Question

# Company X currently paid a \$4 per share dividend on its common stock. Dividends are expected...

Company X currently paid a \$4 per share dividend on its common stock. Dividends are expected to grow forever at 6% and investors require a 15% rate of return. Company X's management is planning to enter new, risky markets to increase its expected dividend growth. However, due to increased risk, the investors required rate of return will increase to 20%. What must be the new value for the dividend growth to justify entering the new, risky markets and to keep stock price from decreasing?

Expected dividend = 4 x (1+Growth rate) = 4 x (1+6%)

Stock price with current growth rate = Dividend x (1+Growth rate)/(Required rate-Growth rate)

Stock price with current growth rate = 4 x (1+6%)/(15%-6%)

Stock price with current growth rate = \$47.111111

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Now, as new required return has changed to 20%, then keeping same stock price we can get new growth rate:

Stock price = Dividend x (1+Growth) / (Required return-Growth rate)

47.111111 = 4 x (1+Growth rate) / (20%-Growth rate)

47.1111111 x 20% - 47.111111 x Growth rate = 4 + 4 x Growth rate

51.111111 Growth rate = 9.422222 – 4

Growth rate = 5.422222/51.111111

Growth rate = 10.61%