A company in the semiconductor industry has a $1,000 convertible bond with a con
ID: 2768900 • Letter: A
Question
A company in the semiconductor industry has a $1,000 convertible bond with a conversion ratio of 32 and a coupon of 3.9%. The bond is currently priced at $740. The company’s stock trades at $19, and pays an annual dividend of $0.75.
a. Find the conversion value of this bond. Explain what this means.
b. Find the conversion premium in dollars and in percent.
c. Find the payback period. Explain what this means in your own words without quoting the definition of payback period. In addition, state whether or not this is considered to be an acceptable payback period.
Explanation / Answer
Conversion Value = Stock Price x Conversion Ratio
=> $19 x 32 = $608
Conversion Premium in dollar = (Convertible Market Price – Conversion Value) / Convertible Market Price
=> ($740 - $608)/$740 = 0.1784 or 17.84 Points
Conversion Premium in Percentage = (Convertible Market Price – Conversion Value) / Conversion Value
=> ($740 - $608)/$608 = 0.2171 or 21.71%
Payback Period = (Market conversion premium per share)/(Favorable income differential per share)
Market conversion premium per share = Market conversion price - Market price of stock
Market Conversion Price = Market price (CB) / Conversion ratio
=> $740/32 = $23.125
Market conversion premium per share = $23.125 - $19 = $4.125
Favorable income differential per share = (Coupon rate * Par value)/(Conversion ratio - Dividends per share)
=> [(3.9% x $1,000)/(32)] – [0.75] = 0.46875
Payback Period = $4.125/0.46875 = 8.8 Years
The payback period means that you will require 8.8 years to cover the convertible premium.
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