DFB, Inc.,expects earnings this year of $5 per share, and it plans to pay a $3 dividend to
shareholders. DFB will retain $2 per share of its earnings to reinvest in new projects that
have an expected return of 15% 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.
(a) What growth rate of earnings would you forecast for DFB?
(b) If DFB's equity cost of capital is 12%, what price would you estimate for DFB stock?
(c) Suppose instead that DFB paid a dividend of $4 per share this year and retained only $1
per share in earnings. 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?

a) Growth rate of earnings

using the sustainable growth rate formula which is the maximum growth rate that a company can sustain without external financing:

Growth rate = ROE * (1 - retention rate)

= 15% * (1 - 40%)

= 15% * 60%

= 9%  

(Retention rate = 2/5 * 100 = 40%)

b) Price of equity using dividend growth model:

P₀ = D₀ (1 + g) / (re – g)

D₀ = the current dividend (whether just paid or just about to be paid)  = $3

g = the expected dividend future growth rate  = from A above (9%)

re = the cost of equity = 12%

= 3 (1 + 0.09) / (0.12 - 0.09)

= $109

c) Price of equity

P₀ = D₀ (1 + g) / (re – g)

= 4 (1 + 0.09) / (0.12 - 0.09)

= $145.33

Explanation:

At the estimated growth rate of 9%, should DFB increase the dividend payout, the price of equity would amount to $145.33 which is higher than the previous price of $109, so DFB is advised to raise its dividend