Question

Sherwood Forest Products has a convertible bond quoted on the NYSE bond market at 90. (Bond quotes represent percentage of par value. Thus 70 represents \(700, 80 represents \)800, and so on.) It matures in 10 years and carries a coupon rate of 5½ percent. The conversion ratio is 25, and the common stock is currently selling for $33 per share on the NYSE.

1. Compute the conversion premium.
2. At what price does the common stock need to sell for the conversion value to be equal to the current bond price?

Short answer

1. The conversion premium is $75
2. The stock price is $36

Step-by-step solution

Meaning of Common Stock

The standard ownership stake in a firm is called common stock. In other words, it's a strategy of apportioning corporate ownership; as a result, each share of common stock corresponds to a certain extent of an organization.

(a) Computing conversion premium

Given,

Convertible bond quoted on the NYSE bond market at 90 represented as $900

Calculation of Conversion value

$\begin{array}{rcl}\mathit{C}\mathit{o}\mathit{n}\mathit{v}\mathit{e}\mathit{r}\mathit{s}\mathit{i}\mathit{o}\mathit{n}\mathbf{}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e}& \mathbf{=}& \mathit{C}\mathit{o}\mathit{m}\mathit{m}\mathit{o}\mathit{n}\mathbf{}\mathit{s}\mathit{t}\mathit{o}\mathit{c}\mathit{k}\mathbf{}\mathit{p}\mathit{r}\mathit{i}\mathit{c}\mathit{e}\mathbf{\times }\mathit{C}\mathit{o}\mathit{n}\mathit{v}\mathit{e}\mathit{r}\mathit{s}\mathit{i}\mathit{o}\mathit{n}\mathbf{ }\mathit{r}\mathit{a}\mathit{t}\mathit{i}\mathit{o}\\ & \mathbf{=}& \mathbf{33}\mathbf{\times }\mathbf{25}\\ & \mathbf{=}& \mathbf{\$}\mathbf{825}\\ & & \end{array}$

Calculation of Conversion premium

$\begin{array}{rcl}\mathit{C}\mathit{o}\mathit{n}\mathit{v}\mathit{e}\mathit{r}\mathit{s}\mathit{i}\mathit{o}\mathit{n}\mathbf{}\mathit{p}\mathit{r}\mathit{e}\mathit{m}\mathit{i}\mathit{u}\mathit{m}& \mathbf{=}& \mathit{B}\mathit{o}\mathit{n}\mathit{d}\mathbf{}\mathit{p}\mathit{r}\mathit{i}\mathit{c}\mathit{e}\mathbf{-}\mathit{C}\mathit{o}\mathit{n}\mathit{v}\mathit{e}\mathit{r}\mathit{s}\mathit{i}\mathit{o}\mathit{n}\mathbf{}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e}\\ & \mathbf{=}& \mathbf{\$}\mathbf{900}\mathbf{-}\mathbf{\$}\mathbf{825}\\ & \mathbf{=}& \mathbf{\$}\mathbf{75}\\ & & \end{array}$

(b) Explaining the price the common stock needs to sell for the conversion value to be equal to the current bond price

Calculation of price of the bond

$\begin{array}{rcl}\mathit{S}\mathit{t}\mathit{o}\mathit{c}\mathit{k}\mathbf{}\mathit{p}\mathit{r}\mathit{i}\mathit{c}\mathit{e}& \mathbf{=}& \frac{\mathbf{B}\mathbf{o}\mathbf{n}\mathbf{d}\mathbf{}\mathbf{p}\mathbf{r}\mathbf{i}\mathbf{c}\mathbf{e}}{\mathbf{C}\mathbf{o}\mathbf{n}\mathbf{v}\mathbf{e}\mathbf{r}\mathbf{s}\mathbf{i}\mathbf{o}\mathbf{n}\mathbf{}\mathbf{r}\mathbf{a}\mathbf{t}\mathbf{i}\mathbf{o}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{900}}{\mathbf{25}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{36}\\ & & \end{array}$

The stock price is $36; it must sell to be equal to the bond price. At this price, conversion price and bond price are equal.