Question

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

  

Conversion price	$56/share
Coupon rate	6.5%
Par value	$1,000
Yield on nonconvertible debentures   of same quality	9%
Maturity	20 years
Market price of stock	$50 /share

  

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

Multiple Choice

• $857.14

• $769.98

• $892.86

• $1,000.00

• $875.00

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:

= 6.5% / 2 x $ 1,000 (Since the payments are semi annually, hence divided by 2)

= $ 32.5

The YTM will be as follows:

= 9% / 2 (Since the payments are semi annually, hence divided by 2)

= 4.5% or 0.045

N will be as follows:

= 20 x 2 (Since the payments are semi annually, hence multiplied by 2)

= 40

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

= $ 32.5 x [ [ (1 - 1 / (1 + 0.045)⁴⁰ ] / 0.045 ] + $ 1,000 / 1.045⁴⁰

= $ 32.5 x 18.40158442 + $ 171.9287011

= $ 769.98

Convertible value of the bond is computed as follows:

= (Par value / Conversion price) x market price

= ($ 1,000 / $ 56) x $ 50

= $ 892.86

So, the minimum price will be higher of $ 769.98 or $ 892.86.

So, the correct answer is option of $ 892.86

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