91Ó°ÊÓ

Fondren Exploration, Ltd., has 1,000 convertible bonds (\(1,000 par value) outstanding, each of which may be converted to 50 shares of stock. The \)1 million worth of bonds has 25 years to maturity. The current price of the stock is \(26 per share. The firm’s net income in the most recent fiscal year was \)270,000. The bonds pay 12 percent interest. The corporation has 150,000 shares of common stock outstanding. Current market rates on long-term nonconvertible bonds of equal quality are 14 percent. A 35 percent tax rate is assumed.

a. Compute diluted earnings per share.

b. Assume the bonds currently sell at a 5 percent conversion premium over conversion value (based on a stock price of \(26). However, as the price of the stock increases from \)26 to \(37 due to new events, there will be an increase in the bond price, and a zero conversion premium. Under these circumstances, determine the rate of return on a convertible bond investment that is part of this price change, based on the appreciation in value.

c. Now assume the stock price is \)16 per share because a competitor introduced a new product. Would the conversion value be greater than the pure bond value, based on the interest rates stated above? (See Table 16-3 in Chapter 16 to get the bond value without having to go through the actual computation.)

d. Referring to part c, if the convertible traded at a 15 percent premium over the conversion value, would the convertible be priced above the pure bond value?

e. If long-term interest rates in the market go down to 10 percent while the stock price is at $23, with a 6 percent conversion premium, what would the difference be between the market price of the convertible bond and the pure bond value? Assume 25 years to maturity, and once again use Table 16-3 for part of your answer.

Step by step solution

01

Definition of Earnings Per Share

A metric or financial calculation is done by a business entity for the determination of the profitability of each share is known as earnings per share. It is used for analysis by equity investors.

02

Step 2:Calculation of diluted earnings per share

$\begin{array}{c}\mathbf{D}\mathbf{i}\mathbf{l}\mathbf{u}\mathbf{t}\mathbf{e}\mathbf{d}\mathbf{e}\mathbf{a}\mathbf{r}\mathbf{n}\mathbf{i}\mathbf{n}\mathbf{g}\mathbf{s}\mathbf{p}\mathbf{e}\mathbf{r}\mathbf{s}\mathbf{h}\mathbf{a}\mathbf{r}\mathbf{e}\mathbf{=}\frac{\mathbf{A}\mathbf{d}\mathbf{j}\mathbf{u}\mathbf{s}\mathbf{t}\mathbf{e}\mathbf{d}\mathbf{e}\mathbf{a}\mathbf{r}\mathbf{n}\mathbf{i}\mathbf{n}\mathbf{g}\mathbf{s}\mathbf{a}\mathbf{f}\mathbf{t}\mathbf{e}\mathbf{r}\mathbf{t}\mathbf{a}\mathbf{x}}{\mathbf{A}\mathbf{d}\mathbf{j}\mathbf{u}\mathbf{s}\mathbf{t}\mathbf{e}\mathbf{d}\mathbf{s}\mathbf{h}\mathbf{a}\mathbf{r}\mathbf{e}\mathbf{s}}\\ \mathbf{=}\frac{\mathbf{\$}\mathbf{348}\mathbf{,}\mathbf{000}}{\mathbf{200}\mathbf{,}\mathbf{000}}\\ \mathbf{=}\mathbf{\$}\mathbf{1}\mathbf{.}\mathbf{74}\end{array}$

Working note:

$\begin{array}{c}\mathbf{A}\mathbf{d}\mathbf{j}\mathbf{u}\mathbf{s}\mathbf{t}\mathbf{e}\mathbf{d}\mathbf{s}\mathbf{h}\mathbf{a}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{=}\mathbf{C}\mathbf{o}\mathbf{m}\mathbf{m}\mathbf{o}\mathbf{n}\mathbf{s}\mathbf{t}\mathbf{o}\mathbf{c}\mathbf{k}\mathbf{o}\mathbf{u}\mathbf{s}\mathbf{t}\mathbf{a}\mathbf{n}\mathbf{d}\mathbf{i}\mathbf{n}\mathbf{g}\mathbf{+}\mathbf{C}\mathbf{o}\mathbf{n}\mathbf{v}\mathbf{e}\mathbf{r}\mathbf{t}\mathbf{i}\mathbf{b}\mathbf{l}\mathbf{e}\mathbf{s}\mathbf{e}\mathbf{c}\mathbf{u}\mathbf{r}\mathbf{i}\mathbf{t}\mathbf{i}\mathbf{e}\mathbf{s}\\ \mathbf{=}\mathbf{150}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{50}\mathbf{,}\mathbf{000}\\ \mathbf{=}\mathbf{200}\mathbf{,}\mathbf{000}\end{array}$

