Question

​DFB, Inc. expects earnings next year of $ 5.23 per​ share, and it plans to pay a $ 3.64 dividend to shareholders​ (assume that is one year from​ now). DFB will retain $ 1.59 per share of its earnings to reinvest in new projects that have an expected return of 15.7 % per year. Suppose DFB will maintain the same dividend payout​ rate, retention​ rate, and return on new investments in the future and will not change its number of outstanding shares. Assume next dividend is due in one year. a. What growth rate of earnings would you forecast for​ DFB? b. If​ DFB's equity cost of capital is 11.5 %​, what price would you estimate for DFB​ stock? c. Suppose instead that DFB paid a dividend of $ 4.64 per share at the end of this year and retained only $ 0.59 per share in earnings. That​ is, it chose to pay a higher dividend instead of reinvesting in as many new projects. If DFB maintains this higher payout rate in the​ future, what stock price would you estimate for the firm​ now? Should DFB raise its​ dividend?

Answer 1

We can calculate the desired results as follows:

Earnings per share for next year = $ 5.23

Dividend per share for next year = $ 3.64

Retained earnings per share for next year = $ 1.59

Retention ratio = Retained earnings per share for next year / Earnings per share for next year

= 1.59 / 5.23

= 0.3040 or 30.40%

Payout ratio = Dividend per share for next year / Earnings per share for next year

= 3.64 / 5.23

= 0.6960 or 69.60%

Expected return on equity = 15.70%

A) Growth rate of earnings = Expected return on equity * Retention ratio

= 15.70% * 30.40%

= 0.1570 * 0.3040

= 0.0477 or 4.77%

B) If cost of equity is 11.50%, then the price of DFB stock is as follows:

= Dividend per share for next year / ( cost of equity - Growth rate of earnings)

= 3.64 / ( 11.50% - 4.77% )

= 3.64 / 6.73%

= $ 54.086 or $ 54.09

C) New Dividend per share for next year = $ 4.64

Retained earnings per share for next year = $ 0.59

Retention ratio = Retained earnings per share for next year / Earnings per share for next year

= 0.59 / 5.23

= 0.1128 or 11.28%

New Growth rate of earnings = Expected return on equity * Retention ratio

= 15.70% * 11.28%

= 0.1570 * 0.1128

= 0.0177 or 1.77%

Price of DFB stock is as follows:

= Dividend per share for next year / ( cost of equity - Growth rate of earnings)

= 4.64 / ( 11.50% - 1.77% )

= 4.64 / 9.73%

= $ 47.688 or $ 47.69

When dividend was increased, the stock price reduced to $ 47.69 from $ 54.09.

So it is better to reinvest than not to increase the dividend.

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