About bonds callculation?

Question

Suppose you own a bond with the current market price of $1200 and annual coupon rate
of 14%. The bond matures in 20 years and is callable in 4 years at a price $1050.
(a) What is this bond’s yield to maturity?
(b) What is this bond’s yield to call?
(c) Do you think your bond will be called? Why?

Answer 1

When setting this up in a financial calculator, it's important to remember that bonds pay semiannually, so you have to divide the coupon by 2 and multiply the maturity by 2. Then the yield you solve for has to be doubled.

So the general set up is as follows:

PV = -120
PMT = 7

a.) There are 40 compounding periods prior to maturity, and at maturity, the future value will be 100. Solving for the yield to maturity you get 11.44%

b.) There are 8 compounding periods prior to call, and at call the future value will be 105.
Solving for the yield to call you get 9.00%

c.) I suspect the bond will be called because both the yield to call and the yield to maturity are lower than the coupon rate. This implies that the company could reissue debt with a lower coupon than the 14% it is currently paying. Even pricing in the 5% call premium doesn't bring the yield up to where the coupon rate is.