91Ó°ÊÓ

Health Systems Inc. is considering a 15 percent stock dividend. The capital accounts are as follows:

Common stock (6,000,000 shares at \(10 par)	\)60,000,000
Capital in excess of par*	\(35,000,000
Retained earnings	\)75,000,000
Net worth	\(170,000,000

* The increase in capital in excess of par as a result of a stock dividend is equal to the shares created times (Market price - Par value).

The company’s stock is selling for \)32 per share. The company had total earnings of \(19,200,000 with 6,000,000 shares outstanding and earnings per share were \)3.20. The firm has a P/E ratio of 10.

a. What adjustments would have to be made to the capital accounts for a 15 percent stock dividend? Show the new capital accounts.

b. What adjustments would be made to EPS and the stock price? (Assume the P/E ratio remains constant).

c. How many shares would an investor have if he or she originally had 80?

d. What is the investor’s total investment worth before and after the stock dividend if the P/E ratio remains constant? (There may be a slight difference due to rounding.)

e. Assume Mr. Heart, the president of Health Systems, wishes to benefit stockholders by keeping the cash dividend at a previous level of \(1.25 in spite of the fact that the stockholders now have 15 percent more shares. Because the cash dividend is not reduced, the stock price is assumed to remain at \)32.

What is an investor’s total investment worth after the stock dividend if he/she had 80 shares before the stock dividend?

f. Under the scenario described in part e, is the investor better off?

g. As a final question, what is the dividend yield on this stock under the scenario described in part e?

Step by step solution

01

Changes in capital accounts

The balance of common stock will be $69,000,000, capital in excess of par will be $54,800,000, and the balance of retained earnings will be $46,200,000.

Common stock (6,900,000 shares at $10 par)	$69,000,000
Capital in excess of par*	$54,800,000
Retained earnings	$46,200,000
Net worth	$170,000,000

$$\begin{gathered} \mathbf{Number}\mathbf{}\mathbf{of}\mathbf{}\mathbf{shares}\mathbf{=}\mathbf{Existing}\mathbf{}\mathbf{shares}\mathbf{×}\mathbf{Stock}\mathbf{}\mathbf{split}\mathbf{}\mathbf{ratio} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{6}\mathbf{,}\mathbf{000}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{(}\mathbf{6}\mathbf{,}\mathbf{000}\mathbf{,}\mathbf{000}\mathbf{×}\mathbf{15}\mathbf{\%}\mathbf{)} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{6}\mathbf{,}\mathbf{900}\mathbf{,}\mathbf{000} \end{gathered}$$

$$\begin{gathered} \mathbf{Capital}\mathbf{}\mathbf{in}\mathbf{}\mathbf{excess}\mathbf{}\mathbf{of}\mathbf{}\mathbf{par}\mathbf{=}\mathbf{Initial}\mathbf{}\mathbf{balance}\mathbf{+}\mathbf{[}\mathbf{Shares}\mathbf{}\mathbf{issued}\mathbf{×}\left(\mathrm{Market}\mathrm{price}-\mathrm{Par}\mathrm{value}\right)\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{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{35}\mathbf{,}\mathbf{000}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{[}\mathbf{900}\mathbf{,}\mathbf{000}\mathbf{×}\left(\$32-\$10\right)\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{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{35}\mathbf{,}\mathbf{000}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{[}\mathbf{900}\mathbf{,}\mathbf{000}\mathbf{×}\mathbf{\$}\mathbf{22}\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{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{35}\mathbf{,}\mathbf{000}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{\$}\mathbf{19}\mathbf{,}\mathbf{800}\mathbf{,}\mathbf{000} \\ \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{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{54}\mathbf{,}\mathbf{800}\mathbf{,}\mathbf{000} \end{gathered}$$

$$\begin{gathered} \mathbf{\text{Retained earnings}}\mathbf{=}\mathbf{\text{Beginning balance}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{-}\mathbf{\text{Transfer to common stock}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{-}\mathbf{\text{Transfer to capital in excess of par}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{75}\mathbf{,}\mathbf{000}\mathbf{,}\mathbf{000}\mathbf{-}\mathbf{\$}\mathbf{9}\mathbf{,}\mathbf{000}\mathbf{,}\mathbf{000}\mathbf{-}\mathbf{\$}\mathbf{19}\mathbf{,}\mathbf{800}\mathbf{,}\mathbf{000} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{46}\mathbf{,}\mathbf{200}\mathbf{,}\mathbf{000} \end{gathered}$$

