the stock of cacique corp is expected to have earnings per share (EPS) next year

Question

the stock of cacique corp is expected to have earnings per share (EPS) next year of $6 per share. The required return for its stock is 15 %

a) what is the price of the stockk if Cacique retains 50% of its earnings to finance future growth and these funds aare invested in projects with a return on eauity (ROE) of 15%? Assume that right now Ccacique has more projects and it has to retain 70% instead of 50%. What is the price of stock now?

b) assume right now that Cacique C.A. can earn a ROE of 18% on its investments. What is the price if the retention ratio is 50% What is the price if Cacique retains 70%?

c. can you explain the difference obtained in the results of (a) and (b)?

Explanation / Answer

a) Current Price = D/Ke + (r/Ke)(E-D)/Ke

= 3/0.15 + (0.15/0.15)(6-3)/0.15 = 20 + 20 = 40 (So current price is 40 per share at 50% Dividend payout)

Now if Payout is 30% and 70 % is retained then Price=

= 1.8/0.15+ (0.15/0.15)(6-1.8)/0.15 = 12 + 28 = 40

There would be no change in price even if payout is only 30%.

b) Now if ROE is 18%

Price when Retention is 50%

P = 3/0.15 + (0.18/0.15)(6-3)/0.15 = 20 + 24 = 44

Price when retention is 70%

P = 1.8/0.15 + (0.18/0.15)(6-1.8)/0.15 = 12 + 33.6 = 45.6

c) When the firm's cost of capital and required rate of return are same i.e. 15% then no matters whether dividend is distributed or retained because ultimately investors and company are earning same return. So price would remain same.

But when ROE is 18 % which is more than Company's rate of return which means if more dividend is distributed then investors has better earning prospects than company. So price of share goes up by 4 when dividend payout is 50% and by 5.6 when dividend payout is 70%

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