# Callable and convertible bonds

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Callable and convertible bonds

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.

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

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.

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

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

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.

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