$\begin{array}{c}\mathbf{A}\mathbf{d}\mathbf{j}\mathbf{u}\mathbf{s}\mathbf{t}\mathbf{e}\mathbf{d}\mathbf{e}\mathbf{a}\mathbf{r}\mathbf{n}\mathbf{i}\mathbf{n}\mathbf{g}\mathbf{s}\mathbf{a}\mathbf{f}\mathbf{t}\mathbf{e}\mathbf{r}\mathbf{t}\mathbf{a}\mathbf{x}\mathbf{=}\mathbf{A}\mathbf{c}\mathbf{t}\mathbf{u}\mathbf{a}\mathbf{l}\mathbf{e}\mathbf{a}\mathbf{r}\mathbf{n}\mathbf{i}\mathbf{n}\mathbf{g}\mathbf{s}\mathbf{+}\mathbf{(}\mathbf{B}\mathbf{o}\mathbf{n}\mathbf{d}\mathbf{×}\mathbf{C}\mathbf{o}\mathbf{u}\mathbf{p}\mathbf{o}\mathbf{n}\mathbf{r}\mathbf{a}\mathbf{t}\mathbf{e}\mathbf{)}\mathbf{×}\mathbf{(}\mathbf{1}\mathbf{-}\mathbf{T}\mathbf{a}\mathbf{x}\mathbf{r}\mathbf{a}\mathbf{t}\mathbf{e}\mathbf{)}\\ \mathbf{=}\mathbf{\$}\mathbf{270}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{(}\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{000}\mathbf{,}\mathbf{000}\mathbf{×}\mathbf{0}\mathbf{.}\mathbf{12}\mathbf{)}\mathbf{×}\mathbf{(}\mathbf{1}\mathbf{-}\mathbf{0}\mathbf{.}\mathbf{35}\mathbf{)}\\ \mathbf{=}\mathbf{\$}\mathbf{270}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{\$}\mathbf{78}\mathbf{,}\mathbf{000}\\ \mathbf{=}\mathbf{\$}\mathbf{348}\mathbf{,}\mathbf{000}\end{array}$

03

 Step 3: Computation of rate of return

$\begin{array}{c}\mathbf{R}\mathbf{a}\mathbf{t}\mathbf{e}\mathbf{o}\mathbf{f}\mathbf{r}\mathbf{e}\mathbf{t}\mathbf{u}\mathbf{r}\mathbf{n}\mathbf{=}\frac{\mathbf{F}\mathbf{u}\mathbf{t}\mathbf{u}\mathbf{r}\mathbf{e}\mathbf{v}\mathbf{a}\mathbf{l}\mathbf{u}\mathbf{e}\mathbf{-}\mathbf{C}\mathbf{u}\mathbf{r}\mathbf{r}\mathbf{e}\mathbf{n}\mathbf{t}\mathbf{v}\mathbf{a}\mathbf{l}\mathbf{u}\mathbf{e}}{\mathbf{C}\mathbf{u}\mathbf{r}\mathbf{r}\mathbf{e}\mathbf{n}\mathbf{t}\mathbf{v}\mathbf{a}\mathbf{l}\mathbf{u}\mathbf{e}}\\ \mathbf{=}\frac{\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{850}\mathbf{-}\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{365}}{\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{365}}\\ \mathbf{=}\mathbf{35}\mathbf{.}\mathbf{53}\mathbf{\%}\end{array}$

Working note:

$\begin{array}{c}\mathbf{C}\mathbf{u}\mathbf{r}\mathbf{r}\mathbf{e}\mathbf{n}\mathbf{t}\mathbf{v}\mathbf{a}\mathbf{l}\mathbf{u}\mathbf{e}\mathbf{=}\mathbf{(}\mathbf{S}\mathbf{h}\mathbf{a}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{×}\mathbf{S}\mathbf{t}\mathbf{o}\mathbf{c}\mathbf{k}\mathbf{p}\mathbf{r}\mathbf{i}\mathbf{c}\mathbf{e}\mathbf{)}\mathbf{×}\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{p}\mathbf{r}\mathbf{e}\mathbf{m}\mathbf{i}\mathbf{u}\mathbf{m}\mathbf{)}\\ \mathbf{=}\mathbf{(}\mathbf{50}\mathbf{×}\mathbf{\$}\mathbf{26}\mathbf{)}\mathbf{×}\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{05}\mathbf{)}\\ \mathbf{=}\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{300}\mathbf{×}\mathbf{\$}\mathbf{1}\mathbf{.}\mathbf{05}\\ \mathbf{=}\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{365}\end{array}$

