Question

1. A firm issues two bonds with 20-year maturities. Both are callable at $1,050. The first bond is issued at a deep discount to par with a coupon rate of 4% and a price of $580 to yield 8.4%. The second is issued at par with a coupon rate of 8.9%.
   1. What is the yield-to-maturity of the par bond?
   2. If you expect rates to fall substantially in the next 2 years, which bond would you prefer to hold?
   3. In what sense does the discount bond offer “implicit call protection”?
2. Two bonds have identical times to maturity and coupon rates. One is callable at 105 and the other is callable at 110 – which bond should have a higher yield to maturity? Explain. (i.e. which bond should be selling at a lower price? Which call option is the issuing firm more likely to exercise?)

Answer 1

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1. Answer(A):

A bond will sell only at par rate when the yield to maturity of the bond equals the coupon rates

=> YTM = Coupon rate => Bond sells/issued at par rate

In this case the second bond is issued at a par with a coupon rate of 8.9%.

Therefore Yield to maturity of the par bond is 8.9% same as coupon rate

Answer(B):

We are given with the fact that the yield is expected to fall over the next 2 years.

=> If Yield of the bond decreases => Price of the bond increases (inversly proportional)

Therefore if the rates fall we can expect to receive a larger income from the discounted bond than the par bond because there is a greater potential of capital gains from it.

We would hold the first bond i.e; discounted bond when the rates fall

Answer(C):

A callable bond means that the firm has a possibility of calling the bond when the price of the bond exceeds call price of the bond. If the yields are to fall in an unlikely event, then the discounted bond increases in price to exceed the call price to make the firm owners to call the bond. Therefore the discounted bonds are said to have an implicit call protection.

2. Answer:

The Yield to maturity will be the same across the both bonds because it does not consider the fact of callable values. Rather it depends on the coupon rates, years to maturity etc. The bonds are equal in every aspect, so YTM is the same for both the bonds.