Question

Calculate the yield to maturity on the following bonds: a. A 8.3 percent coupon (paid semiannually) bond, with a $1,000 face value and 23 years remaining to maturity. The bond is selling at $900 $914 $1,064. b. An 5.4 percent coupon (paid quarterly) bond, with a $1,000 face value and 10 years remaining to maturity. The bond is selling at .An 7.4 percent coupon (paid annually) bond, with a $1,000 face value and 8 years remaining to maturity. The bond is selling at For all requirements, do not round intermediate calculations. Round your answers to 3 decimal places.(e.g., 32.161) a. Yield to maturity b. Yield to maturity c. Yield to maturity 4.59701% per year 1.635 1 % per year 6.395 % per year

Answer 1

Answer a.

Face value = $1,000
Current price = $900

Annual coupon rate = 8.30%
Semiannual coupon rate = 4.15%
Semiannual coupon = 4.15% * $1,000
Semiannual coupon = $41.50

Time to maturity = 23 years
Semiannual period = 46

Using financial calculator to find semiannual YTM:

N = 46
PV = -900
PMT = 41.50
FV = 1000

I = 4.6833%

Semiannual YTM = 4.6833%
Annual YTM = 2 * 4.6833%
Annual YTM = 9.367%

Answer b.

Face value = $1,000
Current price = $914

Annual coupon rate = 5.40%
Quarterly coupon rate = 1.35%
Quarterly coupon = 1.35% * $1,000
Quarterly coupon = $13.50

Time to maturity = 10 years
Quarterly period = 40

Using financial calculator to find Quarterly YTM:

N = 40
PV = -914
PMT = 13.50
FV = 1000

I = 1.6451%

Quarterly YTM = 1.6451%
Annual YTM = 4 * 1.6451%
Annual YTM = 6.580%

Answer c.

Face value = $1,000
Current price = $1,064

Annual coupon rate = 7.40%
Annual coupon = 7.40% * $1,000
Annual coupon = $74.00

Time to maturity = 8 years

Using financial calculator to find Annual YTM:

N = 8
PV = -1064
PMT = 74
FV = 1000

I = 6.355%

Annual YTM = 6.355%