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# Constant Growth Rate Discounted Dividend Model

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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 for CGC's stock is 15% per year, and the expected ROE on the firm's future investments is 17% per year? Using the constant growth rate discounted dividend model,

a. What is the expected growth rate of dividends?

b. What is the model's estimate of the present value of the stock?

c. If the model is right, what is the expected price of a share a year from now?

d. 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:

i. The expected ROE on the firm's future investments.

ii. The market capitalization rate

iii. The dividend payout ratio.

#### Solution Preview

a. g = earnings retention ratio x ROE = .8 x .17 = .136 = 13.6%

b. P0 = D1/(k-g)

D1 = .2 x \$5 = \$1 per share

P0 = \$1/(.15 -.136) = \$1/.014 = \$71.43

c. The stock price grows at the same rate as dividends, i.e., 13.6% ...

#### Solution Summary

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\$2.19