Question

The following facts apply to a convertible bond making semiannual payments:

  

Conversion price	$35/share
Coupon rate	7%
Par value	$1,000
Yield on nonconvertible debentures   of same quality	10%
Maturity	25 years
Market price of stock	$29 /share

  

What is the minimum price at which the convertible should sell?

Multiple Choice

• $812.00

• $828.57

• $1,000.00

• $726.16

• $795.43

Answer 1

The minimum price is computed as shown below:

Value of the bond is computed as follows:

The coupon payment is computed as follows:

= 7% / 2 x $ 1,000 (Since the payments are semi annually, hence divided by 2)

= $ 35

The YTM will be as follows:

= 10% / 2 (Since the payments are semi annually, hence divided by 2)

= 5% or 0.05

N will be as follows:

= 25 x 2 (Since the payments are semi annually, hence multiplied by 2)

= 50

So, the price of the bond is computed as follows:

Bonds Price = Coupon payment x [ [ (1 - 1 / (1 + r)ⁿ ] / r ] + Par value / (1 + r)ⁿ

= $ 35 x [ [ (1 - 1 / (1 + 0.05)⁵⁰ ] / 0.05 ] + $ 1,000 / 1.05⁵⁰

= $ 35 x 18.25592546 + $ 87.20372697

= $ 726.16

Convertible value of the bond is computed as follows:

= (Par value / Conversion price) x market price

= ($ 1,000 / $ 35) x $ 29

= $ 828.57

So, the minimum price will be higher of $ 726.16 or $ 828.57.

So, the correct answer is option of $ 828.57

Feel free to ask in case of any query relating to this question