How are ordinary shares valued under no growth situation?

The present value (PV) of a stock with zero growth is derived by dividing dividends distributed per period by the required return in that certain period. The formula is not an exact or guaranteed approach for evaluating a stock’s value but is more of a theoretical approach.

The PV of a stock is specific to stocks that have zero or no growth. It is important to note that the period used for dividends and that for the required return must match. For example, for annual dividends, yearly return must be used.

As stated above, the PV formula is more of a theoretical approach than a forcefully applied formula. The idea underlying this theoretical superiority is that a stock is like any other form of financial investment and so it needs to be valued based on discounted future cash flows.

There are various other factors besides only dividends for considering the utility of a stock. Some of the examples of other factors considered may include expected future earnings based on news, overall economy (the inflation, production, and capital), and appreciation of a stock after retained earnings. Also, there are numerous methods or models used in determining the value of a stock.

How to Calculate PV of a Stock with Zero Growth

The PV of a stock is broadly assumed as the addition of all the discounted future cash flows. Dividends are the future cash flows as the real appreciation of a stock is not realized unless it is sold. As a stock has no maturity, it can be considered as a perpetuity, where dividends are to be received forever.

The formula for the PV of a stock with no growth indicates that the stock is a kind of perpetuity where dividends will be paid on an ongoing basis for a never-ending period of time.

Dividend Discount Model

The following formula gives the PV in Dividend Discount Model −

$$\mathrm{𝑉 =\frac{𝐷_{1}}{(1 + 𝑘)}+\frac{𝐷_{2}}{(1 + 𝑘)^2}+...+\frac{𝐷_{n}}{(1 + 𝑘)^n}}$$

Where,

𝑉 = Present Value

𝐷_𝑛 = Dividend in the next period

𝑘 = Required rate of return