A stock is expected to pay dividends of $1.00, $0.75 and $2.00 for the next 3 years, respectively. After that time, dividends are expected to grow at a constant rate of 6% indefinitely. The required return on the stock is 10% during the non-constant growth period and 8% afterwards. Compute the fair market value of the stock today.

The fair market value of the stock today is $82.67

Explanation:

The fair value of the stock can be calculated using the dividend discount model which bases the value or fair price of a stock today based on the present value of the expected future dividends from the stock. The dividends are discounted to the present value using an appropriate discount rate.

When the dividend growth rate of a stock becomes constant, we calculate the terminal value of the stock and discount it back too. The terminal value of the stock will be calculated at the end of year 3 using the required rate of return of 8% and will be discounted back 3 years to present value using the rate of 10%.

Thus, the price today of the given stock will be,

P0 = 1 / (1+0.1)  +  0.75 / (1+0.1)^2  +  2 / (1+0.1)^3  +

[ (2 * (1+0.06)  /  (0.08-0.06))  /  (1+0.1)^3 ]

P0 = $82.67