Question

Today, a bond has a coupon rate of 9.82 percent, par value of 1,000 dollars, YTM of 5.44 percent, and semi-annual coupons with the next coupon due in 6 months. One year ago, the bond’s price was 986.71 dollars and the bond had 11 years until maturity. What is the current yield of the bond today? Answer as a rate in decimal format so that 12.34% would be entered as .1234 and 0.98% would be entered as .0098.

Help on homework, thanks

Answer 1

face value = 1000

semiannual coupon rate =9.82%/2 = 4.91%

semiannual coupon amount = 1000*4.91% = 49.10

years to maturity now = 11-1 = 10

semiannual periods to maturity (n) = 10*2 =20

YTM = 5.44%

semiannula YTM (i) = 5.44%/2 =2.72%

Bond price formula = Coupon amount * (1 - (1/(1+i)^n)/i + face value/(1+i)^n

(49.1*(1-(1/(1+2.72%)^20))/2.72%) + (1000/(1+2.72%)^20)

=1334.413678

Current yield of bond = semiannual coupon * number of coupons in year/current bond price

=49.1*2/1334.413678

=0.07359037277

So current yield is 0.0736