The Bell Weather Co. is a new firm in a rapidly growing industry. The company is planning on increasing its annual dividend by 18 percent a year for the next 4 years and then decreasing the growth rate to 3 percent per year. The company just paid its annual dividend in the amount of $1.80 per share. What is the current value of one share of this stock if the required rate of return is 7.30 percent?

The price of the stock today is $72.245

Explanation:

The two stage growth model of the Gordon growth model will be used to calculate the value of the stock today.

The first four year's dividend will be increased by a constant rate of 18% and discounted back to today by using a discount rate of 7.3%. The terminal value will be calculated at year 4 using the constant growth rate till perpetuity and it will also be discounted back.

P0 or V = 1.8 * (1+0.18) / (1+0.073) + 1.8 * (1+0.18) ² / (1+0.073) ² + 1.8 * (1+0.18) ³ / (1+0.073) ³ + 1.8 * (1+0.18) ^4 / (1+0.073) ^4 + [1.8 * (1+0.18) ^4 * (1+0.03) / 0.073-0.03] / (1+0.073) ^4

P0 = $72.245

The answer is: Price of the stock $72.25.

Explanation:

The price of the stock is the sum of:

+ Present value of growing annuity from dividend stream in the next 4 years which is calculated as : (1.8 x 1.18 / 1.073) + (1.8 x 1.18^2 / 1.073^2) + (1.8 x 1.18^3 / 1.073^3) + (1.8 x 1.18^4 / 1.073^4) = $9.183;

+ Present value of the perpetual annuity paid 5 years from now, which is calculated as: [ Dividend paid in year five / (Required rate of return - growth rate) ] / 1.18^4 = [ (1.8 x 1.18^4 x 1.03) / (7.3% - 3%) ] / 1.073^4 = $63.062;

=> Price of the stock = 9.183 + 63.062 = $72.245