Question

1. An investor needs to choose between three bonds. The first bond will give the investor five equal payments of P1, paid monthly and beginning in one month. The second bond will give the investor three equal payments of P2, paid every second month and beginning now. The third bond is a coupon bond with face value F, coupon rate c per month, maturity in five months, and monthly payments beginning in one month. The return over a one month period is R and stays at this rate for the life of all three bonds.

(a) Write a formula in terms of P1 and R which gives the present value of the first bond (at time t = 0).

(b) Write a formula in terms of P2 and R which gives the present value of the second bond (at time t = 0).

(c) Write a formula in terms of F, c and R which gives the present value of the third bond (at time t = 0).

(d) Write a formula for the present value of the second bond which is valid for any time t between t = 0 and t = 4 months. Hint: write this formula in terms of three zero-coupon bonds P(t, Ti) with i = 1, 2, 3 and T1 = 0, T2 = 2 months and T3 = 4 months.

(e) For P1 = $82 , P2 = $100 , F = $200 , c = 8% per month , and R = 1.04 , which bond is the best choice for the investor? In other words, which bond has the larger present value (at time t = 0)?

Answer 1