91Ó°ÊÓ

The conversion price of equity is the price per share at which a convertible instrument is converted into common stock. Before discharging convertibles to the open, the management of a business may select the conversion price of equity.

$\begin{array}{rcl}\mathit{C}\mathit{o}\mathit{n}\mathit{v}\mathit{e}\mathit{r}\mathit{s}\mathit{i}\mathit{o}\mathit{n}\mathbf{}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e}& \mathbf{=}& \mathit{S}\mathit{h}\mathit{a}\mathit{r}\mathit{e}\mathit{s}\mathbf{×}\mathit{P}\mathit{e}\mathit{r}\mathbf{}\mathit{s}\mathit{h}\mathit{a}\mathit{r}\mathit{e}\mathbf{}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e}\\ & \mathbf{=}& \mathbf{20}\mathbf{×}\mathbf{\$}\mathbf{36}\\ & \mathbf{=}& \mathbf{\$}\mathbf{720}\\ & & \end{array}$

$\begin{array}{rcl}\mathit{C}\mathit{o}\mathit{n}\mathit{v}\mathit{e}\mathit{r}\mathit{s}\mathit{i}\mathit{o}\mathit{n}\mathbf{}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e}& \mathbf{=}& \mathit{S}\mathit{h}\mathit{a}\mathit{r}\mathit{e}\mathit{s}\mathbf{×}\mathit{P}\mathit{e}\mathit{r}\mathbf{}\mathit{s}\mathit{h}\mathit{a}\mathit{r}\mathit{e}\mathbf{}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e}\\ & \mathbf{=}& \mathbf{20}\mathbf{×}\mathbf{\$}\mathbf{30}\mathbf{.}\mathbf{50}\\ & \mathbf{=}& \mathbf{\$}\mathbf{610}\\ & & \end{array}$

C = coupon payment = $60.00 (Par Value * Coupon Rate)

n = number of years

i = market rate, or required yield = 10% = 0.10

k = number of coupon present in 1 year = 2

P = value at maturity, or par value = 1000

$\begin{array}{rcl}Bondprice& =& \frac{C}{k}×\frac{\left[1-\left[\frac{1}{{\left(1+i/k\right)}^{nk}}\right]\right]}{i/k}+\frac{P}{{\left(1+i/k\right)}^{nk}}\\ & =& \frac{60}{2}×\frac{\left[1-\left[\frac{1}{{\left(1+0.1/2\right)}^{15×2}}\right]\right]}{0.1/2}+\frac{1000}{{\left(1+0.1/2\right)}^{15×2}}\\ & =& 30.00×\frac{\left[1-\left[\frac{1}{{\left(1+0.05\right)}^{30}}\right]\right]}{0.05}+\frac{1000}{{\left(1+0.05\right)}^{30}}\\ & =& 30.00×\frac{\left[1-\left[\frac{1}{4.322}\right]\right]}{0.05}+\frac{1000}{4.322}\\ & & \end{array}$

Further,

$\begin{array}{rcl}\mathit{B}\mathit{o}\mathit{n}\mathit{d}\mathbf{}\mathit{p}\mathit{r}\mathit{i}\mathit{c}\mathit{e}& \mathbf{=}& \mathbf{30}\mathbf{.}\mathbf{00}\mathbf{×}\frac{\mathbf{1}\mathbf{-}\mathbf{0}\mathbf{.}\mathbf{2314}}{\mathbf{0}\mathbf{.}\mathbf{05}}\mathbf{+}\frac{\mathbf{1000}}{\mathbf{4}\mathbf{.}\mathbf{322}}\\ & \mathbf{=}& \mathbf{30}\mathbf{.}\mathbf{00}\mathbf{×}\mathbf{15}\mathbf{.}\mathbf{37}\mathbf{+}\mathbf{231}\mathbf{.}\mathbf{38}\\ & \mathbf{=}& \mathbf{461}\mathbf{.}\mathbf{17}\mathbf{+}\mathbf{231}\mathbf{.}\mathbf{38}\\ & \mathbf{=}& \mathbf{\$}\mathbf{692}\mathbf{.}\mathbf{55}\\ & & \end{array}$

For the time being, the stock price will not have as much of an impact as the pure bond value ($692.55). The pure bond value is $82.55 more than the conversion value of $610.00. The stock will have a greater impact than the pure bond value when the price approaches the parity mark ($692.55/20 shares) of $34.63.

Market price of bond = Pure bond value = $692.55

$\begin{array}{rcl}\mathit{C}\mathit{o}\mathit{n}\mathit{v}\mathit{e}\mathit{r}\mathit{s}\mathit{i}\mathit{o}\mathit{n}\mathbf{}\mathit{p}\mathit{r}\mathit{e}\mathit{m}\mathit{i}\mathit{u}\mathit{m}& \mathbf{=}& \mathit{P}\mathit{u}\mathit{r}\mathit{e}\mathbf{}\mathit{b}\mathit{o}\mathit{n}\mathit{d}\mathbf{-}\mathit{C}\mathit{o}\mathit{n}\mathit{v}\mathit{e}\mathit{r}\mathit{s}\mathit{i}\mathit{o}\mathit{n}\mathbf{}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e}\\ & \mathbf{=}& \mathbf{\$}\mathbf{692}\mathbf{.}\mathbf{55}\mathbf{-}\mathbf{610}\mathbf{.}\mathbf{00}\\ & \mathbf{=}& \mathbf{\$}\mathbf{82}\mathbf{.}\mathbf{55}\\ & & \end{array}$

Calculating conversion premium percentage

$\begin{array}{rcl}\mathit{C}\mathit{o}\mathit{n}\mathit{v}\mathit{e}\mathit{r}\mathit{s}\mathit{i}\mathit{o}\mathit{n}\mathbf{}\mathit{p}\mathit{r}\mathit{e}\mathit{m}\mathit{i}\mathit{u}\mathit{m}\mathbf{}\mathit{p}\mathit{e}\mathit{r}\mathit{c}\mathit{e}\mathit{n}\mathit{t}\mathit{a}\mathit{g}\mathit{e}& \mathbf{=}& \frac{\mathbf{C}\mathbf{o}\mathbf{n}\mathbf{v}\mathbf{e}\mathbf{r}\mathbf{s}\mathbf{i}\mathbf{o}\mathbf{n}\mathbf{}\mathbf{p}\mathbf{r}\mathbf{e}\mathbf{m}\mathbf{i}\mathbf{u}\mathbf{m}}{\mathbf{C}\mathbf{o}\mathbf{n}\mathbf{v}\mathbf{e}\mathbf{r}\mathbf{s}\mathbf{i}\mathbf{o}\mathbf{n}\mathbf{}\mathbf{v}\mathbf{a}\mathbf{l}\mathbf{u}\mathbf{e}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{82}\mathbf{.}\mathbf{55}}{\mathbf{610}\mathbf{.}\mathbf{00}}\\ & \mathbf{=}& \mathbf{13}\mathbf{.}\mathbf{53}\mathbf{\%}\\ & & \end{array}$