The current cost of a $1000 6% yield bond, the bond's price for ten years is $920. By summing up all annual coupons paid and dividing that number by the bond's face value, the coupon rate is calculated.
Working Note:
i= 6%
=6%/2 (compounded semi-annually)
=3%
n= 10
=10 x 2 (compounded semi-annually)
=20 years
Step 1: Calculation of coupon payments:
Coupon payments= FV x (coupon rate/ no. of compounding)
=$1,000 x (8%/2)
=$40
Step 2: Calculation of bond’s MV:
MV of bonds= Coupon payments x [tex][1-{1/(1+i)^n}/i]+ FV/(1+i)^n[/tex]
=40 x[tex][1-{1/(1+3%)^20}/3%][/tex]+ 1,000/(1+3%)^20
=40 x 14.88 + 553.68
=595.10 + 553.68
= 1,148.77
Where,
FV= face value
MV= market value
i= yield
n= no. of period
Hence, the bond’s MV is $1,148.77.
The yield to maturity is determined using the current price of $800 as the starting point: 800 equals 1000 / (1 plus yield to maturity) Yield to Maturity = 1.25 times 1. yield to maturity is 25 percent
A bond's coupon rate can be determined by dividing the total annual coupon payments made by the security by the bond's par value. The coupon rate, for instance, is 5% on a $1,000 face value bond that pays a $25 coupon twice a year.
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