GIVE ME A CALL

Bond Loving Company LLC $("$BLC$")$ is a telecom company located in the US$.$ BLC has one of

the first companies in the US to issue debt in the public markets in the form of corporate bonds.

Many others have followed this path after BLC and therefore the bond market in the US has

become one of the most profitable and liquid markets in the world.

BLC has one of the most sophisticated trading desks in the world, with the ability to trade its

own bonds and squeeze results

You are part of a new team inside BLC$,$ a structuring team that is in charge of designing the

structure of new bonds. You have come across a new idea, "callable bonds". This new type of

bonds will allow BLC to redeem the bond at any time before its maturity by paying the bond's

principal $($i$.$e$.$ USD $100)$

Additionally, you have included in the bond the following characteristics:

Coupon $-5\%($annual payments$)$

Term $-4$ years

Interest rates for similar bonds in the market are $6\mathrm{.}5\%$ right now

First, you want to show your boss how good an analyst you are and all you have learned in your

Eng Economy classes, so without taking into account the call option:

What is the price of the bond without taking into account the call option?

What will be the price of the bond now if interest rates increase to $7\%?$ To $8\%?$ And what

if they decrease to $6\%?5\%?4\%?($Make a graph showing how the price changes

depending on different interest rates$)$

Assuming interest rates do not change, what will be the price in one year? In two? In

three? Make a graph to show how the price of the bond changes once it approaches

maturity

Now, that you dominate the "normal" bonds, you want to really impress your boss with this new

innovative idea you have. So now taking into account the call option:

What is the price of the bond?

$2.$ What will be the price of the bond now if interest rates increase to $7\%?$ To $8\%?$ And what

if they decrease to $6\%?5\%?4\%?($Make a graph showing how the price changes

depending on different interest rates$)$

$3.$ Assuming interest rates do not change, what will be the price in one year? In two? In

three? Make a graph to show how the price of the bond changes once it approaches

maturity

Hint: Your intuition is that the price of this bond will be $$capped$$ at $100($as nobody will acquire

a bond for more than $100$ that you can automatically redeem at any time at $100)$