Question

A bond with a face value of 1000 and a redemption value of 1010 has an annual coupon rate of 8.8% payable semiannually. The bond is bought to yield an annual nominal rate of 9.9% convertible semiannually. At this yield rate, the present value of the redemption value is 423 on the purchase date. P Calculate the purchase price of the bond.

Answer 1

The purchase price of the bond is $1059.71.

Step-by-step explanation:

To calculate the purchase price of the bond, we need to use the present value formula. The formula is:

PV = C/(1+r/n)^nt + F/(1+r/n)^nt

Where PV is the purchase price, C is the coupon payment, F is the redemption value, r is the yield rate, n is the number of coupon payments per year, and t is the number of years until redemption.

1. Substitute the given values into the formula: C = (0.088/2) * 1000 = 44, F = 1010, r = 0.099/2 = 0.0495, n = 2, and t = 1.
2. Calculate the present value of the coupon payments: PV_coupon = 44/(1+0.0495)^2 * 1 + 44/(1+0.0495)^1 * 0 = 87.47.
3. Calculate the present value of the redemption value: PV_redemption = 1010/(1+0.0495)^2 * 1 = 972.24.
4. Calculate the purchase price of the bond: PV = PV_coupon + PV_redemption = 87.47 + 972.24 = 1059.71.

Therefore, the purchase price of the bond is $1059.71.