91Ó°ÊÓ

These bonds are convertible credits that can be traded for pre-determined shares, giving investors the alternative to change over them. Ordinarily, companies issue these bonds to lower their coupon rate on debt.

Given,

Par value = $1,000

Coupon rate = 10%

Maturity years = 20 years

Conversion price = $55

Selling price = $48 per share

Current yield = 12%

Calculation of conversion value

$\begin{array}{rcl}\mathit{N}\mathit{u}\mathit{m}\mathit{b}\mathit{e}\mathit{r}\mathbf{}\mathit{o}\mathit{f}\mathbf{}\mathit{s}\mathit{h}\mathit{a}\mathit{r}\mathit{e}\mathit{s}\mathbf{}\mathit{i}\mathit{s}\mathit{s}\mathit{u}\mathit{e}\mathit{d}& \mathbf{=}& \frac{\mathbf{P}\mathbf{a}\mathbf{r}\mathbf{}\mathbf{v}\mathbf{a}\mathbf{l}\mathbf{u}\mathbf{e}}{\mathbf{C}\mathbf{o}\mathbf{n}\mathbf{v}\mathbf{e}\mathbf{r}\mathbf{s}\mathbf{i}\mathbf{o}\mathbf{n}\mathbf{}\mathbf{p}\mathbf{r}\mathbf{i}\mathbf{c}\mathbf{e}}\\ & \mathbf{=}& \frac{\mathbf{1}\mathbf{,}\mathbf{000}}{\mathbf{55}}\\ & \mathbf{=}& \mathbf{18}\mathbf{.}\mathbf{19}\\ & & \end{array}$

$\begin{array}{rcl}\mathit{C}\mathit{o}\mathit{n}\mathit{v}\mathit{e}\mathit{r}\mathit{s}\mathit{i}\mathit{o}\mathit{n}\mathbf{}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e}& \mathbf{=}& \mathit{N}\mathit{u}\mathit{m}\mathit{b}\mathit{e}\mathit{r}\mathbf{}\mathit{o}\mathit{f}\mathbf{}\mathit{s}\mathit{h}\mathit{a}\mathit{r}\mathit{e}\mathit{s}\mathbf{×}\mathit{S}\mathit{e}\mathit{l}\mathit{l}\mathit{i}\mathit{n}\mathit{g}\mathbf{}\mathit{p}\mathit{r}\mathit{i}\mathit{c}\mathit{e}\mathbf{}\mathit{o}\mathit{f}\mathbf{}\mathit{c}\mathit{o}\mathit{m}\mathit{m}\mathit{o}\mathit{n}\mathbf{}\mathit{s}\mathit{t}\mathit{o}\mathit{c}\mathit{k}\\ & \mathbf{=}& \mathbf{18}\mathbf{.}\mathbf{19}\mathbf{×}\mathbf{\$}\mathbf{48}\\ & \mathbf{=}& \mathbf{\$}\mathbf{873}\mathbf{.}\mathbf{12}\\ & & \end{array}$

Calculation of pure bond

$\begin{array}{rcl}\mathit{I}\mathit{n}\mathit{t}\mathit{e}\mathit{r}\mathit{e}\mathit{s}\mathit{t}\mathbf{}\mathit{a}\mathit{m}\mathit{o}\mathit{u}\mathit{n}\mathit{t}& \mathbf{=}& \mathit{P}\mathit{a}\mathit{r}\mathbf{}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e}\mathbf{×}\mathit{C}\mathit{o}\mathit{u}\mathit{p}\mathit{o}\mathit{n}\mathbf{}\mathit{r}\mathit{a}\mathit{t}\mathit{e}\\ & \mathbf{=}& \mathbf{1}\mathbf{,}\mathbf{000}\mathbf{×}\mathbf{10}\mathbf{\%}\\ & \mathbf{=}& \mathbf{100}\\ & & \end{array}$

