Application of the Information Ratio
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Conversion value (parity value) is the value of a bond if it is converted into common shares at the prevailing market price.
$$ \text{Conversion value}=\text{Underlying share price} \times \text{Conversion ratio} $$
$$ \text{Minimum value of the convertible bond} = \text{max(Conversion value, Straight value)} $$
Where:
Straight value is the value of the underlying option-free bond.
Pallab Pujar, CFA, is analyzing a convertible bond. The characteristics of the bond and the underlying common stock are given below:
$$ \textbf{Characteristics of the convertible bond} \\ \begin{array}{c|c} \text{Par value} & 100 \\ \hline \text{Annual coupon rate} & 5.00\% \\ \hline \text{Conversion ratio} & 2.58 \\ \hline \text{Market price} & {110\% \text{ of par value}} \\ \hline \text{Straight value} & {90\% \text{ of par value}} \\ \end{array} $$ $$ \textbf{Underlying common stock characteristics} \\ \begin{array}{c|c} \text{Current market price} & {$35 \text{ per share}} \\ \hline \text{Annual cash dividend} & {$2.20 \text{ per share}} \end{array} $$
$$\begin{align*} \text{Conversion value} &=\text{Underlying share price} \times \text{Conversion ratio} \\ &=$35\times2.58=90.3 \end{align*} $$
$$\begin{align*} \text{Min. value of the convertible bond} &=\text{max}{\left(90.3, 90\%\times100\right)} \\ \text{max}{\left(90.3,90\right)} & =$90.3 \end{align*} $$
The market conversion price is the amount investors pay for a stock when exercising their option to exchange convertible bonds into the company’s common stocks.
$$ \text{Market conversion price}=\frac{\text{Convertible bond price}}{\text{Conversion ratio}} $$
The market conversion premium per share is the premium or discount payable when buying the convertible bond rather than the underlying share.
$$ \begin{align*} & \text{Market conversion premium per share} \\ & = \text{Market conversion price}-\text{Underlying share price} \end{align*} $$
The market conversion premium ratio is the percentage of the premium or discount investors have to pay in relation to the shares’ current market price.
$$ \begin{align*} \text{Market conversion premium ratio} =\frac{\text{Market conversion premium per share}}{\text{Underlying share price}} \end{align*} $$
Pallab Pujar, CFA, is analyzing a convertible bond. The characteristics of the bond and the underlying common stock are given below:
$$ \textbf{Characteristics of the convertible bond} \\ \begin{array}{c|c} \text{Par value} & 100 \\ \hline \text{Annual coupon rate} & 5.00\% \\ \hline \text{Conversion ratio} & 2.58 \\ \hline \text{Market price} & {110\% \text{ of par value}} \\ \hline \text{Straight value} & {90\% \text{ of par value}} \\ \end{array} $$ $$ \textbf{Underlying common stock characteristics} \\ \begin{array}{c|c} \text{Current market price} & {$35 \text{ per share}} \\ \hline \text{Annual cash dividend} & {$2.20 \text{ per share}} \end{array} $$
$$ \begin{align*} \text{Market conversion price} &=\frac{\text{Convertible bond price}}{\text{Conversion ratio}} \\ &=110\%\times\frac{100}{2.58}=$42.64 \end{align*} $$
$$ \begin{align*} \text{Market conversion premium per share} & = \text{Market conversion price} \\ & -\text{Underlying share price} \\ & =$42.64 – $35 = $7.62 \end{align*} $$
$$ \begin{align*} \text{Market conversion } & \text{premium ratio} \\ & =\frac{\text{Market conversion premium per share}}{\text{Underlying share price}} \\ & =\frac{$7.62}{$35}=21.8\% \end{align*} $$
The value of a straight bond can be used as a benchmark of the downside risk of a convertible bond. The following metric can thus be computed.
$$ \text{Premium over straight value} =\frac{\text{Bond price}}{\text{Straight value}}-1 $$
The higher the premium over straight value, the less attractive the convertible bond is holding all else constant. However, this measure is not accurate as the straight value varies with changes in the interest rates and credit spreads.
Consider a convertible bond with a market price of $110 and a straight value of $90. The issuing company’s stock is currently $35 per share. The bond’s premium over straight value is closest to:
$$ \begin{align*} \text{Premium over straight value} &=\frac{\text{Convertible bond price}}{\text{Straight value}}-1 \\ &=\frac{$110}{$90}-1=22.2\% \end{align*} $$
The upside potential of a convertible bond depends on the expectation of the underlying common stock.
Question
Consider a convertible bond that pays 10% annual coupons issued on 01/01/2018 and maturing on 31/12/2020. The bond’s characteristics and market information are outlined in the following table:
$$ \begin{array}{c|c} \text{Issue date} & {01 \text{ January } 2018} \\ \hline \text{Maturity date} & {31 \text{ December } 2020} \\ \hline \text{Annual Coupon} & 10.00\% \\ \hline \text{Issue Size} & 1,000,000 \\ \hline \text{Issue price} & 1,000 \\ \hline \text{Conversion ratio} & 25 \\ \hline \text{Straight value} & 990 \\\hline \text{Common stock market price} & {$30 \text{ per share}} \\ \hline \text{Annual Cash Dividend} & {$2.4 \text{ per share}} \end{array} $$
The market conversion premium per share is closest to:
- $10.
- $30.
- $40.
Solution
The correct answer is A.
$$ \begin{align*} & \text{Market conversion premium per share} \\ & = \text{Market conversion price} -\text{Underlying share price} \end{align*} $$
Where:
$$ \begin{align*} \text{Market conversion price} &=\frac{\text{Convertible bond price}}{\text{Conversion ratio}} \\ \\ & = \frac{$1000}{$25}=$40 \end{align*} $$
$$ \text{Market conversion premium per share} = $40-$30 = $10 $$
Reading 30: Valuation and Analysis of Bonds with Embedded Options
LOS 30 (o) Calculate and interpret the components of a convertible bond’s value.