Question

1. The Constant Growth Corporation (CGC) has expected earnings per share (E₁) of $5. It has a history of paying cash dividends equal to 20% of earnings. The market capitalization rate (discount rate) for CGC’s stock is 15% per year, and the expected return on the firm’s future investments is 17% per year? Based on the constant-growth DDM
   1. What is the expected growth rate of dividends?
   2. What is the model’s estimate of the present value of the stock?
   3. If the model is right, what is the expected price of a share a year from now?
   4. Suppose that the current price of a share is $50. By how much would you have to adjust each of the following model parameters to “justify” this observed price:
      1. the expected return on the firm’s future investments,
      2. the market capitalization rate (discount rate), and
      3. the dividend payout ratio.

Answer 1

Dividend Payout	20%
Retained earnings	80%
Future investment rate	17%
Growth rate=	Retained earnings * Future investment rate
Growth rate=	80%*17%
Growth rate=	13.600%
Share price=	Dividend expected next year/(Discount rate - growth rate)
Share price=	(5*20%)/(15%-13.60%)
Share price=	71.43
Share price 1 year from now
Expected dividend after 1 year	5*(1+13.60%)*20%
Expected dividend after 1 year	1.136
Share price=	1.136/(15%-13.60%)
Share price=	81.14
Let's adjust variables with the share price of 50
Change the future investment rate
50=	(5*20%)/(15%-g)
15%-g=	1/50
15%-g=	2.00%
g=	13%
Retained earnings	80%
Future investment rate	13%/80%
Future investment rate	16.2500%
Change the discount rate
50=	(5*20%)/(D-13.60%)
D-13.6%=	1/50
D-13.6%=	2%
D=	15.60%
Change dividend payout ratio
50=	(5*20%)/(15%-g)
15%-g=	1/50
15%-g=	2%
g=	13%
g=	Retention ratio * future investment rate
13%=	Retention ratio * 17%
Retention ratio=	13%/17%
Retention ratio=	76.47%