Question

A stock is expected to have net income of $2 per share by the end of the coming year. Dividends are expected to grow at a constant rate g per year forever. You know that the company pays out 80% of its earnings as didvidend and has a constant return on equity of 30%. The stock's required return is 12%. What is the fair price for this stock today? What is the present value of growth opportunities? 

Use 3 decimal points in your calculations.

Answer 1

With the given information, we can calculate the fair price of the stock and the present value of growth opportunities as follows

Expected Dividend by the end of year = $ 2

Return on equity = 30%

Required rate of return = 12%

Dividend Pay out ratio = 80% or 0.80

Retention Ratio = (1 - Dividend Pay out ratio)

= 1 - 0.80 = 0.20 or 20%

In order to understand dividend pay out and retention ratio, lets take an example where we assume that a company earns $ 100 during the year, then as per the above dividend pay out ratio and retention ratio, it pays $ 80 as dividend and retains $ 20 with itself.

Growth opportunity = retention ratio * return on equity

= 0.20 * 30% = 0.06 or 6%

Therefore the present value of growth opportunity is 6%

Now the present value of stock can be calculated using the below formula

= Dividend to be paid in next year / ( Stock's required return - growth rate )

= 2 / ( 12 - 6 ) = 2 / 6%

= $ 33.33

Therefore using the formula the present value of stock comes out to be $ 33.33