Suppose an investor, desiring to earn a higher interest than the average paid by bank on savings, purchases two bonds, say bond A and bond B, and intends to sell them immediately after getting the third coupon payment. The characteristics of the two bonds are as follows. Bond A has 20 years to maturity, carries an 8% coupon rate, and its purchase price is $1,105.9403. Bond B has 10 years to maturity, carries an 5% coupon rate, and its purchase price is $859.5285. For simplicity, assume that coupon payments are made annually and face value of both bonds is $1,000. Using this information, please answer the following questions. Carry out your computations and provide answers with precision to the forth decimal place.
(a) At the time of purchase, i.e., t0 = 0, what is the yield to maturity for bond A and bond B? Is it the same for both bonds? Should it be the same?
(b) At the time of purchase, what is the current yield for both bonds? Is it the same? Should it be the same?
(c) For what bond is the current yield a better approximation to the yield to maturity? Why?
(d) During the three years while the investor is holding the bonds, the interest rate in market has moved up to 10%. What is the fair value price for both bonds if the investor sells them soon after obtaining the third coupon payment?
(e) Assume the investor sells the bonds at the fair value prices you have found in (d). What are the net returns on each bond?
(f) Using the numbers for net returns, compute the rate of return on each bond. Annualize the rates of return.
(g) Carefully explain the difference or similarity in rates of returns on the two bonds.