Chapter 22 Convertibles, Exchangables, and Warrants

The value of a nonconvertible bond with the same coupon rate, maturity, and default risk as the convertible bond.

(1 + i/2)1
(1 + i/2)2
(1 + i/2) 2*n
VSB =
+
+ ... +
I / 2
I / 2 + F
= S
2*n
t=1
(1 + i/2)t
= (I / 2)(PVIFA i/2, n) + F (PVIF i/2, n)
(1 + i/2)2*n
+
F
I / 2
I / 2
Straight Bond Value

Company C has a convertible debenture outstanding that provides an 8% coupon (interest is paid semiannually) and continues exactly 20 years until final maturity. A similar nonconvertible bond will currently provide a 5% semiannual yield to maturity. What is the straight bond value of Company C’s convertible bond?

Company C has a convertible debenture outstanding that provides an 8% coupon (interest is paid semiannually) and continues exactly 20 years until final maturity. A similar nonconvertible bond will currently provide a 5% semiannual yield to maturity. What is the straight bond value of Company C’s convertible bond?

V = $40 (PVIFA5%, 20 x 2) + $1,000 (PVIF5%, 20 x 2)

= $40 (17.159) + $1,000 (0.142)

= $686.36 + $142

= $828.36

Straight Bond Value of the Convertible

The convertible bond value equals straight bond value plus conversion option value.

• The convertible bond value equals straight bond value plus conversion option value.
• The $828.36 represents a floor (minimum) below which the convertible value will not fall. This occurs when the conversion option value is essentially worthless.
• The straight bond value is subject to change as interest rates, firm risk, and time change. This, in turn, is likely to impact the convertible bond value.