Question

A firm's bonds have a maturity of 14 years with a $1,000 face value, have an 8% semiannual coupon, are callable in 7 years at $1,072, and currently sell at a price of $1,134.54.

a. What is their nominal yield to maturity? Round your answer to two decimal places.

b. What is their nominal yield to call? Round your answer to two decimal places.

c. What return should investors expect to earn on these bonds?

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

Answer 1

Answer a.

Face Value = $1,000
Current Price = $1,134.54

Annual Coupon Rate = 8.00%
Semiannual Coupon Rate = 4.00%
Semiannual Coupon = 4.00% * $1,000
Semiannual Coupon = $40

Time to Maturity = 14 years
Semiannual Period = 28

Let Semiannual YTM be i%

$1,134.54 = $40 * PVIFA(i%, 28) + $1,000 * PVIF(i%, 28)

Using financial calculator:
N = 28
PV = -1134.54
PMT = 40
FV = 1000

I = 3.26%

Semiannual YTM = 3.26%
Annual YTM = 2 * 3.26%
Annual YTM = 6.52%

Answer b.

Call Value = $1,072
Current Price = $1,134.54
Semiannual Coupon = $40

Time to Call = 7 years
Semiannual Period = 14

Let Semiannual YTC be i%

$1,134.54 = $40 * PVIFA(i%, 14) + $1,072 * PVIF(i%, 14)

Using financial calculator:
N = 14
PV = -1134.54
PMT = 40
FV = 1072

I = 3.208%

Semiannual YTC = 3.208%
Annual YTC = 2 * 3.208%
Annual YTC = 6.416% or 6.42%

Answer c.

Investors would expect the bonds to be called and to earn the YTC because the YTC is less than the YTM.