Ross et al.: Fundamentals
of Corporate Finance, Sixth
Edition, Alternate EditionV. Risk and Return 14. Options and Corporate
Finance© The McGraw−Hill^507
Companies, 2002Value of a Convertible Bond Even though the conversion feature of the convertible
bond cannot be detached like a warrant, the value of the bond can still be decomposed
into the bond value and the value of the conversion feature. We discuss how this is done
next.
The easiest way to illustrate convertible bond valuation is with an example. Suppose
a company called Micron Origami (MO) has an outstanding convertible bond issue. The
coupon rate is 7 percent and the conversion ratio is 15. There are 12 remaining coupons,
and the stock is trading for $68.
Straight Bond Value The straight bond valueis what the convertible bond would sell
for if it could not be converted into common stock. This value will depend on the gen-
eral level of interest rates on debentures and on the default risk of the issuer.
Suppose straight debentures issued by MO are rated B, and B-rated bonds are priced
to yield 8 percent. We can determine the straight bond value of MO convertible bonds
by discounting the $35 semiannual coupon payment and maturity value at 8 percent, just
as we did in Chapter 6:
Straight bond value $35 (1 1/1.04^12 )/.04 1,000/1.04^12
$328.48 624.60
$953.08The straight bond value of a convertible bond is a minimum value in the sense that the
bond is always worth at least this amount. As we discuss, it will usually be worth more.
Conversion Value The conversion valueof a convertible bond is what the bond
would be worth if it were immediately converted into common stock. This value is com-
puted by multiplying the current price of the stock by the number of shares that will be
received when the bond is converted.
For example, each MO convertible bond can be converted into 15 shares of MO
common stock. MO common was selling for $68. Thus, the conversion value was 15
$68 $1,020.
A convertible cannot sell for less than its conversion value, or an arbitrage opportu-
nity exists. If MO’s convertible had sold for less than $1,020, investors would have
bought the bonds and converted them into common stock and sold the stock. The arbi-
trage profit would have been the difference between the value of the stock and the
bond’s conversion value.
Floor Value As we have seen, convertible bonds have two floor values: the
straight bond value and the conversion value. The minimum value of a convertible
bond is given by the greater of these two values. For the MO issue, the conversion
value is $1,020 and the straight bond value is $953.08. At a minimum, this bond is
thus worth $1,020.
Figure 14.3 plots the minimum value of a convertible bond against the value of the
stock. The conversion value is determined by the value of the firm’s underlying com-
mon stock. As the value of the common stock rises and falls, the conversion value rises
and falls with it. For example, if the value of MO’s common stock increases by $1, the
conversion value of its convertible bonds will increase by $15.
In Figure 14.3, we have implicitly assumed that the convertible bond is default-free. In
this case, the straight bond value does not depend on the stock price, so it is plotted as
a horizontal line. Given the straight bond value, the minimum value of the convertible
depends on the value of the stock. When the stock price is low, the minimum value of a
CHAPTER 14 Options and Corporate Finance 479straight bond value
The value a convertible
bond would have if it
could not be converted
into common stock.conversion value
The value a convertible
bond would have if it
were to be immediately
converted into common
stock.For more on convertible
bonds, see
http://www.convertbond.com.