Question

Plunkett Gym Equipment Inc. has a \(1,000 par value convertible bond outstanding that can be converted into 25 shares of common stock. The common stock is currently selling for \)34.75 a share, and the convertible bond is selling for $960.

a. What is the conversion value of the bond?

b. What is the conversion premium?

c. What is the conversion price?

Short answer

Answer

1. The conversion value of the bond is $868.75

2. The conversion premium is $91.25

3. The conversion price is $40

Step-by-step solution

Computation of conversion value of the bond-

$$\begin{gathered} \mathit{C}\mathit{o}\mathit{n}\mathit{v}\mathit{e}\mathit{r}\mathit{s}\mathit{i}\mathit{o}\mathit{n}\mathbf{}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e}\mathbf{=}\mathit{S}\mathit{t}\mathit{o}\mathit{c}\mathit{k}\mathbf{}\mathit{p}\mathit{r}\mathit{i}\mathit{c}\mathit{e}\mathbf{\times }\mathit{N}\mathit{u}\mathit{m}\mathit{b}\mathit{e}\mathit{r}\mathbf{}\mathit{o}\mathit{f}\mathbf{}\mathit{S}\mathit{h}\mathit{a}\mathit{r}\mathit{e}\mathit{s} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{34}\mathbf{.}\mathbf{75}\mathbf{\times }\mathbf{25} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{868}\mathbf{.}\mathbf{75} \end{gathered}$$

Computation of conversion premium-

$$\begin{gathered} \mathit{C}\mathit{o}\mathit{n}\mathit{v}\mathit{e}\mathit{r}\mathit{s}\mathit{i}\mathit{o}\mathit{n}\mathbf{}\mathit{p}\mathit{r}\mathit{e}\mathit{m}\mathit{i}\mathit{u}\mathit{m}\mathbf{=}\mathit{B}\mathit{o}\mathit{n}\mathit{d}\mathbf{}\mathit{p}\mathit{r}\mathit{i}\mathit{c}\mathit{e}\mathbf{-}\mathit{C}\mathit{o}\mathit{n}\mathit{v}\mathit{e}\mathit{r}\mathit{s}\mathit{i}\mathit{o}\mathit{n}\mathbf{}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{960}\mathbf{-}\mathbf{\$}\mathbf{868}\mathbf{.}\mathbf{75} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{91}\mathbf{.}\mathbf{25} \end{gathered}$$

Computation of Conversion price-

$$\begin{gathered} \mathit{C}\mathit{o}\mathit{n}\mathit{v}\mathit{e}\mathit{r}\mathit{s}\mathit{i}\mathit{o}\mathit{n}\mathbf{}\mathit{p}\mathit{r}\mathit{i}\mathit{c}\mathit{e}\mathbf{=}\frac{\mathbf{C}\mathbf{o}\mathbf{n}\mathbf{v}\mathbf{e}\mathbf{r}\mathbf{t}\mathbf{i}\mathbf{b}\mathbf{l}\mathbf{e}\mathbf{}\mathbf{b}\mathbf{o}\mathbf{n}\mathbf{d}\mathbf{}\mathbf{p}\mathbf{a}\mathbf{r}\mathbf{}\mathbf{v}\mathbf{a}\mathbf{l}\mathbf{u}\mathbf{e}}{\mathbf{N}\mathbf{u}\mathbf{m}\mathbf{b}\mathbf{e}\mathbf{r}\mathbf{}\mathbf{o}\mathbf{f}\mathbf{}\mathbf{s}\mathbf{h}\mathbf{a}\mathbf{r}\mathbf{e}\mathbf{s}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{000}}{\mathbf{25}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{40} \end{gathered}$$