Question

Last year Carson Industries issued a 10-year, 12% semiannual coupon bond at its par value of $1,000. Currently, the bond can be called in 6 years at a price of $1,060 and it sells for $1,200. What are the bond's nominal yield to maturity and its nominal yield to call? Do not round intermediate calculations. Round your answers to two decimal places.

Answer 1

Answer:

YTM = 8.93%

YTC = 8.47%

Explanation:

$P = \frac{C}{2} \times\frac{1-(1+YTC/2)^{-2t} }{YTC/2} + \frac{CP}{(1+YTC/2)^{2t}}$

The first part is the present value of the coupon payment until the bond is called.

The second is the present value of the called amount

P = market price value = 1,200

C = annual coupon payment = 1,000 x 12% 120

C/2 = 60

CP = called value = 1,060

t = time = 6 years

$P = 60 \times\frac{1-(1+YTC/2)^{-2\times 6} }{YTC/2} + \frac{1,060}{(1+YTC/2)^{2\times 6}}$

Using Financial calculator we get the YTC

8.467835879%

$P = 60 \times\frac{1-(1+YTM/2)^{-2\times 10} }{YTM/2} + \frac{1,000}{(1+YTM/2)^{2\times 10}}$

The first part is the present value of the coupon payment until manurity

The second is the present value of the redeem value at maturity

P = market price value = 1,200

C = coupon payment = 1,000 x 12%/2 = 60

C/2 = 60

F = face value = 1,060

t = time = 10 years

Using Financial calculator we get the YTM

8.9337714%