Question

1. ABC issued 12-year bonds at a coupon rate of 8% with semi-annual payments. If the bond currently sells for $1050 of par value, what is the YTM?
2. ABC issued 12-year bonds 2 years ago at a coupon rate of 8% with semi-annual payments. If the bond currently sells for 105% of par value, what is the YTM?
3. A bond has a quoted price of $1,080.42. It has a face value of $1000, a semi-annual coupon of $30, and a maturity of five years. What is the current yield? What is the yield to maturity?

Answer 1

Answer to Question 1:

Face Value = $1,000
Current Price = $1,050

Annual Coupon Rate = 8%
Semiannual Coupon Rate = 4%
Semiannual Coupon = 4%*$1,000 = $40

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

Let semiannual YTM be i%

$1,050 = $40 * PVIFA(i%, 24) + $1,000 * PVIF(i%, 24)

Using financial calculator:
N = 24
PV = -1050
PMT = 40
FV = 1000

I = 3.683%

Semiannual YTM = 3.683%
Annual YTM = 2 * 3.683%
Annual YTM = 7.366% or 7.37%