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 stock if Cacique retains 50% of its earnings to finance future growth and these funds are invested in projects with a return on equity of 15 percent? Assume that right now Cacique has more projects and it has to retain 70% instead of 50%. What is the price of the stock now if the return on equity is still 15 percent?

(b)Assume right now that Cacique C.A. can earn 18% (ROE=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)?

Answer 1

According to Gordon growth model, we know that P0= D1/(r-g), where P0 is the current stock price, D1 is the expected dividend for next year, r = required return from stock, g = growth rate (Retention ratio* ROE).

Dividing above equation by E1 on both sides, we get, P0/E1= p/(r-g), where E1 is expected EPS for next year, p = payout ratio also equal to 1- Retention ratio

Therefore P0= [p/(r-g)]* EPS. Using this equation, we solve the problem

ROE EPS Required return (r) a) ROE 15% EPS 6.00 Required return (r) 15% Retention ratio Payout ratio Growth rate (RR) (p) (1-RR) =RR*ROE 50% 50% 7.5% 70% 30% 10.5% Price (P) Retention ratio (RR) 18% 6.00 15% Payout ratio (p) (1-RR) 50% 30% =[p/(r-g)]*EPS Growth Price (P) rate (g) =RR*ROE =[p/(r-g)]*EPS 9.0% 50 12.6% 75 50% 70% 40

c) In subdivision a), Required return of stock & ROE are same. Therefore whatever be the payout ratio, price of the stock remains the same, which is not the case in subdivision b). So the price increases with increase in retention ratio.