$\begin{array}{c}\mathbf{F}\mathbf{u}\mathbf{t}\mathbf{u}\mathbf{r}\mathbf{e}\mathbf{v}\mathbf{a}\mathbf{l}\mathbf{u}\mathbf{e}\mathbf{=}\mathbf{S}\mathbf{h}\mathbf{a}\mathbf{r}\mathbf{e}\mathbf{×}\mathbf{I}\mathbf{n}\mathbf{c}\mathbf{r}\mathbf{e}\mathbf{a}\mathbf{s}\mathbf{e}\mathbf{d}\mathbf{p}\mathbf{r}\mathbf{i}\mathbf{c}\mathbf{e}\mathbf{o}\mathbf{f}\mathbf{s}\mathbf{t}\mathbf{i}\mathbf{c}\mathbf{k}\\ \mathbf{=}\mathbf{50}\mathbf{×}\mathbf{\$}\mathbf{37}\\ \mathbf{=}\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{850}\end{array}$

04

Computation of straight conversion value

$\begin{array}{c}\mathbf{S}\mathbf{t}\mathbf{r}\mathbf{a}\mathbf{i}\mathbf{g}\mathbf{h}\mathbf{t}\mathbf{c}\mathbf{o}\mathbf{n}\mathbf{v}\mathbf{e}\mathbf{r}\mathbf{s}\mathbf{i}\mathbf{o}\mathbf{n}\mathbf{v}\mathbf{a}\mathbf{l}\mathbf{u}\mathbf{e}\mathbf{=}\mathbf{S}\mathbf{h}\mathbf{a}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{×}\mathbf{S}\mathbf{t}\mathbf{o}\mathbf{c}\mathbf{k}\mathbf{p}\mathbf{r}\mathbf{i}\mathbf{c}\mathbf{e}\\ \mathbf{=}\mathbf{50}\mathbf{×}\mathbf{\$}\mathbf{16}\\ \mathbf{=}\mathbf{\$}\mathbf{800}\end{array}$

05

Computation of straight conversion value

$\begin{array}{c}\mathbf{S}\mathbf{t}\mathbf{r}\mathbf{a}\mathbf{i}\mathbf{g}\mathbf{h}\mathbf{t}\mathbf{c}\mathbf{o}\mathbf{n}\mathbf{v}\mathbf{e}\mathbf{r}\mathbf{s}\mathbf{i}\mathbf{o}\mathbf{n}\mathbf{v}\mathbf{a}\mathbf{l}\mathbf{u}\mathbf{e}\mathbf{=}\mathbf{C}\mathbf{o}\mathbf{n}\mathbf{v}\mathbf{e}\mathbf{r}\mathbf{s}\mathbf{i}\mathbf{o}\mathbf{n}\mathbf{v}\mathbf{a}\mathbf{l}\mathbf{u}\mathbf{e}\mathbf{×}\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{P}\mathbf{r}\mathbf{e}\mathbf{m}\mathbf{i}\mathbf{u}\mathbf{m}\mathbf{)}\\ \mathbf{=}\mathbf{\$}\mathbf{800}\mathbf{×}\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{15}\mathbf{)}\\ \mathbf{=}\mathbf{\$}\mathbf{800}\mathbf{×}\mathbf{1}\mathbf{.}\mathbf{15}\\ \mathbf{=}\mathbf{\$}\mathbf{920}\end{array}$

06

Step 6:Computation of current value

$\begin{array}{c}\mathbf{C}\mathbf{u}\mathbf{r}\mathbf{r}\mathbf{e}\mathbf{n}\mathbf{t}\mathbf{v}\mathbf{a}\mathbf{l}\mathbf{u}\mathbf{e}\mathbf{=}\mathbf{(}\mathbf{S}\mathbf{h}\mathbf{a}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{×}\mathbf{S}\mathbf{t}\mathbf{o}\mathbf{c}\mathbf{k}\mathbf{p}\mathbf{r}\mathbf{i}\mathbf{c}\mathbf{e}\mathbf{)}\mathbf{×}\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{p}\mathbf{r}\mathbf{e}\mathbf{m}\mathbf{i}\mathbf{u}\mathbf{m}\mathbf{)}\\ \mathbf{=}\mathbf{(}\mathbf{50}\mathbf{×}\mathbf{\$}\mathbf{23}\mathbf{)}\mathbf{×}\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{06}\mathbf{)}\\ \mathbf{=}\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{150}\mathbf{×}\mathbf{\$}\mathbf{1}\mathbf{.}\mathbf{06}\\ \mathbf{=}\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{219}\end{array}$

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