Question

I know that Par Value is assumed to be 1000$ and that since it is a semiannual- pay bond there will be 2 payments every year. So, then we have to divide the 9.2% by 2 as well as the 97.5% of par by 2 as well? We are trying to find the YTM, but I am not sure where else to go from here or if I am missing anything.

"XKL Co.has 9.2 percent semiannual-pay coupon bonds that sell for 97.5 percent of par and mature in 22 years. What is the yield to maturity for these bonds in percent?"

Answer 1

Par Value = $1,000

Current Price = 97.50% * Par Value
Current Price = 97.50% * $1,000
Current Price = $975

Annual Coupon Rate = 9.20%
Semiannual Coupon Rate = 4.60%
Semiannual Coupon = 4.60% * $1,000
Semiannual Coupon = $46

Time to Maturity = 22 years
Semiannual Period = 44

Let Semiannual YTM be i%

$975 = $46 * PVIFA(i%, 44) + $1,000 * PVIF(i%, 44)

Using financial calculator:
N = 44
PV = -975
PMT = 46
FV = 1000

I = 4.736%

Semiannual YTM = 4.736%
Annual YTM = 2 * 4.736%
Annual YTM = 9.47%