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

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