Synovec Co. is growing quickly. Dividends are expected to grow at a rate of 20 percent for the next three years, with the growth rate falling off to a constant 5 percent thereafter. If the required return is 10 percent, and the company just paid a dividend of $2.20, what is the current share price

The price of the stock today is $67.85

Explanation:

The company's dividends are growing in two stages. Thus, the two stage growth model of the DDM will be used to calculate the current share price. The first stage is of rapid growth in dividend at a rate of 20% and the second stage includes the constant growth. The formula to calculate the price of such a stock is,

P0 or V0 = D1 / (1+r) + D2 / (1+r) ^2 + ... + [Dn * (1+g) / (r - g) ] / (1+r) ^n

P0 = 2.2 * (1+0.2) / (1+0.1) + 2.2 * (1+0.2) ^2 / ((1+0.1) ^2 +

2.2 * (1+0.2) ^3 / (1+0.2) ^3 + [{2.2 * (1+0.2) ^3 * (1+0.05) } / (0.1 - 0.05) ] / (1+0.1) ^3

P0 = $67.85