One method of pricing a stock is to discount the stream of...

One method of pricing a stock is to discount the stream of future dividends of the stock. Suppose that a stock pays $$\$ P$$ per year in dividends, and historically, the dividend has been increased $i \%$ per year. If you desire an annual rate of return of $r \%$, this method of pricing a stock states that the price that you should pay is the present value of an infinite stream of payments: $$ \text { Price }=P+P \cdot \frac{1+i}{1+r}+P \cdot\left(\frac{1+i}{1+r}\right)^2+P \cdot\left(\frac{1+i}{1+r}\right)^3+\cdots $$ The price of the stock is the sum of an infinite geometric series. Suppose that a stock pays an annual dividend of $$\$ 4.00$$, and historically, the dividend has been increased $3 \%$ per year. You desire an annual rate of return of $9 \%$. What is the most you should pay for the stock?

One method of pricing a stock is to discount the stream of future dividends of the stock. Suppose that a stock pays $$\$ P$$ per year in dividends, and historically, the dividend has been increased $i \%$ per year. If you desire an annual rate of return of $r \%$, this method of pricing a stock states that the price that you should pay is the present value of an infinite stream of payments:
$$
\text { Price }=P+P \cdot \frac{1+i}{1+r}+P \cdot\left(\frac{1+i}{1+r}\right)^2+P \cdot\left(\frac{1+i}{1+r}\right)^3+\cdots
$$
The price of the stock is the sum of an infinite geometric series. Suppose that a stock pays an annual dividend of $$\$ 4.00$$, and historically, the dividend has been increased $3 \%$ per year. You desire an annual rate of return of $9 \%$. What is the most you should pay for the stock?

Key Concepts

Infinite Geometric Series

The valuation technique involves summing an infinite geometric series because the expected dividend payments form a sequence where each term is a fixed multiple of the previous term. Recognizing that the series has a common ratio less than one allows the use of the formula for the sum of an infinite geometric series, thereby simplifying the calculation of the stock's price.

Dividend Discount Model

The dividend discount model (DDM) is a valuation method that determines the price of a stock by discounting its expected future dividend payments back to their present value. It is based on the premise that the intrinsic value of a company’s stock is the sum total of all its future dividends, adjusted for growth and the time value of money.

Gordon Growth Model

The Gordon Growth Model is a specific form of the dividend discount model that assumes dividends increase at a constant rate indefinitely. This model simplifies the valuation process by enabling the use of a closed-form formula, relating the current dividend, the growth rate of dividends, and the required rate of return to compute the present value of future dividends.

Present Value and Discounting

Present value and discounting are fundamental financial concepts that involve determining the current worth of future cash flows by applying a discount rate. This reflects the time value of money, accounting for the fact that a dollar received in the future is worth less than a dollar today due to factors like inflation and opportunity cost.

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