Question

Your firm has a regular bond outstanding. The bond has a face value of $1,000. The price or value of the bond today is $1,045. The bond has 12 years to maturity. Coupons are paid semi-annually. The coupon rate is 12.25%. What is the effective annual rate of return?

Answer 1

Face Value = $1,000
Current Price = $1,045

Annual Coupon Rate = 12.25%
Semiannual Coupon Rate = 6.125%
Semiannual Coupon = 6.125% * $1,000
Semiannual Coupon = $61.25

Time to Maturity = 12 years
Semiannual Period to Maturity = 24

Let Semiannual YTM be i%

$1,045 = $61.25 * PVIFA(i%, 24) + $1,000 * PVIF(i%, 24)

Using financial calculator:
N = 24
PV = -1045
PMT = 61.25
FV = 1000

I = 5.774%

Semiannual YTM = 5.774%

Effective Annual Return = (1 + Semiannual YTM)^2 - 1
Effective Annual Return = (1 + 0.05774)^2 - 1
Effective Annual Return = 1.1188 - 1
Effective Annual Return = 0.1188 or 11.88%