Question

matt purchased a 20 year par value bond with 8 semiannual coupon at a price of 1772.25. The bond can be called at par value X on any coupon date startinga t the end of year 15. The price guarantees that Matt will receive a nominal semiannual yield of at least 6%. Bert purchases a 20-year par value bond identical to the one purchased by Matt, eexcept that it is not callable. Assume a nominal semiannual yield of 6%, the cost of the bond puirchased by Bert is P. Calculate P.

Answer 1

The cost of the bond purchased = $ 1,440

Step-by-step explanation:

Since the coupon rate of 8% is greater than the yield to maturity (YTM) of 6% annually, the bond is selling at a premium. Hence, the bond will be called at the earliest i.e. 15 years.

Coupon = Call Price * Semi-annual coupon rate = X * [0.08 / 2] = X * 0.04

Yield to call = 6% annually = 3% (half a year).

Time = 15 years * 2 = 30

Current Price of bond = Coupon * [1 - (1 + YTC)-call date] / YTC + Call Price / (1 + YTC) call date

1,722.25 = [X * 0.04] * [1 - (1 + 0.03)-30] / 0.03 + [X / (1 + 0.03)30]

1,722.25 = [X * 0.04] * 19.60 + [X * 0.41]

1,722.25 = X * [(0.04 * 19.60) + 0.41]

1,722.25 = X * 1.194

X = 1,722.25 / 1.194

X = $ 1,442.42

X = $ 1,440

Thus, the cost of the bond purchased = $ 1,440