Question

Calculate the yield to maturity on the following bonds:

A. A 9.9 percent coupon (paid semiannually) bond, with a $1000 face value and 24 years remaining to maturity. The bond is selling at $940.

B. A 10.4 percent coupon (paid quarterly) bond, with a $1000 face value and 10 years remaining to maturity. The bond is selling at $906.

C. An 9.4 percent coupon (paid annually) bond, with a $1000 face value and 10 years remaining to maturity. The bond is selling at $1056

Answer 1

Answer of Part a:

Face Value = $1,000
Current Price = $940

Annual Coupon Rate = 9.9%
Semiannual Coupon Rate = 4.95%
Semiannual Coupon = 4.95%*$1,000 = $49.5

Time to Maturity = 24 years
Semiannual Period to Maturity = 48

Let semiannual YTM be i%

$940 = $49.5 * PVIFA(i%, 48) + $1,000 * PVIF(i%, 48)

Using financial calculator:
N = 48
PV = -940
PMT = 49.5
FV = 1000

I = 5.30%

Semiannual YTM = 5.30%
Annual YTM = 2 * 5.30%
Annual YTM = 10.60%

Answer of Part b:

Face Value = $1,000
Current Price = $906

Annual Coupon Rate = 10.4%
Quarterly Coupon Rate = 2.6%
Quarterly Coupon = 2.6%*$1,000 = $26

Time to Maturity = 10 years
Quarterly Period to Maturity = 40

Let quarterly YTM be i%

$906 = $26 * PVIFA(i%, 40) + $1,000 * PVIF(i%, 40)

Using financial calculator:
N = 40
PV = -906
PMT = 26
FV = 1000

I = 3.01%

Quarterly YTM = 3.01%
Annual YTM = 4 * 3.01%
Annual YTM = 12.04%

Answer of Part c:

Face Value = $1,000
Current Price = $1,056

Annual Coupon Rate = 9.4%
Annual Coupon = 9.4%*$1,000 = $94

Time to Maturity = 10 years

Let annual YTM be i%

$1,056 = $94 * PVIFA(i%, 10) + $1,000 * PVIF(i%, 10)

Using financial calculator:
N = 10
PV = -1056
PMT = 94
FV = 1000

I = 8.54%

Annual YTM = 8.54%