Question

A bond's market price is $1.075. It has a $1,000 par value, will mature in 14 years, and has a coupon interest rate of 9 percent annual interest, but makes its interest payments semiannually. What is the bond's yield to maturity? What happens to the bond's yield to maturity in 28 years? What if it matures in 7 years?.

Answer 1

Answer a.

Par Value = $1,000
Current Price = $1,075

Annual Coupon Rate = 9.00%
Semiannual Coupon Rate = 4.50%
Semiannual Coupon = 4.50% * $1,000
Semiannual Coupon = $45

Time to Maturity = 14 years
Semiannual Period = 28

Let Semiannual YTM be i%

$1,075 = $45 * PVIFA(i%, 28) + $1,000 * PVIF(i%, 28)

Using financial calculator:
N = 28
PV = -1075
PMT = 45
FV = 1000

I = 4.047%

Semiannual YTM = 4.047%

Annual YTM = 2 * 4.047%
Annual YTM = 8.09%

Answer b.

Par Value = $1,000
Current Price = $1,075

Annual Coupon Rate = 9.00%
Semiannual Coupon Rate = 4.50%
Semiannual Coupon = 4.50% * $1,000
Semiannual Coupon = $45

Time to Maturity = 28 years
Semiannual Period = 56

Let Semiannual YTM be i%

$1,075 = $45 * PVIFA(i%, 56) + $1,000 * PVIF(i%, 56)

Using financial calculator:
N = 56
PV = -1075
PMT = 45
FV = 1000

I = 4.153%

Semiannual YTM = 4.153%

Annual YTM = 2 * 4.153%
Annual YTM = 8.31%

Answer c.

Par Value = $1,000
Current Price = $1,075

Annual Coupon Rate = 9.00%
Semiannual Coupon Rate = 4.50%
Semiannual Coupon = 4.50% * $1,000
Semiannual Coupon = $45

Time to Maturity = 7 years
Semiannual Period = 14

Let Semiannual YTM be i%

$1,075 = $45 * PVIFA(i%, 14) + $1,000 * PVIF(i%, 14)

Using financial calculator:
N = 14
PV = -1075
PMT = 45
FV = 1000

I = 3.799%

Semiannual YTM = 3.799%

Annual YTM = 2 * 3.799%
Annual YTM = 7.60%