Chapter 15, Problem 8P

ALTERNATIVE DIVIDEND POLICIES Rubenstein Bros. Clothing is expecting to pay an annual dividend per share of $0.75 out of annual earnings per share of $2.25. Currently, Rubenstein Bros.' stock is selling for $12.50 per share. Adhering to the company's target capital structure, the firm has $10 million in total invested capital, of which 40% is funded by debt. Assume that the firm's book value of equity equals its market value. In past years, the firm has earned a return on equity (ROE) of 18%, which is expected to continue this year and into the foreseeable future.

1. a. Based on this information, what long-run growth rate can the firm be expected to maintain? (Hint: g = Retention rate × ROE.)
2. b. What is the stock's required return?
3. c. If the firm changed its dividend policy and paid an annual dividend of $1.50 per share, financial analysts would predict that the change in policy will have no effect on the firm's stock price or ROE. Therefore, what must be the firm’s new expected long-run growth rate and required return?
4. d. Suppose instead that the firm has decided to proceed with its original plan of dis bursing $0.75 per share to shareholders, but the firm intends to do so in the form of a stock dividend rather than a cash dividend. The firm will allot new shares based on the current stock price of $12.50. In other words, for every $12.50 in dividends due to shareholders, a share of stock will be issued. How large will the stock dividend be relative to the firm's current market capitalist ion? (Hint. Remember that market capitalization = P₀× number of shares outstanding.)
5. e. If the plan in part d is implemented, how many new shares of stock will be issued, and by how much will the company’s earnings per share be diluted?

Summary Introduction

To calculate: Long run growth rate a firm can expect to maintain.

Dividend Policy:

It is the rules and regulations or protocols which a company sets to share its earning with its shareholders. Dividend payment includes payment to be made legally as well as financially.

Explanation of Solution

Calculate dividend payout ratio.

Given,

Dividend per share is $0.75.

Earnings per share are $2.25.

Formula to calculate dividend payout ratio,

$\text{Divident}\text{payout}\text{ratio}=\frac{\text{Dividend}\text{per}\text{share}}{\text{Earning}\text{per}\text{share}}$

Substitute $0.75 for dividend per share and $2.25 for earnings per share.

$\begin{array}{c}\text{Divident}\text{payout}\text{ratio}=\frac{\$0.75}{\$2.25}\\ =0.33\end{array}$

So, dividend payout ratio is 0.33.

Calculate growth rate.

Given,

Return on equity (ROE) is 18%.

Dividend payout ratio is 0.33.

Formula to calculate growth rate,

$\text{Growth}\text{rate}=\text{Return}\text{on}\text{Equity}\times \left(1-\text{Dividend}\text{payout}\text{ratio}\right)$

Substitute 18% for return on equity and 0.33 for dividend payout ratio.

$\begin{array}{c}\text{Growth}\text{rate}=18\%\times \left(1-0.33\right)\\ =12\%\end{array}$

Conclusion

Long run growth rate a firm can expect to maintain is 12%.

Summary Introduction

To calculate: Stock’s required return.

Explanation of Solution

Calculate required return.

Given,

Dividend per share is $0.75.

Stock selling per share is $12.50.

Growth rate is 0.12 or 12%.

Formula to calculate required return,

$\text{Rquired}\text{return}=\frac{\text{Earning}\text{per}\text{share}}{\text{Stock}\text{selling}\text{per}\text{share}}+\text{Growth}\text{rate}$

Substitute $0.75 for Dividend per share, $12.50 for Stock selling per share and 0.12 for Growth rate.

$\begin{array}{c}\text{Required}\text{return=}\frac{\$0.75}{\$12.50}+0.12\\ =0.06+0.12\\ =0.18\\ =18\%\end{array}$

Conclusion

Stock’s required return is 18%.

Summary Introduction

To calculate: The long run growth rate and the required return when annual pay of dividend is $1.50.

Explanation of Solution

Calculate dividend payout ratio.

Given,

Dividend per share is $1.50.

Earnings per share are $2.25.

Formula to calculate dividend payout ratio,

$\text{Divident}\text{payout}\text{ratio}=\frac{\text{Dividend}\text{per}\text{share}}{\text{Earning}\text{per}\text{share}}$

Substitute $1.50 for dividend per share and $2.25 for earnings per share.

$\begin{array}{c}\text{Divident}\text{payout}\text{ratio}=\frac{\$1.50}{\$2.25}\\ =0.66\end{array}$

So, dividend payout ratio is 0.66.

Calculate growth rate.

Given,

Return on equity (ROE) is 18%.

Dividend payout ratio is 0.66.

Formula to calculate growth rate,

$\text{Growth}\text{rate}=\text{Return}\text{on}\text{Equity}\times \left(1-\text{Dividend}\text{payout}\text{ratio}\right)$

Substitute 18% for return on equity and 0.33 for dividend payout ratio.

$\begin{array}{c}\text{Growth}\text{rate}=18\%\times \left(1-0.66\right)\\ =6\%\end{array}$

So growth rate is 6%.

Calculate required return.

Given,

Dividend per share is $1.50.

Stock selling per share is $12.50.

Growth rate is 0.06 or 6%.

