A convertible bond has a 8% coupon and 15 years to maturity. The face value is $1,000 and the conversion ratio is 40. The stock currently sells for $20 7/8 per share. Similar nonconvertible bonds are priced to yield 9%. The value of the convertible bond is at least:

Question

Quizplus · Accepted Answer

First, we need to calculate the annual coupon payment:

$1,000 x 8% = $80 per year

Next, we need to calculate the conversion price:

$1,000 / 40 = $25 per share

Since the stock is currently selling for $20 7/8 per share, it is not optimal to convert the bond to stock.

Now, we can calculate the present value of the bond's cash flows:

PV of coupon payments = $80 / (1 + 0.09)^1 + $80 / (1 + 0.09)^2 + ... + $80 / (1 + 0.09)^15
PV of coupon payments = $815.94

PV of face value = $1,000 / (1 + 0.09)^15
PV of face value = $310.22

The minimum value of the convertible bond is the higher of the present value of its cash flows and the value of a similar nonconvertible bond. In this case, the nonconvertible bond is priced to yield 9%, so its value is:

$1,000 / (1 + 0.09)^15 = $310.22

Therefore, the minimum value of the convertible bond is $815.94.

A Convertible Bond Has a 8% Coupon and 15 Years