BOND YIELDS Last year Carson Industries issued a 10year 15 s

BOND YIELDS Last year Carson Industries issued a 10-year, 15% semiannual coupon bond at its par value of $1,000. Currently, the bond can be called in 6 years at a price of $1,075 and it sells for $1,280. What is the bond\'s nominal yield to maturity? Do not round intermediate calculations. Round your answer to two decimal places. % What is the bond\'s nominal yield to call? Do not round intermediate calculations. Round your answer to two decimal places. % Would an investor be more likely to earn the YTM or the YTC?

What is the current yield? (Hint: Refer to Footnote 7 for the definition of the current yield and to Table 7.1.) Round your answer to two decimal places. %

Solution

Answer a.

Face Value = $1,000
Current Price = $1,280

Annual Coupon Rate = 15%
Semiannual Coupon Rate = 7.50%
Semiannual Coupon = 7.50% * $1,000
Semiannual Coupon = $75

Time to Maturity = 10 years
Semiannual Period to Maturity = 20

Let semiannual YTM be i%

$1,280 = $75 * PVIFA(i%, 20) + $1,000 * PVIF(i%, 20)

Using financial calculator:
N = 20
PV = -1280
PMT = 75
FV = 1000

I = 5.213%

Semiannual YTM = 5.213%
Annual YTM = 2 * 5.213%
Annual YTM = 10.426% or 10.43%

Answer b.

Call Price = $1,075
Current Price = $1,280
Semiannual Coupon = $75

Time to Call = 6 years
Semiannual Period to Call = 12

Let semiannual YTC be i%

$1,280 = $75 * PVIFA(i%, 12) + $1,075 * PVIF(i%, 12)

Using financial calculator:
N = 12
PV = -1280
PMT = 75
FV = 1075

I = 4.844%

Semiannual YTC = 4.844%
Annual YTC = 2 * 4.844%
Annual YTC = 9.688% or 9.69%

Answer c.

Current Yield = Annual Coupon / Current Price
Current Yield = 2 * $75 / $1,280
Current Yield = 11.72%