Question

# A stock just paid a dividend of \$2 per share. This dividend has been growing at...

A stock just paid a dividend of \$2 per share. This dividend has been growing at a rate of 3.75% per year. The return on the equity market is 10%, and the return on the short-term treasuries are 3%. If the company’s beta is 1.2, what is the price of the stock 5 years from now?

** If you can please explain. Thanks!

We can find the value of stock after 5 years by using the constant Dividend growth model formula

Price of stock after 5th year = Dividend at the end of year 6 / (Required Return - Constant growth Rate)

Dividend will grow at a constant rate of 3.75%, so dividend at the end of 6th year will be

= Present Dividend ( 1 + Constant growth rate)^6

= 2 ( 1 + 3.75%)^6

= 2.4943

Dividend at the end of 6th year.

Required Return can be derived by using CAPM formula:

Required Return = Risk Free Rate + Beta (Return on Equity Market - Risk Free Rate)

Short Term Securities is considered as the Risk Free Rate

Required Return = 3 + 1.2 ( 10 - 3)

= 11.4%

Price of stock after 5th year = Dividend at the end of year 6 / (Required Return - Constant growth Rate)

= 2.4943 / (11.4% - 3.75%)

= 32.6052

The stock price at the end of 5th year is \$32.6052

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