A stock pays a dividend of $2 next year and has a perpetual growth rate of 0%. If the stock price today is $40, what is the cost of equity implied by the Gordon Growth Model?

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Study for the Finance and Investment Challenge Test. Approaches include flashcards and multiple-choice questions with hints and explanations. Ready yourself to ace the exam!

Multiple Choice

A stock pays a dividend of $2 next year and has a perpetual growth rate of 0%. If the stock price today is $40, what is the cost of equity implied by the Gordon Growth Model?

Explanation:
The Gordon Growth Model values a stock as the next dividend divided by the difference between the cost of equity and the growth rate: P0 = D1 / (r − g). Here the next dividend is 2, the growth rate is 0%, and the current price is 40. Solve for the cost of equity: r = D1 / P0 + g = 2 / 40 + 0 = 0.05, or 5% per year. So the implied cost of equity is 5%, which also checks since a constant dividend of 2 forever would be worth 2 / 0.05 = 40. If the return were 4% or 6%, the price would be respectively 50 or about 33.33, not 40, so 5% fits the given inputs.

The Gordon Growth Model values a stock as the next dividend divided by the difference between the cost of equity and the growth rate: P0 = D1 / (r − g). Here the next dividend is 2, the growth rate is 0%, and the current price is 40. Solve for the cost of equity: r = D1 / P0 + g = 2 / 40 + 0 = 0.05, or 5% per year. So the implied cost of equity is 5%, which also checks since a constant dividend of 2 forever would be worth 2 / 0.05 = 40. If the return were 4% or 6%, the price would be respectively 50 or about 33.33, not 40, so 5% fits the given inputs.

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