Question

A company will pay a $2 per share dividend in 1 year. The dividend in 2 years will be $4 per share, and it is expected that dividends will grow at 2% per year thereafter. The expected rate of return on the stock is 12%. a. What is the current price of the stock? (Do not round intermediate calculations. Round your answer to 2 decimal places.) b. What is the expected price of the stock in a year? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

Answer:

(a) $ 46.43

(b) $ 50.00

Explanation:

In 1 year the dividend is:

D1 = $2

In 2 years, the dividend is:

D2 = $4

(a)

Now,

⇒  $D3=D2\times (1+g)$

          $=4\times (1+4 \ percent)$

          $=4.16$ ($)

In 2 years, the price will be:

⇒  $P2=\frac{D3}{(r-g)}$

          $=\frac{4.16}{12 -14}$

          $=52.00$ ($)

Today's price will be:

⇒  $P0=\frac{D1}{(r-g)}+\frac{D2+P2}{(1+r)^2}$

          $=\frac{2}{1.12}+\frac{(4+52) }{1.12^2}$

          $=46.43$ ($)

(b)

In 1 year, the price will be:

⇒  $P1=\frac{(D2+P2)}{(1+r)}$

          $=\frac{4+52}{1.12}$

          $=50.00$ ($)