Question

Rubenstein Bros. Clothing is expecting to pay an annual dividend per share of $0.50 out of annual earnings per share of $5.00. Currently, Rubenstein Bros.' stock is selling for $26.00 per share. Adhering to the company's target capital structure, the firm has $9 million in total invested capital, of which 50% 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 13%, which is expected to continue this year and into the foreseeable future.

a) Based on this information, what long-run growth rate can the firm be expected to maintain? (Hint: g = Retention rate × ROE.) Do not round intermediate calculations. Round your answer to two decimal places. %
b) What is the stock's required return? Do not round intermediate calculations. Round your answer to two decimal places. %
c) If the firm changed its dividend policy and paid an annual dividend of $1.00 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 the firm's new expected long-run growth rate? Do not round intermediate calculations. Round your answer to two decimal places. %
d) If this plan is implemented, what must the firm's required return be? Do not round intermediate calculations. Round your answer to two decimal places. %
e) Suppose instead that the firm has decided to proceed with its original plan of disbursing $0.5 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 $26.00. In other words, for every $26.00 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 capitalization? (Hint: Remember market capitalization = P0 × number of shares outstanding.) Do not round intermediate calculations. Round your answer to two decimal places. %
f) If the plan in part d is implemented, how many new shares of stock will be issued? Do not round intermediate calculations. Round your answer to the nearest whole number. shares
g) If the plan in part d is implemented, by how much will the company's earnings per share be diluted? Do not round intermediate calculations. Round your answer to the nearest cent. $ per share

Answer 1

The expected long-run growth rate for Rubenstein Bros. is 11.70%, and the stock's required return is 13.69%. If the dividend policy changes to $1.00 per share, the new long-run growth rate would be 10.40%. For stock dividends, the dividend is 1.92% relative to market capitalization, with the actual earnings dilution being dependent on the number of shares outstanding.

Step-by-step explanation:

When analyzing the expected long-run growth rate for Rubenstein Bros. Clothing, we utilize the formula g = Retention rate × ROE. The retention rate can be found by subtracting the dividend payout ratio from 1 (since the dividend payout ratio is the proportion of earnings paid out as dividends). In this case, with an annual dividend of $0.50 and earnings per share of $5.00, the dividend payout ratio is $0.50 / $5.00 = 0.10. Therefore, the retention rate is 1 - 0.10 = 0.90. Multiplying this by the ROE of 13% gives us a growth rate of 0.90 × 0.13 = 0.117 or 11.70%.

The stock's required return can be calculated using the Gordon Growth Model, which states that P0 = D1 / (k - g), where P0 is the current stock price, D1 is the expected dividend next year, k is the required return, and g is the growth rate. Rearranging the formula to solve for k and using the current stock price of $26.00 and a growth rate of 11.70%, we get k = (D1 / P0) + g = ($0.50 / $26.00) + 0.117 = 0.1369, or the required return is 13.69%.

If the firm changes its dividend policy to an annual dividend of $1.00 per share, and the analysts expect no effect on the stock price or ROE, then the new retention rate would be (1 - $1.00 / $5.00) = 0.80, and the new long-run growth rate would be 0.80 × 0.13 = 0.104 or 10.40%. The required return would remain at 13.69% since the ROE and stock price are predicted not to change.

Regarding the stock dividend, if the firm proceeds with a $0.5 per share stock dividend, the market capitalization must be considered. Suppose there are n shares outstanding; then the market capitalization is $26.00 × n. The value of the total stock dividend would be $0.50 × n, so the stock dividend relative to the market capitalization would be ($0.50 × n) / ($26.00 × n) = 1.92%. Finally, to calculate the number of new shares to be issued, we divide the total dividend disbursement by the stock price: ($0.50 × n) / $26.00, which simplifies to n / 52. The earnings per share dilution would then be the original earnings per share minus the new earnings per share after considering the additional shares, which depends on the actual number of shares outstanding.