Question 16.2: A 30-year, 0.08 bond ($1,000 face value) is convertible into...
A 30-year, 0.08 bond ($1,000 face value) is convertible into 25 shares of common stock. The price of the common stock is currently $50 per share, and the common stock price is expected to increase steadily to $391 at the end of year 30 (a 7-percent growth rate). The common stock is paying a $2-per-share dividend that is expected to continue for the entire 30 years. The yield for comparable bonds without a conversion feature is 0.09.We want to determine the present value of the convertible bond if it is converted just before maturity. Assume that the investor does not pay taxes.
The value of the convertible bond with conversion in 30 years using 0.09 as the opportunity cost and the common stock price of $391 per share (25 shares are worth $9,775) is
\sum\limits_{t=1}^{30}{\$80 (1.09)^{-t} } + 25 (\$391) (1.09)^{-30}
= ($80 × 10.2737)+ ($9,775 × 0.0754)
= $821.90 + $737.07
= $1,558.94.
The value of the security as a straight bond is $897.30, using 0.09 and 30-year present value factors:
$1,000 × 0.0754 = $ 75.40
$80 ×10.2737 = 821.90
$ 75.40+821.90 = $897.30
The total value of the bond is equal to the sum of the straight bond plus the value of the conversion feature. If the price of the bond is $1,558.94, the value being placed on the conversion privilege is
value of conversion package = $1,558.94 − $897.30 = $661.64
on the basis of converting at time 30.