How to find the value of a stock?

How do you find the value per share stock?

• A stock company is expected to pay $1.50 per share dividend at the end of this year. The didvidend is expeceted to grow at a constant rate of 7% a year. The required rate of return on the stock is 15%. What is the value per share of the stock?

• Answer:

  What they are trying to teach you is usually called the DDM or Gordon's formula which is: P0 = D1 / ( r - g ) Notice that the dividend is stated as D1, that's because it's the next dividend. The problem will either be stated as the next dividend or that a dividend has just passed. As you can see, the relationship between the next dividend and the dividend just passed is D1 = D0 * ( 1 + g ) What this equation really is, is the discounted cash flow of all the dividends to eternity. You can think of it as how much you would have to deposit in a savings account at the required rate of return so that you can withdraw the dividend every year. Obviously that would be saving the amount needed to save up for each dividend. If we express this in terms of a dividend just passed, it's: P0 = D0 * ( 1 + g ) / ( 1 + r ) + D0 * ( 1 + g )^2 / ( 1 + r )^2 + D0 * ( 1 + g )^3 / ( 1 + r )^3 + ... to infinity You factor out D0 * ( 1 + g ) / ( 1 + r ) and get: P0 = D0 * ( 1 + g ) / ( 1 + r ) * [ 1 + ( 1 + g ) / (1 + r ) + ( 1 + g )^2 / ( 1 + r )^2 + ... to inifinity ] Keep in mind that ( 1 + g )^n / ( 1 + r )^n = [ ( 1 + g ) / ( 1 + r ) ]^n You will notice that what is in the square brackets is a summation of an infinite geometric sequence therefore instead of calculating the amount needed for each and every dividend payment, you can rewrite the equation as: P0 = [ D0 * ( 1 + g ) / ( 1 + r ) ] / [ 1 - ( 1 + g ) / ( 1 + r ) ] .: P0 = D0 * ( 1 + g ) / [ ( 1 + r ) - ( 1 + g ) ] P0 = D0 * ( 1 + g ) / ( 1 + r - 1 - g ) P0 = D0 * ( 1 + g ) / ( r - g ) Since we know that D1 = D0 * ( 1 + g ), this gives you the equation they expect you to memorize which is: P0 = D1 / ( r - g ) and your answer is: P0 = $1.50 / ( 0.15 - 0.07 ) .: P0 = $18.75 But you must understand that this is simply the highest price that would still give you the 15% per annum return which you require and only if the future dividends are actually paid as expected so it's really only a guideline as to the value of the stock.