In the Gordon Growth Model, if the perpetual growth rate g equals the required return r, what happens to the equity price?

• A. Finite and constant
• B. Declines to zero
• C. Undefined/diverges to infinity
• D. Becomes negative

Answer: (C)

In the Gordon Growth Model, the stock price is the present value of an infinite sequence of dividends that grow at a constant rate: P0 = D1 / (r - g). The key idea is that the discount rate r must exceed the growth rate g for the series to converge to a finite value. If the growth rate equals the required return, the denominator r - g becomes zero, and the usual formula breaks down.

Mathematically, with r = g, the ratio used to discount future dividends becomes 1, so each future dividend contributes the same amount after discounting. Summing an infinite number of equal amounts leads to an infinite total, meaning the price is undefined or diverges to infinity. Intuitively, when dividends grow at the same pace as the return investors require, there’s no finite cap on the total value of the infinite stream of cash flows, according to this model.