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 5% per year thereafter. The expected rate of return on the stock is 12%.

Required:
a. What is the current price of the stock?
b. What is the expected price of the stock in a year?
c. Show that the expected return, 12%, equals dividend yield plus capital appreciation.

Answer 1

current price P = $ 52.81

The expected price of the stock after one year = $57.16

The Total expected return for any investor after one year = 12%

Step-by-step explanation:

Given that:

Dividend paid in 1 year = $2/ share

Dividend paid in 2 years = $4/share

Expect growth rate of the dividends g = 5% = 0.05

Expected rate of return on the stock r =12% = 0.12

Required:

a. What is the current price of the stock?

To calculate the current price of the stock ; we need to first determine the terminal value of the stock which can be done by using the formula:

`Terminal \ Value = (Dividend \ for \ the \ second \ year*(1+g))/(r-g)`

`Terminal \ Value = (4*(1+0.05))/(0.12-0.05)`

`Terminal \ Value = (4*(1.05))/(0.07)`

`Terminal \ Value = (4.2)/(0.07)`

Terminal value = $60

Now; the current price of the stock is calculate as follows:

`current \ price \ P = (\$ 2)/((1+0.12)^1) + (\$ 4 )/((1+0.12)^2) + (\$ 60)/((1+0.12)^2)`

`current \ price \ P = (\$ 2)/(1.12) + (\$ 4 )/(1.2544) + (\$ 60)/(1.2544)`

current price P = $1.79 + $3.19 + $47.83

current price P = $ 52.81

b) What is the expected price of the stock in a year?

The expected price of the stock after one year =
`(\$ 4)/((1+0.12)^1)+ (\$60)/((1+0.12)^1)`

The expected price of the stock after one year = $3.58 + $53.58

The expected price of the stock after one year = $57.16

c. Show that the expected return, 12%, equals dividend yield plus capital appreciation.

We understand now that the current price of the sock = $52.81

and the expected price of the stock after one year = $57.16 ; so any investor who purchased the stock at the current price will receive a dividend of $2 after one year.

Hence;

The Total expected return for any investor after one year =( (price after one year - current price ) + Dividend received) /current price

The Total expected return for any investor after one year =( ($57.16 - $52.81)+ $2 )/$52.81

The Total expected return for any investor after one year = ($4.35+$2)/$52.81

The Total expected return for any investor after one year = 0.12

The Total expected return for any investor after one year = 12%