02

Calculation of changes in EPS and stock price

The EPS will be $2.78 and the stock price will be $27.8.

$$\begin{gathered} \mathbf{\text{EPS}}\mathbf{=}\frac{\mathbf{\text{Earnings}}}{\mathbf{\text{Shares outstanding}}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{\$}\mathbf{19}\mathbf{,}\mathbf{200}\mathbf{,}\mathbf{000}}{\mathbf{6}\mathbf{,}\mathbf{900}\mathbf{,}\mathbf{000}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{2}\mathbf{.}\mathbf{78} \end{gathered}$$

role="math" localid="1651043927972" $$\begin{gathered} \mathbf{\text{Stock price}}\mathbf{=}\mathbf{\text{EPS}}\mathbf{×}\frac{\mathbf{\text{P}}}{\mathbf{E}}\mathbf{\text{ratio}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{2}\mathbf{.}\mathbf{78}\mathbf{×}\mathbf{10} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{27}\mathbf{.}\mathbf{8} \end{gathered}$$

03

Calculation of the number of shares held by an investor

The investor will own 92 shares.

$$\begin{gathered} \mathbf{\text{Number of shares}}\mathbf{=}\mathbf{\text{Shares held}}\mathbf{×}\left(\text{100}+\text{Stock dividend ratio}\right) \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{80}\mathbf{×}\left(100+15\%\right) \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{80}\mathbf{×}\mathbf{115}\mathbf{\%} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{92} \end{gathered}$$

04

Calculation of investment worth before and after the stock dividend

The investment worth before stock dividend will be $2,560 and after stock dividend will be $2,557.6.

$$\begin{gathered} \mathbf{\text{Investment worth}}\mathbf{=}\mathbf{\text{Shares held}}\mathbf{×}\mathbf{\text{Market price}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{80}\mathbf{×}\mathbf{\$}\mathbf{32} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{2}\mathbf{,}\mathbf{560} \end{gathered}$$

$$\begin{gathered} \mathbf{\text{Investment worth}}\mathbf{=}\mathbf{\text{Shares held}}\mathbf{×}\mathbf{\text{Stock price}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{92}\mathbf{×}\mathbf{\$}\mathbf{27}\mathbf{.}\mathbf{8} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{2}\mathbf{,}\mathbf{557}\mathbf{.}\mathbf{6} \end{gathered}$$

05

Calculation of investment worth before stock dividend

The investment worth before stock dividend will be $2,944 when the stock price remains same after stock dividend.

$$\begin{gathered} \mathbf{\text{Investment worth}}\mathbf{=}\mathbf{\text{Shares held}}\mathbf{×}\mathbf{\text{Stock price}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{92}\mathbf{×}\mathbf{\$}\mathbf{32} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{2}\mathbf{,}\mathbf{944} \end{gathered}$$

06

Impact on investor’s worth when the stock price remains constant

The investors will be benefitted if the cash dividend remains constant as the investor will get more cash dividends and also the investment worth will increase by $386.40.

07

Calculation of dividend yield if the stock price remains constant

The dividend yield will be 3.9%.

$$\begin{gathered} \mathbf{\text{Dividend yield}}\mathbf{=}\frac{\mathbf{\text{Cash dividend}}}{\mathbf{\text{Market price}}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{\$}\mathbf{1}\mathbf{.}\mathbf{25}}{\mathbf{\$}\mathbf{32}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{3}\mathbf{.}\mathbf{9}\mathbf{\%} \end{gathered}$$

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