Question

Note: If not otherwise stated, assume that:

• Firms make annual dividend payments

• Stock prices are the present value of all future dividends and don’t include dividends that were just paid.

Analysts expect that Cotton Corp. (CC) will report earnings of $5 million one year from today. CC’s policy is to pay out 60% of its earnings in dividends (it just paid its dividends for this year). CC’s return on equity (ROE) is 9%, and its required rate of return is 12%. The company has 3 million shares outstanding. Assume that the numbers above are representative of the foreseeable future.

a) What is CC’s expected rate of dividend growth?

Select one:

5.4%

4.8%

3.6%

7.2%

0.0%

9.0%

12.0%

40.0%

b) Suppose the board of directors decided to change the dividend policy and pay out 100% of CC’s earnings in dividends (i.e., CC would pay out the full $5 million in dividends next year and then maintain this dividend policy forever). What would be the stock price under this dividend policy? Would shareholders benefit from this decision?

Select one:

a. No, because NPVGO > 0

b. No, because r < ROE

c. No, because r > ROE

d. No, the stock price would drop to $11.9

e. Yes, because NPVGO > 0

f. Yes, because the firm's growth rate will go up

g. Yes, because the stock price would increase to $13.9

h. Insufficient information

NOTE: Please show all the work, without using excel, unless necessary. (step by step with equations) Thanks!

Answer 1

Sol (a) To calculate CC's expected rate of dividend growth we would use the Sustainable Growth Rate Formula = ROE* (1-Dividend Payout Ratio). In our case ROE = 9%, Dividend Payout is 60% or 0.6 thus inputting these variables in the formula we would get = 9%*(1-0.6) = 3.60%

Sol (b) Stock price can be valued by using the Dividend Discount Model where P = D1 / r-g; Here P= Current Company's Stock Price; D1= Next Year Dividends; r= Company's Required Rate and G= Dividend Growth Rate.

Thus when Dividend was growing at 3.60% at a sustainable growth rate the Price of Share = D1= 60% of Future Earnings = 60%*5mn = $ 3mn; R = 12% and G= 3.60%. thus substituting the values in the formula would yield = 3000000/ 12%- 3.60% = 35714285.71 this when divided by 3000000 outstanding shares will provide share price of one share = $11.9

Now when Dividend growing at 0% in case 2 the Price of Share = D1= 100% of Future Earnings = 100%*5mn = $ 5mn; R = 12% and G= 0%. thus substituting the values in the formula would yield = 5000000/ 12% = 41666666.67 this when divided by 3000000 outstanding shares will provide share price of one share = $13.9

Thus our answer should be Yes, because the stock price will increase to $13.9