Question

What is the price of a bond that has the following conditions:

At the end of the 4th year there is a coin flip, Heads the bond matures in the 5th year, Tails it matures in the 10th year.

Assume a flat Treasury yield curve at 3%. The required return on this bond is at a 125 basis points premium.

Interest payments: No payments in year 1 and 2

Years 3, 5, 7, 9, 11, 13, 15, 17, 19 = 4%

Years 4, 6, 8, 10, 12, 14, 16, 18, 20 = 3%

Assume annual payments and $1000 par

Answer 1

The has 50% probability to have a maturity of 5 years and 50% probability that its maturity will be 10 years.

Required rate of return of the bond is 3% + 1.25% = 4.25%.

Bond value if maturity is 5 years:

PV = 0 + 0 + 35.30 + 25.40 + 844.60 = $905.30

Bond value if maturity is 10 years:

PV = 0 + 0 + 35.30 + 25.40 + 32.48 + 23.37 + 29.89 + 21.50 + 27.50 + 679.32 = $874.76

The bond value today will be average of both as both have equal (50%) probability.

Hence, Bond Value = ($905.30 + $874.76) / 2 = $890