Question

You are the CFO of a video Arcade company, called uncertainty Corporation. You want to raise money, for creating a new game. You have decided to issue a type of bond that the holder can convert into a specified number of shares, of common stock, issued by your company. In essence, you have created a hybrid security with debt and equity like features. How will you determine the price at which you will issue this hybrid security today? please clearly state your assumptions, terminology and notation.

Answer 1

Pricing of a hybrid security or a convertible bond is as follows.

To prevent the arbitrage, A convertible bond is priced at higher of

A) conversion value(CV)

B ) bond investment value(BIV)

Conversion value is the value of shares the bondholder gets after conversion it is given by

CV= St× F/ CP

Where

St= stock price

F= face value of bond

CP= conversion price

Bond investment value is nothing but the value of a bond without the option

BIV= l(1-(1+r)^n)/r + F/(1+r)^n

Where

I= coupon amout = F× coupon rate

n= maturity of bond

F= face value

r = Yield of a similar bond without option

Similar bond means a bond having same risk characterstics, ratings, maturity, face value etc.

The model explained above however looks simple but it is not that easy to use in practice because of stock price movements, interest rate movements and sometimes it os not that easy to find similer bond.