Question

Keenan Industries has a bond outstanding with 15 years to maturity, an 8.25% nominal coupon, semiannual payments, 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 $1,085. What is the bonds nominal yield to call? Which is an investor that buys the bond today more likely to earn?

Answer 1

Answer:

a.- YTC 6.097621350%

b.- The yield to call is considered a more accurate estimate of the bonds expected return than YTM

Explanation:

1,000 8.25% 15 years

callable in 6 years

YTM 6.50

YTC  ???

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

The first part is the present value of the coupon payment

and the second the present value of the called bond.

P = the current market price = ??

C = coupon payment = 1,00 x 8.25% = 82.5

CP =  the call price = 1,085

t = year unit called = 6

YTC = the yield to call

$P = \frac{82.5}{2} \times\frac{1-(1+YTC/2)^{-2\times6} }{YTC/2} + \frac{1,085}{(1+YTC/2)^{2\times6}}$

We need the market price, which can be get using the yield to maturity rate.

The formula will be the same with these changes:

• time would be equal to 15 years

• and we calculate the present value of the 1,000 face value received at the end of the bonds life

$P = \frac{82.5}{2} \times\frac{1-(1+6.5%/2)^{-2\times15} }{6.5%/2} + \frac{1,000}{(1+6.5%/2)^{2\times15}}$

coupon pv 783.004093 + final payment 383.087684

 = 1166.091777 Market Price

Now we have the market price, we can solve for the YTC using:

(A)financial calculator. with the above formula.

(B) listing the cashflow and use the IRR function on excel

(C) calculate the YTC using iterative process

(D) use the approximation formula

A and B will give us the exact YTC 6.097621350%

C and D will give us a rate with a certing margin of error