Formula to calculate required return

$\text{Rquired}\text{return}=\frac{\text{Earning}\text{per}\text{share}}{\text{Stock}\text{selling}\text{per}\text{share}}+\text{Growth}\text{rate}$

Substitute $1.50 for dividend per share, $12.50 for Stock selling per share and 0.06 for growth rate.

$\begin{array}{c}\text{Required}\text{return=}\frac{\$1.50}{\$12.50}+0.06\\ =0.12+0.06\\ =0.18\\ =18\%\end{array}$

So, required return is 18%.

Conclusion

So, the long run growth rate is 6% while the required return is 18% at $1.50 dividend pay.

Summary Introduction

To calculate: Stock dividend at firm’s current market capitalization.

Explanation of Solution

Calculate amount of equity capital.

Given,

Total capital is $10,000,000.

Equity ratio is 0.06.

Formula to calculate amount of equity capital,

$\text{Amount}\text{of}\text{equity}\text{capital}=\text{Total}\text{capital}\times \text{Equity}\text{ratio}$

Substitute $10,000,000 for total capital and 0.06 for equity ratio.

$\begin{array}{c}\text{Amount}\text{of}\text{equity}\text{capital}=\$10,000,000\times 0.06\\ =\$6,000,000\end{array}$

So, amount of equity capital is $6,000,000.

Calculate amount of net income.

Given,

Equity capital is $6,000,000.

Return on equity is 0.18.

Formula to calculate amount of net income,

$\text{Net}\text{Income}=\text{Equity}\text{capital}\times \text{Return}\text{on}\text{Equity}$

Substitute $6,000,000 for equity capital and 0.18 for return on equity.

$\begin{array}{c}\text{Net}\text{Income}=\$6,000,000\times 0.18\\ =\$1,080,000\end{array}$

So, amount of net income is $1,080,000.

Calculate number of shares.

Given,

Earnings per share are $2.25.

Net income is $1,080,000.

Formula to calculate number of shares,

$\text{Earning}\text{per}\text{share}=\frac{\text{Net}\text{Income}}{\text{Number}\text{of}\text{shares}}$

Substitute $2.25 for earnings per share and $1,080,000 for net income.

$\begin{array}{c}\$2.25=\frac{\$1,080,000}{\text{Number}\text{of}\text{share}}\\ \text{Number}\text{of}\text{shares}=\frac{\$1,080,000}{\$2.25}\\ \text{Number}\text{of}\text{shares}=480,000\end{array}$

So, number of shares is 480,000 and total dividend is $360,000 $\left(\$0.75\times 480,000\right)$.

Calculate current market capitalization.

Given,

Net income is $6,000,000.

Dividend paid is $360,000.

Formula to calculate current market capitalization,

$\text{Current}\text{market}\text{capitalisation}=\frac{\text{Dividend}\text{paid}}{\text{Net}\text{income}}$

Substitute $6,000,000 for net income and $360,000 for dividend paid.

$\begin{array}{c}\text{Current}\text{market}\text{capitalisation=}\frac{\$360,000}{\$6,000,000}\\ =0.06\\ =6\%\end{array}$

Conclusion

Current market capitalization is 6%.

Summary Introduction

To calculate: New shares of stock issued and earnings of a company diluted per share.

Explanation of Solution

Calculate number of new shares.

Given,

Dividend paid is $360,000.

Price per share is $12.50.

Formula to calculate number of new shares,

$\text{Number}\text{of}\text{new}\text{shares}=\frac{\text{Dividend}\text{value}}{\text{Price}\text{per}\text{share}}$

Substitute $360,000 for dividend paid and $12.50 for price per share.

$\begin{array}{c}\text{Number}\text{of}\text{new}\text{shares}=\frac{\$360,000}{\$12.50}\\ =28,800\end{array}$

So, number of new shares is 28,800.

Calculate new earnings per share.

Given,

Net income is $1,080,000.

Old number of shares outstanding is 480,000.

New shares outstanding are 28,800.

Formula to calculate new earnings per share,

$\text{New}\text{earnings}\text{per}\text{share}=\frac{\text{Net}\text{Income}}{\left(\text{Old}\text{shares}\text{outstanding}+\text{New}\text{shares}\text{outstanding}\right)}$

Substitute $1,080,000 for net income, 480,000 for old shares outstanding and 28,800 for new shares outstanding.

$\begin{array}{c}\text{New}\text{earnings}\text{per}\text{share}=\frac{\$1,080,000}{\left(480,000+28,800\right)}\\ =\$2.1266\end{array}$

So, new EPS is $2.1266.

Calculate dilution of EPS.

Given,

Old EPS is $2.25.

New EPS is $2.1266.

Formula to calculate dilution of EPS,

$\text{Dilution}\text{of}\text{EPS}=\text{Old}\text{EPS}-\text{New}\text{EPS}$

Substitute $2.25 for old EPS and $2.1266 for new EPS.

$\begin{array}{c}\text{Dilution}\text{of}\text{EPS}=\$2.25-\$2.1266\\ =\$0.1234\end{array}$

Conclusion

New shares of stock will be issued are 28,800 and earnings of a company will be diluted per share is $0.1234.