Question

Manpower Electric Company has 6 percent convertible bonds outstanding. Each bond has a \(1,000 par value. The conversion ratio is 20, the stock price \)36, and the bonds mature in 16 years.

1. What is the conversion value of the bond?
2. Assume after one year, the common stock price falls to $30.50. What is the conversion value of the bond?
3. Also, assume after one year, interest rates go up to 10 percent on similar bonds. There are 15 years left to maturity. What is the pure value of the bond? Use semiannual analysis.
4. Will the conversion value of the bond (part b) or the pure value of the bond (part c) have a stronger influence on its price in the market?
5. If the bond trades in the market at its pure bond value, what would be the conversion premium (stated as a percentage of the conversion value)?

Short answer

1. Conversion value is $720
2. Conversion value is$610
3. The pure value of the bond is$692.55
4. The stock will start to have a greater impact than the pure bond value when it approaches the parity threshold of$34.63,which is where the stock price is now.
5. The conversion premium is$82.55

Step-by-step solution

Meaning of Conversion Price

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.

(a) Computing the conversion value of the bond.

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

(b) Calculating the conversion value of the bond

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

(c) Calculating the pure value of the bond

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

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

Further,

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

(d) Explaining the conversion value of the bond (part b) or the pure value of the bond (part c) has a stronger influence on its price in the market

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.

(e) Computing conversion premium

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

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