Present value of Coupons

$\begin{array}{rcl}\mathit{P}\mathit{r}\mathit{e}\mathit{s}\mathit{e}\mathit{n}\mathit{t}\mathbf{}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e}\mathbf{}\mathit{o}\mathit{f}\mathbf{ }\mathit{c}\mathit{o}\mathit{u}\mathit{p}\mathit{o}\mathit{n}\mathit{s}& \mathbf{=}& \frac{\mathbf{I}\mathbf{n}\mathbf{t}\mathbf{e}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{t}\mathbf{}\mathbf{a}\mathbf{m}\mathbf{o}\mathbf{u}\mathbf{n}\mathbf{t}}{\mathbf{2}}\mathbf{×}\mathit{P}\mathit{V}\mathit{F}\mathit{I}\mathit{A}\mathbf{@}\frac{\mathbf{12}\mathbf{\%}}{\mathbf{2}}\mathbf{,}\left(Maturityyears×2\right)\\ & \mathbf{=}& \frac{\mathbf{100}}{\mathbf{2}}\mathbf{×}\mathit{P}\mathit{V}\mathit{I}\mathit{F}\mathit{A}\mathbf{@}\mathbf{6}\mathbf{\%}\mathbf{,}\left(20×2 i.e,40\right)\mathit{y}\mathit{e}\mathit{a}\mathit{r}\mathit{s}\\ & \mathbf{=}& \mathbf{50}\mathbf{×}\mathbf{15}\mathbf{.}\mathbf{0463}\\ & \mathbf{=}& \mathbf{752}\mathbf{.}\mathbf{315}\\ & & \end{array}$

Calculating the present value of maturity value

$\begin{array}{rcl}\mathit{V}\mathit{a}\mathit{l}\mathit{u}\mathit{e}\mathbf{}\mathit{o}\mathit{f}\mathbf{}\mathit{m}\mathit{a}\mathit{t}\mathit{u}\mathit{r}\mathit{i}\mathit{t}\mathit{y}& \mathbf{=}& \mathit{P}\mathit{a}\mathit{r}\mathbf{}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e}\mathbf{×}\mathit{P}\mathit{V}\mathit{F}\mathit{I}\mathbf{@}\frac{\mathbf{12}\mathbf{\%}}{\mathbf{2}}\mathbf{,}\left(Maturityyears×2\right)\\ & \mathbf{=}& \mathbf{1}\mathbf{,}\mathbf{000}\mathbf{×}\mathit{P}\mathit{V}\mathit{I}\mathit{F}\mathbf{@}\mathbf{6}\mathbf{\%}\mathbf{,}\left(20×2 i.e,40\right)\mathit{y}\mathit{e}\mathit{a}\mathit{r}\mathit{s}\\ & \mathbf{=}& \mathbf{1}\mathbf{,}\mathbf{000}\mathbf{×}\mathbf{0}\mathbf{.}\mathbf{0972}\\ & \mathbf{=}& \mathbf{97}\mathbf{.}\mathbf{2}\\ & & \end{array}$

Calculating Pure bond value

$\begin{array}{rcl}\mathit{P}\mathit{u}\mathit{r}\mathit{e}\mathbf{}\mathit{b}\mathit{o}\mathit{n}\mathit{d}\mathbf{}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e}& \mathbf{=}& \mathit{P}\mathit{r}\mathit{e}\mathit{s}\mathit{e}\mathit{n}\mathit{t}\mathbf{}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e}\mathbf{}\mathit{o}\mathit{f}\mathbf{}\mathit{c}\mathit{o}\mathit{u}\mathit{p}\mathit{o}\mathit{n}\mathit{s}\mathbf{+}\mathit{P}\mathit{r}\mathit{e}\mathit{s}\mathit{e}\mathit{n}\mathit{t}\mathbf{}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e}\mathbf{ }\mathit{o}\mathit{f}\mathbf{}\mathit{m}\mathit{a}\mathit{t}\mathit{u}\mathit{r}\mathit{i}\mathit{t}\mathit{y}\mathbf{}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e}\\ & \mathbf{=}& \mathbf{752}\mathbf{.}\mathbf{315}\mathbf{+}\mathbf{97}\mathbf{.}\mathbf{2}\\ & \mathbf{=}& \mathbf{849}\mathbf{.}\mathbf{515}\\ & & \end{array}$

Note: PVIF = Present Value Interest Factor

And PVIFA = Present Value Interest Factor of Annuity.