 year from now)

Present Value at end of Year 1 = (100 + 3.5) / (1+2.8%)

Present Value at end of Year 1 = 103.5 / 1.028

Present Value at end of Year 1 = 100.681

Since the present value at Year 1 is more than put price of 100, the put option will not be exercised.

Present Value today = Value at end of year 1 + Coupon in 1st Year / (1+Spot Rate)

Present Value = (100.681 + 3.5) / (1+1.6%)

Present Value = 104.181 / 1.016

Present Value = 102.54

The value of the puttable bond is 102.54