Question

Red Mountain, Inc. bonds have a face value of $1,000. The bonds carry a 7 percent coupon, pay interest semiannual, and mature in 13.5 years. What is the current price of these bonds if the yield to maturity is 6.82 percent? A. $989.50 B. $994.56 C. $1, 015.72 D. $1.018.27E. $1, 020.00

Answer 1

Answer:

R = 7% x $1,000 = $70

Po= R/2(1-(1+Kd/m)-nm/Kd/m + FV/(1+Kd/m)nm

Po = 70/2(1-(1+0.0682/2)-13.5x2/0.0682/2 + 1,000/(1+0.0682/2)13.5x2

Po = 35(1-(1+0.0341)-27/0.0341 + 1000/(1+0.0341)27

Po = 35(17.4663) + 1,000/2.4728

Po = $611.3205 + $404.40

Po = $1,015.72

The correct answer is C

Explanation:

The current price of a bond is equal to present value of coupon plus the present value of face value of the bond. The bond pays semi-annual interest, thus, we will divide the coupon by 2 and then determine the present value. The bond yield will also be divided by 2.

Po = Current price of the bond, R = Coupon, Kd = Bond yield, FV = Face value, n = Bond maturity and m = No of times coupon is paid in a year