Yield to Maturity: A firm’s bonds have a maturity of 10 years with a $1,000 face value, have an 8% semi-annual coupon, are callable in 5 years at $1,050, and currently sell at a price of $1,100. What are their nominal yield to maturity and their nominal yield to call? What return should investors expect to earn on these bonds?

Answer a.

Face Value = $1,000
Current Price = $1,100
Annual Coupon Rate = 8%
Semiannual Coupon Rate = 4%
Semiannual Coupon = 4%*$1,000 = $40
Semiannual Period to Maturity = 20 (10 years)

Let semiannual YTM be i%

$1,100 = $40 * PVIFA(i%, 20) + $1,000 * PVIF(i%, 20)

Using financial calculator:
N = 20
PV = -1100
PMT = 40
FV = 1000
I/Y = 3.31%

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

Answer b.

Call Price = $1,050
Current Price = $1,100
Semiannual Coupon = $40
Semiannual Period to Call = 10 (5 years)

Let semiannual YTM be i%

$1,100 = $40 * PVIFA(i%, 10) + $1,050 * PVIF(i%, 10)

Using financial calculator:
N = 10
PV = -1100
PMT = 40
FV = 1050
I/Y = 3.24%

Semiannual YTC = 3.24%
Annual YTC = 2*3.24 %
Annual YTC = 6.48%

Answer c.

Investors would not expect the bonds to be called and to earn the YTM because the YTM is greater than the YTC.