Question

Calculate the bonds yield to maturity below:

A $1000 face value, 6 % coupon, twenty year bond, callable at $102 in the tenth year, it is trading currently at $98

firts calculate yield to call then yield to maturity

write up every step

Answer 1

Yield to Call:

Face Value = $1,000
Current Price = 98%*$1,000 = $980
Call Price = 102%*$1,000 = $1,020

Annual Coupon Rate = 6%
Annual Coupon = 6%*$1,000
Annual Coupon = $60

Time to Call = 10 years

Let YTC be i%

$980 = $60 * PVIFA(i%, 10) + $1,020 * PVIF(i%, 10)

Using financial calculator:
N = 10
PV = -980
FV = 1020
PMT = 60

I = 6.43%

So, Annual YTC is 6.43%

Yield to Maturity:

Face Value = $1,000
Current Price = 98%*$1,000 = $980
Annual Coupon = $60
Time to Maturity = 20 years

Let YTM be i%

$980 = $60 * PVIFA(i%, 20) + $1,000 * PVIF(i%, 20)

Using financial calculator:
N = 20
PV = -980
FV = 1000
PMT = 60

I = 6.18%

So, Annual YTM is 6.18%