Question

Alco issued a 20 year bond two years ago the coupon rate was 7.10% the bonds make semi-annual payments the par value is $1,000 the bond sell for 105% of par what is the yield to maturity?

Answer 1

Par Value of Bond = $1,000
Current Price of Bond = 105%*$1,000 = $1,050
Annual Coupon Rate = 7.10%
Semiannual Coupon Rate = 3.55%
Semiannual Coupon = 3.55%*$1,000 = $35.50
Time to Maturity = 18 years
Semiannual Period to Maturity = 36

Let Semiannual YTM be i%

$1,050 = $35.50 * PVIFA(i%, 36) + $1,000 * PVIF(i%, 36)

Using financial calculator, i = 3.31%

Semiannual YTM = 3.31%
Annual YTM = 2 * 3.31%
Annual YTM = 6.62%

So, yield to maturity on this bond is 6.62%