Introduction to Corporate Finance

8: Options

At the time Microsoft issued these bonds, its shares were selling for $25.11 per share. Holding the

price of the bond constant at $1,000, Microsoft’s shares would have to rise by 33% before bondholders

would want to convert their bonds into ordinary shares. This 33% figure equals the bond’s conversion

premium.

At a share price of $25.11, it does not make sense for holders of Microsoft’s convertible bonds to

trade them for shares. Nevertheless, we can still ask: what value will bondholders receive if they do

convert? If Microsoft shares sell for $25.11 and each bond can be exchanged for 29.94 shares, then the

conversion value of one bond equals $751.79 (29.94 × $25.11).

Conversion value is important because it helps define a lower bound on the market value of a

convertible bond. For example, suppose interest rates jump suddenly and the yield on Microsoft’s bonds

increases; the price of the bonds cannot fall below the conversion value of $751.79. If it did, investors

could exploit an arbitrage opportunity by purchasing one bond and immediately converting it into shares.

In general, we can say that the price of a convertible bond will be, at a minimum, the higher of:

(1) the value of an identical bond without conversion rights; or (2) the conversion value. Figure 8.10

demonstrates this pattern for a generic convertible bond with a par value of $1,000 and a conversion ratio

of 20. The horizontal line represents the present value of the convertible bond’s scheduled interest and

principal payments, which we simplify to be $1,000. The upward-sloping straight line shows the bond’s

conversion value at different share prices, and the curved line shows the convertible bond’s price. When

the share price is very low, so too is the probability that the bonds will ever be worth converting into

shares, so the convertible bond sells at a price comparable to an ordinary bond. As the share price rises,

the value of the conversion option increases.

Most convertible bonds issued in Australia and other countries have another feature that slightly

complicates matters. When companies issue convertibles, they almost always retain the right to call

back the bonds. When companies call their outstanding bonds, bondholders can choose, within 30 days

of the call, to receive either the call price in cash or a quantity of shares equal to the conversion ratio.

conversion premium

The percentage increase in

the underlying stock that must

occur before it is profitable to

exercise the option to convert

a bond into shares

conversion value

The market price of the

shares, multiplied by the

number of shares that

bondholders receive if they

convert

FIGure 8.10 THE VALUE OF A CONVERTIBLE BOND

The convertible bond must sell for at least its value as a straight bond, or its conversion value, whichever is greater. If the
bond’s value is $1,000 and the conversion ratio is 20, then the conversion price equals $50. For each $1 increase in the
share price beyond $50, the bond’s conversion value rises by $20.

$1,000

$50 Share price

Convertible price

Conversion value

Bond value