Question

6. Assume that ABC Company successfully issues a 6% convertible bond, due 12 years from now at $1,000 per bond. The bond pays interest 2 times per year. Also, assume that the bond is convertible into 100 shares of stock anytime during the life of the bond. Assume the common stock of the company is selling for $8 per share at the time the convertible bond is issued. The last assumption is that if ABC Company issued a regular bond (not convertible), they would have to sell the bond with a 9% coupon instead of the 6% on the convertible.

Using the information above, calculate the minimum value for the convertible if:

(A) ABC common stock trades at $14 per share

(B) The stock trades at $6 per share

Answer 1

a). At $14, the bond would be tradfing "off the stock"

Value = 100 shares x $14 = $1,400

b). The value of the bond as an ordinary bond is calculated as follows:

There would be 2 amortization periods,

FV=$1,000, PMT=$30 (6% x $1,000 divided by 2), I/YR=9%/2 = 4.5%, N=24

You then solve for PV and the answer is $782.56

If the bond was still trading "off the stock", the value would be 100 x $6 = $600.

In other words, if the stock falls to $6, the bond will not fall to $600, but to $782.56, its value as an ordinary bond.

So, the minimum value in this case is $782.56