1. Callable and convertible bonds

2. Callable bonds
Call provision: option held by the company to repurchase the bond at a specified price (call price) before maturity
Call premium: amount by which the call price exceeds the par value. 
Call protected: a bond that cannot be called.

3. Callable bonds: Exemplification
Yield to call:
A 7%, five-year bond, callable next year, has a call price of $1,050 and currently sells at par. The yield to maturity is 7%, and the yield to call is ( )/ = 12%
When do firms call their bonds?
When PV(coupon + principal payments) > call price.
In the above example assume that next year interest rates fall to 3%.
The present value of scheduled future payments becomes:
70/(1.03) + 70/(1.03)2 + 70/(1.03)3 + 1,070/(1.03)4 = $ 1,148.68
Hence, the firm will call the bond

4. Callable bonds: Valuation
MV(callable bond) = MV(plain bond) – MV(call option)
The call option is given to the issuer, hence it reduces the MV of the bond.

5. Callable bonds: Relationship between price and yields
Bond price
YTM
Critical yield

6. Plain bond + call option (issuer) + option to convert (bond holder)
Convertible bonds
Plain bond + call option (issuer) + option to convert (bond holder)

7. Convertible bonds: Glossary
conversion ratio: number of shares of stock that can be received for one bond upon voluntary conversion
conversion value: number of shares of stock that can be exchanged for one bond times the price per share
conversion price: face value divided by conversion ratio
voluntary conversion: conversion of the bond into stock at the initiative of the bondholder 
call price: price at which the firm issuing the convertible can call (redeem) the bond. 
call protection: provision in the bond indenture that acknowledges the time period that has to pass before the issuer can call the bonds 
call premium: difference between the call price and face value. 

8. Convertible bonds: Exemplification
A firm issues convertible debt at a call price of $105/bond and a conversion ratio of 1 bond for 2 shares. The stock currently sells at $30/share. Hence the conversion value is $60.
After three years, the market price of the bond is $90 and the share price is $45. The conversion value is therefore $90. The bondholder is indifferent between holding a bond worth $90 or two shares of stock worth $90, other things held constant.
After another year, the market price of the bond is still $90, the stock price goes to $55. The conversion value is $110. The firm should call the bonds.
Conversion rule of thumb: conversion value > bond price
Calling rule of thumb: conversion value > bond price