Answer:
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%
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:
[tex]Terminal \ Value = \dfrac{Dividend \ for \ the \ second \ year*(1+g)}{r-g}[/tex]
[tex]Terminal \ Value = \dfrac{4*(1+0.05)}{0.12-0.05}[/tex]
[tex]Terminal \ Value = \dfrac{4*(1.05)}{0.07}[/tex]
[tex]Terminal \ Value = \dfrac{4.2}{0.07}[/tex]
Terminal value = $60
Now; the current price of the stock is calculate as follows:
[tex]current \ price \ P = \dfrac{\$ 2}{(1+0.12)^1} + \dfrac{\$ 4 }{(1+0.12)^2} + \dfrac{\$ 60}{(1+0.12)^2}[/tex]
[tex]current \ price \ P = \dfrac{\$ 2}{1.12} + \dfrac{\$ 4 }{1.2544} + \dfrac{\$ 60}{1.2544}[/tex]
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 = [tex]\dfrac{\$ 4}{(1+0.12)^1}+ \dfrac{\$60}{(1+0.12)^1}[/tex]
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%
