Question

Jerome Corporation's bonds have 15 years to maturity, an 8.75% coupon paid semiannually, and a $1,000 par value. The bond has a 6.50% nominal yield to maturity, but it can be called in 6 years at a price of $1,195. What is the bond's nominal yield to call?

Select the correct answer.

a. 7.32%

b. 7.16%

c. 7.64%

d. 7.48%

Answer 1

Answer is 7.00%.

Calculation of current price:

Face Value = $1,000

Annual Coupon Rate = 8.75%
Semiannual Coupon Rate = 4.375%
Semiannual Coupon = 4.375% * $1,000
Semiannual Coupon = $43.75

Annual YTM = 6.50%
Semiannual YTM = 3.25%

Time to Maturity = 15 years
Semiannual Period to Maturity = 30

Current Price = $43.75 * PVIFA(3.25%, 30) + $1,000 * PVIF(3.25%, 30)
Current Price = $43.75 * (1 - (1/1.0325)^30) / 0.0325 + $1,000 / 1.0325^30
Current Price = $1,213.55

Calculation of YTC:

Current Price = $1,213.55
Call Price = $1,195
Semiannual Coupon = $43.75

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

Let semiannual YTC be i%

$1,213.55 = $43.75 * PVIFA(i%, 12) + $1,195 * PVIF(i%, 12)

Using financial calculator:
N = 12
PV = -1213.55
PMT = 43.75
FV = 1195

I = 3.50%

Semiannual YTC = 3.50%
Annual YTC = 2 * 3.50%
Annual YTC = 7.00%