Answer:
Coupon (R) = 6.8% x 10,000 = $680
Face value (FV) = $10,000
Number of times coupon is paid in a year (m) = 2
No of years to maturity = 8 years
Yield to maturity (Kd) = 8% = 0.08
Po = R/2(1- (1 + r/m)-nm) + FV/ (1+r/m)n m
r/m
Po = 680/2(1-(1+0.08/2)-8x2) + 10,000/(1 + 0.08/2 )8x2
0.08/2
Po = 340(1 - (1 + 0.04)-16) + 10,000/(1 + 0.04)16
0.04
Po = 340(1-0.5339) + 10,000/1.8730
0.04
Po = 3,961.85 + 5,339.03
Po = $9,300.88
Explanation:
The current market price of a bond is a function of the present value of semi-annual coupon and present value of the face value. The present value of semi-annual coupon is obtained by multiplying the coupon by the present value of annuity factor at 8% for 8 years. The present value of face value is obtained by discounting the face value at the discount factor for 8 years. The addition of the two gives the present value of the bond. All these explanations have been captured by the formula.
