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Wize University Introduction to Finance Textbook > Equity Valuation

Common Shares (Non-Constant Growth)

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Non-Constant Growth Model

Companies will often change the growth rate of their dividends for a variety of reasons, like offering very high growth during periods during which they expect higher earnings or attracting additional investments. When dividends are growing at a higher rate than normal, this is called super-normal growth.

Solving for the stock price using non-constant growth models is done by segmenting the timeline into multiple annuities and perpetuities and summing their respective present values.

Growing Annuities

A growing annuity is a recurring cash stream where payments are increasing at a constant rate for a finite period of time. For example, receiving a $4 dividend this year and 5% more each year for 5 years.

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Example: Non-Constant Growth Model

ABC Inc. just paid a dividend of $2. It plans to increase its dividend by 15% for the next 5 years and then decrease the growth rate to 4% indefinitely.

What is the current price of the company's stock if the required rate of return is 10%?

Practice: Non-Constant Growth Model

Ocram Group will pay a $4 per share dividend next year. It just announced that it will grow its dividends by 8% until year 5, then it will increase dividends by 10% per year until year 10 before decreasing the growth rate to 3% indefinitely thereafter.

What is the price of one share if investors require a return of 14% per year?
Extra Practice
A company is expected to pay its first dividend in 2 years. The first dividend will be $2 per share, which will then grow by 10% per year for the following 2 years before stabilizing and remaining constant thereafter.
If the required rate of return on the stock is 15%, what is the price today?
A stock just paid a dividend of $4 per share and expects to keep it constant for the next 5 years. At the end of year 6, it plans to increase the dividend by 8% and continue to increase it at this rate indefinitely. Investor's expect a risk premium of 10% on these shares and t-bills are yielding 4%.
What will the price of the stock be in one year?
A stock just paid a dividend of $3 per share and expects to keep it constant for the next 7 years. At the end of year 8, it plans to increase the dividend by 5% and continue to increase it at this rate indefinitely. Investor's expect a risk premium of 10% on these shares and t-bills are yielding 4%.
What is the price of the stock today?
Round your work to at least 6 decimal places and final answer to 2 decimal places.
ABC Inc just paid a $5 per share dividend. Dividends are expected to grow by 50% next year, 40% in year 2, 30% in year 3 before settling on an indefinite growth rate of 8% per year thereafter. The required rate of return is 13%.
What is the price of the shares?
Round your work to at least 6 decimal places and final answer to 2 decimal places.
ABC Inc is expected to pay a dividend of $3 at the end of the year. Dividends are then expected to decrease by 1% per year for 3 years before increasing by 2% per year thereafter. The required rate of return is 9%.
What is the price of these shares?
Round your work to at least 6 decimal places and final answer to 2 decimal places.
ABC Inc just paid a dividend of $2.50 per share and expects to increase it by 20% per year for the next 2 years after which the growth rate will be reduced to 5% per year. The required rate of return on these shares is 12%.
What is the price of these shares?
Round your work to at least 6 decimal places and final answer to 2 decimal places.
ABC Inc just paid a dividend of $2 per share and expects to increase it by 10% per year for the next 3 years. It then plans on keeping the dividends constant indefinitely. The required rate of return on these shares is 12%.
What is the price of these shares?
Round your work to at least 6 decimal places and final answer to 2 decimal places.
XYZ Inc just paid a $4 dividend and does not plan on changing the amount for 8 years. In year 9, the company will begin decreasing the dividend by 1% per year. If the required rate of return is 15%, what is the price of the stock today?
ABC Inc just paid a dividend of $2.50 per share and expects to increase it by 25% per year for the next 3 years. In year 4, the company will begin increasing the dividend by 7% per year indefinitely. What is the price of the stock today if the required rate of return is 10%?