Question

A company just paid an annual dividend of \$5.00 per share on its common stock. Due...

A company just paid an annual dividend of \$5.00 per share on its common stock. Due to the success of a new product, the firm expects to achieve a dramatic increase in its short-term growth rate in sales to 30 percent annually for the next three years. After this time, the growth rate in sales is expected to return to the long-term constant rate of 6 percent per year. Assume that the company’s dividend growth rate matches the rate of growth in sales. If the required return on the stock is 15 percent per year, what is the current stock price? Assume that dividends are paid annually.

The value of the stock is computed as shown below:

= Dividend in year 1 / (1 + required rate of return)1 + Dividend in year 2 / (1 + required rate of return)2 + Dividend in year 3 / (1 + required rate of return)3 + 1 / (1 + required rate of return)3 [ ( Dividend in year 3 (1 + growth rate) / ( required rate of return - growth rate) ]

= (\$ 5 x 1.30) / 1.15 + (\$ 5 x 1.302) / 1.152 + (\$ 5 x 1.303) / 1.153 + 1 / 1.153 x [ ((\$ 5 x 1.303 x 1.06) / (0.15 - 0.06) ]

= \$ 6.5 / 1.15 + \$ 8.45 / 1.152 + \$ 10.985 / 1.153 + 1 / 1.153 x [ \$ 129.3788889 ]

= \$ 6.5 / 1.15 + \$ 8.45 / 1.152 + \$ 140.3638889 / 1.153

= \$ 104.33 Approximately

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